Idea Transcript
FIRST YEAR ENGINEERING Structure and Syllabus (From the Academic Year 2013-2014) (Course common to all branches except Architecture and Textile Engineering)
INSTRUCTIONS: There are two groups in each semester:
1. Physics Group and 2. Chemistry Group
Allotment of groups to students: a) Semester I: 50% students from each college will be admitted to Physics Group and remaining 50% will be admitted to Chemistry Group. The concerned College will decide the number and names of the students to be admitted in physics and chemistry groups and inform the same to the University. b) Semester II: The students for Physics group in semester-I will be admitted to Chemistry Group in semester-II. The students for Chemistry Group in semester-I will be admitted to Physics Group in semester-II.
1
First Year Engineering Course Common to All Branches Semester I: Physics Group
Sr. No. 1 2 3 4 5 6 7
Subject
Engineering Physics Engineering Mathematics-I Basic Electrical Engineering Basic Civil Engineering Engineering Graphics# Professional Communication-I Workshop Practice-I Total
L 03 03
Teaching / Week (Hours/Week) P T 02 01
Total 05 04
Examination Scheme (Marks) Theory TW Total 100 25 125 100 25 125
03
02
05
100
25
125
03
02
05
100
25
125
03 01
02 02
05 03
100# --
25 25
125 50
01 17
02 12
03 30
-500
25 200
50 700
01
#Theory paper of 4 hours duration
First Year Engineering Course Common to All Branches Semester I: Chemistry Group
Sr. No. 1 2 3
4 5 6 7
Subject
Engineering Chemistry Engineering Mathematics-I Fundamentals of Electronics and Computer $ Applied Mechanics Basic Mechanical Engineering Professional Communication-II Workshop Practice-II Total
L 03 03
Teaching / Week (Hours/Week) P T 02 01
Total 05 04
Examination Scheme (Marks) Theory TW Total 100 25 125 100 25 125
03
02
05
100
25
125
03
02
05
100
25
125
03
02
05
100#
25
125
01
02
03
--
25
50
01 17
02 12
03 30
-500
25 200
50 700
01
$ should be taught by single faculty ONLY
2
First Year Engineering Course Common to All Branches Semester II: Physics Group
Sr. No. 1 2 3 4 5 6 7
Subject
Engineering Physics Engineering Mathematics-II Basic Electrical Engineering Basic Civil Engineering Engineering Graphics# Professional Communication-I Workshop Practice-I Total
L 03 03
Teaching / Week (Hours/Week) P T 02 01
Total 05 04
Examination Scheme (Marks) Theory TW Total 100 25 125 100 25 125
03
02
05
100
25
125
03
02
05
100
25
125
03 01
02 02
05 03
100# --
25 25
125 50
01 17
02 12
03 30
-500
25 200
50 700
01
#Theory paper of 4 hours duration
First Year Engineering Course Common to All Branches Semester II: Chemistry Group
Sr. No. 1 2 3 4 5 6 7
Subject
Engineering Chemistry Engineering Mathematics-II Basic Electrical Engineering Basic Civil Engineering Engineering Graphics# Professional Communication-I Workshop Practice-I Total
L 03 03
Teaching / Week (Hours/Week) P T 02 01
Total 05 04
Examination Scheme (Marks) Theory TW Total 100 25 125 100 25 125
03
02
05
100
25
125
03
02
05
100
25
125
03 01
02 02
05 03
100# --
25 25
125 50
01 17
02 12
03 30
-500
25 200
50 700
01
$ should be taught by single faculty ONLY
3
INDEX Sr. No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Subject Engineering Physics Engineering Mathematics I Basic Electrical Engineering Basic Civil Engineering Engineering Graphics Professional communication I Workshop Practice I Engineering Chemistry Fundamental of Electronics and Computer Programming Applied Mechanics Basic Mechanical Engineering Engineering Mathematics II Workshop Practice II Professional communication II
Page No. 5 17 54 66 77 91 -95 110 124 145 156 -185
4
FE Engineering Semester I & II Engineering Physics Course
Engineering Physics
Examination Scheme Max. Marks Contact Hours/ week Prepared by
Course Code
40901
Theory
Term Work
POE
Total
100 3
25 6
25 --
150 9
Date
Prerequisites Atomic Structure, energy levels, concept of diffraction, polarization and interference, total internal reflection, Rayleigh‟s criterion, concept of quanta, nature of light, scattering of light. Course Outcomes At the end of the course the students should be able to: CO1 Understand the concepts of diffraction, polarization and apply the knowledge gained, for practicals. CO2 study the basics of laser and fibre optics and to acknowledge the role of laser and optical fibers in various fields CO3 Know the origin of nuclear fission and nuclear fusion and study reactors. CO4 To differentiate various crystal systems and to study the X-ray diffraction by crystal. CO5 Deal with the concepts of Quantum mechanics and solve numericals. CO6 Generate awareness of newly introduced nanotechnology and to study synthesis, properties and applications of nanomaterials. Mapping of COs with POs POs
a
b
c
d
E
f
G
h
i
j
k
l
COs
CO1 CO2 CO3 CO4 CO5 CO6
√ √ √ √ √ √
√ √ √
√
√ √ √ √
√
√
√
5
Course Contents Unit No.
Title
No. of Hours Section I
1.
Diffraction and Polarization
07
2.
Laser and Fibre Optics
07
3
Nuclear Energy
07 Section II
4. 5..
Crystallography Quantum Physics
07
6.
Nano Physics
07
07
Reference Books: Sr. No. 1
Title of Book Solid State Physics : Structure & Electron Related Properties
Author S. O. Pillai
Publisher/Edition Eastern Ltd, New Age International Ltd.
Topics Unit 4, Unit 5
2
Introduction to Solid State Physics
Wiley India Pvt. Ltd.
Unit 4
3
Engineering Physics
Charles Kittle, Wiley India Pvt. Ltd.(8thEdtion). B. K. Pandey and S. Chaturvedi
Cengage Learning-2012
All units
4
Modern Physics
B. L. Theraja
S. Chand & Company Ltd., Delhi
Unit 6
5
Nanotechnology
Pandey
Cengage Publication
Unit 5
6
Optics
Subramanyam & Brij Lal
S. Chand & Company (P.) Ltd.
Unit 1 and 2
6
Scheme of Marks Section I
Unit No. 1 2 3 4 5 6
II
Title Diffraction and Polarization Laser and Fibre Optics Nuclear Energy Crystallography Quantum Physics Nano Physics
Marks 17 17 16 17 17 16
Course Unitization Section
Unit
I
No. 1
Title Diffraction and Polarization
2
Laser and Fibre Optics
3
Nuclear Energy
4
Crystallography
5
Quantum Physics Nano Physics
II
6
Course Outcomes
Understand the concepts of diffraction, polarization and apply the knowledge gained, for practicals. study the basics of laser and fibre optics and to acknowledge the role of laser and optical fibers in various fields Know the origin of nuclear fission and nuclear fusion and study reactors. To differentiate various crystal systems and to study the X-ray diffraction by crystal. Deal with the concepts of Quantum mechanics and solve numericals. Generate awareness of newly introduced nanotechnology and to study synthesis, properties and applications of nanomaterials.
No. of Questions in CAT-I CAT-II 1
1
1 1
1 1
7
Unit wise Lesson Plan Unit No 1
Unit Title
Section I Diffraction and Polarization
Planned Hrs. Unit Outcomes: Understand the concepts of diffraction, polarization and apply the knowledge gained, for practicals. At the end of this unit the students should be able to: UO1 Explain basic concepts of light, diffraction, resolving power and polarization. UO2 Differentiate between O-ray and e-ray as well as positive crystal and negative crystal. UO3 Derive grating equation and resolving power of diffraction grating. UO4 Realize the use Laurentz half shade polarimeter for determination of specific rotation UO5 Solve numericals of grating equation and specific rotation.
07
CO1 CO1 CO1 CO1 CO1
Lesson schedule Class Details to be covered No. 1 Diffraction: Introduction, , , , 2 diffraction grating - construction, theory 3 resolving power, resolving power of plane transmission grating, 4 numerical of grating equation 5 Polarization: Introduction, double refraction, Huygens‟ theory (positive and negative crystals) 6 optical activity, Laurent‟s half shade polarimeter 7 Numerical of specific rotation, Photo-elasticity Unit No 2
Unit Title
LASER and Fiber Optics
Planned Hrs. Unit Outcomes: study the basics of laser and fibre optics and to acknowledge the role of laser and optical fibers in various fields At the end of this unit the students should be able to: UO1 Understand the concept of atom, different atomic energy levels. Understand the role of quantum mechanics in atomic model. UO2 Relate Quantum Mechanics used in Bohr‟s postulates with the stability of atom and also with the energy emission by an atom. UO3 Explain the transitions takes place between energy levels.
07
CO1 CO1 CO1
UO4
Describe the stimulated absorption, spontaneous and stimulated emission. Ultimately to study the LASER emission.
CO1
UO5
Explain conditions for lasing action. To list different characteristics of laser.
CO1
UO6
Study different types of laser and study Ruby laser (Solid State Laser) in
CO1 8
detail (construction, working and energy level diagram). UO7
Acknowledge the structure of an optical fiber and describe total internal reflection in the core of fiber.
CO1
UO8
Differentiate between single mode and multi mode fiber. Study multimode fiber in detail with the help of diagram.
CO1
UO9
Acknowledge the applications of optical fiber and laser in day today life.
CO1
UO10
Solve numerical of numerical aperture.
CO1
Lesson schedule Class Details to be covered No. 1 Absorption, spontaneous emission, stimulated emission, 2 Lasing action, pumping energy, population inversion 3 Types of laser, characteristics of laser, Ruby laser, construction, working with energy level diagram. 4 applications of laser (industrial & medical), Holography (construction, reconstruction, and applications). 5 Principle, structure of optical fibre, propagation of light, acceptance angle and acceptance cone (no derivation), 6 numerical aperture (no derivation), types of optical fibre, 7 Applications (medical, military, entertainment, communication, optical fiber sensors), advantages of optical fibres.
Unit No 3
Unit Title
Nuclear Energy
Planned 07 Hrs. Unit Outcomes: Know the origin of nuclear fission and nuclear fusion and study reactors. At the end of this unit the students should be able to: UO1 Identify the basic principles of the mass-energy equivalence concept. CO2 UO2 Define and calculate the mass defect and the binding energy of the nucleus. CO2 UO3 Define nuclear fission and chain reaction. CO2 UO4 Understand how the binding energy curve leads to nuclear fission and CO2 nuclear fusion. UO5 Have a basic understanding of the construction nuclear reactor (fission and CO2 fusion). UO6 Have a basic understanding of conditions for fusion reactor. CO2 UO7 Be able to calculate energy generated in fission of 1 kg of U235 in joule, CO2 KWh, and calorie. UO8 Be able to perform simple criticality calculations for efficiency of nuclear CO2 reactor, nuclear power and fission rate. Lesson schedule 9
Class No. 1 2 3 4 5 6 7
Details to be covered Introduction, structure of nucleus, 1a.m.u.relation with energy, . Binding energy, binding energy curve, energy released by 1 Kg. of U-235 Chain reaction, its types, multiplication factor nuclear reactor and their classification, essentials of nuclear reactor numericals for energy released by Uranium Nuclear fusion (p-p chain, c-n cycle), conditions for fusion reaction, fusion reactor.
Review Questions Q1 Distinguish between positive & negative crystals CO1 Q2 Explain the theory of plane diffraction grating & obtain grating equation CO1 6 marks Q3 Write a note on „ Laurent‟s half shade polarimeter‟ CO1 Q4 Define resolving power & obtain expression for it. CO1 Q5 Define double refraction & Find the angular separations between two sodium CO1 lines, whose wavelength are 5890A0 & 5898A0 respectively for the plane diffraction grating with 1800 lines/inch in first order spectrum. Q6 Explain optical activity & State the formula for specific rotation CO1 Q7 Diffraction grating used at normal incidence gives the line of wavelength λ1 CO1 = 6000A0 in certain order superimposed on another line λ2 =4500 A0 of the next higher order. if the angle of diffraction is 300, calculate The number of lines in 1 cm of grating. Q1 Distinguish between positive & negative crystals CO2 Q2 Explain the theory of plane diffraction grating & obtain grating equation CO2 6 marks Q3 Write a note on „ Laurent‟s half shade polarimeter‟ CO2 Q4 Define resolving power & obtain expression for it. 5 marks CO2 Q5 Define double refraction & Find The angular separations between two CO2 sodium lines, whose wavelength are 5890A0 & 5898A0 respectively for the plane diffraction grating with 1800 lines/inch in first order spectrum. Q1 Define, Chain reaction and critical size CO3 Q2 Discuss the classification of nuclear reactor. CO3 Q3 Distinguish between fission and fusion. CO3 Q4 Discuss the requirements of thermonuclear fusion power reactor CO3 Q5 Explain thermonuclear reactions according to sun and st CO3 Q6 Describe fusion power reactor with neat diagram CO3 Q7 Define nuclear fission. Calculate the energy released by 1 kg.of U235 in kwh CO3 Q8 A city requires 5000 MWh electric energy per day. This is to be obtained by CO3 nuclear reactor of efficiency 30% . Calculate the mass of U235 needed for one day operation of nuclear reactor. Assume the energy released per fission of U235 is 200MeV. Q9 A railway engine develops an average power of 1000 kW during a ten hour CO3 run from one station to another. If the engine is driven by an atomic power 10
plant of 20% efficiency, How much U-235 would be consumed on the run? Each U- 235 atom on fission releases 200MeV of energy. Section II Unit No 4
Unit Title
Crystallography
Planned Hrs. Unit Outcomes: To differentiate various crystal systems and to study the X-ray diffraction by crystal. At the end of this unit the students should be able to: UO1 Define crystal structure, Unit cell, lattice point, and space lattice. UO2 Familiar with crystal systems to develop the relationships between axial length and interfacial angles. UO3 Understand the characteristics of sc, fcc and bcc lattice with the help of suitable diagrams. UO4 Understand the fundamentals of how crystals relates with the diffraction. UO5 Calculate the density, lattice constant of crystal UO6 Determine the crystal structure by knowing number of atoms per unit cell. UO7 Revise basics of X-ray properties using Laue spot and relate it with diffraction by crystals. Derive Bragg's law for diffraction with usual diagram. UO8 Describe real application of Bragg‟s law in Braggs X-ray spectrometer. UO9 To solve numerical problems on Braggs law.
07
CO4 CO4 CO4 CO4 CO4 CO4 CO4
CO4 CO4
Lesson schedule Class Details to be covered No. 1 Introduction matter, states of matter, Unit cell, 2 properties of unit cell i..e (number of atoms per unit cell, coordination number, atomic radius, packing fraction) for BCC, FCC and SC structure 3 Fourteen Bravais lattices, symmetry elements in cube 4 relation between density and lattice constant, relation between interplaner distance and lattice constant, numericals for both relations 5 Miller indices - procedure, features and sketches for different planes. 6 X-ray diffraction, Bragg's law, 7 Bragg's x-ray spectrometer, numericals for Bragg‟s law
Unit No 5
Unit Title
Section II Quantum Physics
Planned Hrs. Unit Outcomes: Deal with the concepts of Quantum mechanics and solve numericals. At the end of this unit the students should be able to: UO1 Distinguish Classical mechanics from Quantum mechanics and provides a general scheme for understanding a vast range of physical phenomena. UO2 Basic understanding of the key concepts of elementary quantum mechanics,.
05
CO5 CO5
11
UO3 UO4
Be able to deal with conceptually rich and technically difficult theoretical problems. Know how to use the theory to discuss quantum phenomena quantitatively.
CO5 CO5
Lesson schedule Class Details to be covered No. 1 Introduction to quantum mechanics. Wave-particle duality, 2 De- Broglie Hypothesis. Determination of wavelength of matter waves. 3 Properties of matter waves. Compton Effect. 4 Derivation of Compton shift. 5 Numericals for Compton shift and de-Broglie‟s wavelength. Unit No Unit Title NanoPhysics Planned 6 Hrs. Unit Outcomes: Generate awareness of newly introduced nanotechnology and to study synthesis, properties and applications of nanomaterials. At the end of this unit the students should be able to: UO1 Study scale of structure of material and study fundamentals of nanomaterials. UO2 Provide understanding of nanostructure properties and applications. UO3 The definition of nanotechnology, including the nanoscale and property changes. UO4 Characterization Techniques for nanostructured materials. UO5 Relevant applications, products or technologies. UO6 Explain structure & working of different instruments used in nanotechnology. UO7 Synthesis, processing and manufacturing of nanocomponents and nanosystems.
07
CO6 CO6 CO6 CO6 CO6 CO6 CO6
Lesson schedule Class Details to be covered No. 1 Basic concepts – nanoscale, nanomatrerials. Introduction to nanotechnology. 2 Production techniques for nanomaterials- top down approach. 3 Production techniques for nanomaterials- bottom up approach, properties and applications of nanomaterials. 4 Properties and applications of nanomaterials. 5 Characterization tools Scanning Tunneling Microscopy. 6 Characterization tools Atomic Force Microscopy. 7 Introduction to CNT, Properties and applications. Review Questions Q1 Explain seven systems of crystals in terms of relations of intercepts & interfacial angles. List the name of 14 bravais lattices.
CO4
12
Q2 Q3 Q4 Q5 Q6 Q7 Q8
Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20
Define packing factor & calculate the values of packing factor for S.C. , BCC, FCC lattices What are Miller indices? Explain the procedure to find Miller indices & obtain the properties of Miller indices. Show that for cubic lattice, the lattice constant is given by a3 = nA /þN, where the symbols have usual meaning Explain Element of symmetry in cubic lattice. s State Bragg‟s law. Describe the construction & working of Braggs spectrometer used for crystal analysis. Derive Bragg‟s relation. A beam of x-ray of wavelength 0.842 Å is incident on a crystal at a glancing angle of 80 35‟ when the 1st order Bragg‟s reflection occurs. Calculate the glancing angle for 3rd order reflection. Lead is face centered cubic with an atomic radius of r=1.746A0. Find the spacing of (200) (220) (111) planes. Obtain the Miller indices for the plane making intercepts of 1 A0,2 A0,3 A0 along x, y & z axes. State the De- Broglie‟s hypothesis of matter wave. Derive an expression for wavelength of matter wave in terms of kinetic energy of particle. State the properties of matter wave. State & explain Heisenberg uncertainty principle. What is Compton Effect? Derive an expression for Compton shift. Explain in brief production techniques used in nanomaterial. Discuss in brief construction & working of STM. Write the properties &application of nanomaterial. Explain two types of CNT & state any four application. Explain in brief AFM.
CO4 CO4 CO4 CO4 CO4 CO4 CO4
CO4 CO4 CO5 CO5 CO5 CO5 CO5 CO6 CO6 CO6 CO6 CO6
13
Model Question Paper
Course Title : Duration
Engineering Physics 3hrs.
Max. Marks 100
Instructions: 1. Figures to the right indicate full marks. 2. Use of electronic calculator is allowed. Section-I 1
a b c d
2
a b c d
3
a b
c d
4
a b c
Explain the theory of plane diffraction grating & obtain grating equation. Explain the construction & working of Laurent‟s half shade polarimeter. What is double refraction? Distinguish between positive & negative crystal. Define resolving power? Hence determine resolving power in second order for a light of wavelength 5000 A0 which falls on a grating normally. Two adjacent principle maxima occur at sinθ 1=0.2 & sinθ2=0.3 respectively. Also calculate the grating element (Given: The width of grating surface is 2.5). Explain the construction & working of ruby laser. Explain the terms, a) Population inversion b) Pumping energy c) Stimulated emission Explain the construction of optical fibre & explain propagation of light through fibre. What are the advantages of optical fibre communication system over conventional method of communication? Hence determine numerical aperture of optical fibre if refractive index of core & cladding is 1.60 & 1.57 respectively. Explain the essentials of nuclear fission reactor. Calculate the power output of a nuclear reactor which consumes 25 gm of U235 per day. Assume 5% reactor efficiency& energy released per fission of U235 is 200MeV. Explain the conditions of fusion reactor. Explain nuclear chain reaction and Critical size. Section-II Explain seven systems of crystals in terms of relations of intercepts & interfacial angles. List the name of 14 bravais lattices. Explain Element of symmetry in cubic lattice. What are Miller indices? Obtain the Miller indices for the plane making intercepts of 1 A0,2 A0,3 A0 along x, y & z axes.
Marks 6 6 5 5
6 6 5 5
6 5
5 5 Marks 6 6 5 14
5
6
d a b c d a b c d
State & derive Bragg‟s law of X-ray diffraction. What is Compton Effect? Derive expression for Compton shift. State the hypothesis of matter wave. Hence obtain relation for wavelength of matter wave in terms of kinetic energy. State & explain Heisenberg‟s uncertainty principle. State the properties of matter wave. Explain in brief two production techniques used in synthesis of nanomaterials. Discuss in brief the construction & working of scanning tunneling microscope. What are carbon nanotubes (CNT‟s). State it‟s any three applications. State different properties of nanomaterials.
5 6 6 5 5 6 5 5 5
Assignments List of experiments/assignments to meet the requirements of the syllabus: 1. Calculation of divergence of LASER beam. 2. Determination of wavelength of LASER using diffraction grating. 3. Diffraction grating using mercury vapor lamp. 4. Polarimeter. 5. Verification of inverse square law of intensity of light. 6. Measurement of band gap energy. 7. Study of crystal structure. 8. Study of symmetry elements of cube. 9. Determination of „d‟(interplaner distance) using XRD pattern. 10. Study of Planes with the help of models related Miller Indices. Assignment No. 1 Assignment Title Diffraction and polarization Batch I Batch II Batch III
Assignment Title
Batch I
CO1
Explain the theory of plane diffraction grating & obtain grating equation. What is double refraction? Write difference between O-ray and e-ray. Explain the construction & working of Laurent‟s half shade polarimeter. What is the difference between positive and negative crystal? Explain the theory of plane diffraction grating & obtain grating equation. Explain the construction & working of Laurent‟s half shade polarimeter. Assignment No. 2 Laser and Fiber Optics
CO2
Define spontaneous absorption, spontaneous emission and stimulated emission. Explain fiber optics communication system
15
Batch II Batch III
Assignment Title
Explain construction and working of Ruby laser. What are different types of optical fiber? Write different applications of laser. What are advantages of optical fiber? Assignment No.3 Nuclear energy
Batch I
Calculate energy released by 1gm of U235.
Batch II Batch III
Calculate energy released by 1kg of U235. Calculate energy released by 20kg of U235.
Assignment Title Batch I Batch II Batch III
Assignment Title Batch I Batch II Batch III
Assignment Title Batch I Batch II
CO3
Assignment No.4 Crystallography CO4 Explain seven systems of crystals in terms of relations of intercepts & interfacial angles. List the name of 14 bravais lattices. Explain Element of symmetry in cubic lattice. What are Miller indices? Write procedure to determine miller indices.Obtain the Miller indices for the plane making intercepts of 1 A0,2 A0,3 A0 along x, y & z axes. Assignment No.5 Quantum Physics CO5 What is Compton Effect? Derive expression for Compton shift. State the hypothesis of matter wave. Hence obtain relation for wavelength of matter wave in terms of kinetic energy. State & explain Heisenberg‟s uncertainty principle. State properties of matter waves. Assignment No.6 Nanophysics CO6 Explain in brief two production techniques used in synthesis of nanomaterials. Discuss in brief the construction & working of scanning tunneling microscope. What are carbon nanotubes (CNT‟s). State it‟s any three applications.
Batch III List of additional assignments /experiments Experiment No. 1 Experiment Title
Least Count of Instruments
16
FE Engineering Semester I Engineering Mathematics I Course
Engineering Mathematics I
Examination Scheme Max. Marks Contact Hours/ week Prepared by
Theory
Term Work
100 3
25 1
Course Code
BH102
POE
Total
25 --
125 4
Date
30.04.2014
--
Ms. Patil P. V.
Prerequisites
Algebra of matrices Basic knowledge of Complex numbers and algebra Basic knowledge of limits Basic knowledge of derivatives and its applications Basic knowledge of partial derivative
Course Outcomes At the end of the course the students should be able to: CO1 To find the rank of the matrix & to solve simultaneous linear equations by matrix method. CO2 To find Eigen values & Eigen vectors CO3 Use of De Moivres theorem, roots of complex numbers, meaning of circular functions, hyperbolic functions & inverse hyperbolic functions. CO4 To obtain expansions of functions at x=o & x=a Also to evaluate indeterminate forms CO5 Partial differentiation: - meaning, Euler‟s theorem, applications of partial differentiation CO6 To solve simultaneous linear equations by different numerical techniques. Mapping of COs with POs POs COs CO1 CO2 CO3 CO4 CO5 CO6
a
b
c
d
E
f
G
h
i
j
k
l
√ √
√ √
√
√ √
17
Course Contents Unit No.
1.
2.
3.
4.
5.
Title Section I Matrices and solution of linear system equations 1.Rank of matrix: definition, normal form and Echelon form 2. Consistency of linear system equations 3. System of linear homogeneous equations 4. System of linear Non-homogeneous equations Eigen Values and Eigen vectors 1. Linear dependence and independence of vectors 2. Eigen Values 3. Properties of Eigen Values 4. Eigen vectors 5. Properties of Eigen vectors 6. Cayley-Hamilton's theorem (Without proof) 7. Inverse and higher powers of matrix by using Cayley-Hamilton's theorem Complex Numbers 1. De Moivre's Theorem (Without proof) 2. Roots of complex numbers by using De Moivre's Theorem 3. Expansion of sinnθ and cosnθ in powers of sinθ and /or cosθ. 4. Circular functions of a complex variable - definitions 5. Hyperbolic Functions, Relation between Circular & Hyperbolic functions 6. Inverse Hyperbolic Functions 7. Separation into real and imaginary parts Section II Expansion of Functions and Indeterminate forms: 1. Maclaurin's theorem 2. Standard expansions 8 3. Taylor's theorem 4. Expansion of function in power series by using i) Standard series method, ii) Differentiation and integration method, iii) Substitution method 5. Indeterminate forms and L' Hospital's rule Partial Differentiation: 1. Partial derivatives: Introduction 2. Total derivatives 3. Differentiation of implicit function 4. Euler's theorem on homogeneous function of two variables 5. Change of variables 6. Jacobian, Properties of Jacobian, Jacobian of Implicit function, 7. Errors and Approximation
No. of Hours 5
8
8
7
8
18
6.
8. Maxima and Minima of functions of two variables Numerical Solution of linear simultaneous equations: 1. Gauss elimination method 2. Gauss-Jordan method 3. Jacobi‟s iteration method 4. Gauss-Seidel iteration method 5. Determination of Eigen values by iteration
6
Reference Books: Sr. No. 1
Title of Book Higher Engineering Mathematics
2
A text book of Applied Mathematics, Vol.-I,II,III
3
Advanced Engineering Mathematics A textbook of Engineering Mathematics Volume I
4
5 6
Mathematical methods of Science and Engineering Numerical Methods
7
A textbook of Engineering Mathematics
8.
Higher Engineering Mathematics
Author Dr. B. S. Grewal
Publisher/Edition Khanna Publishers, Delhi. P. N. Wartikar & J. Pune Vidyarthi N. Wartikar Griha Prakashan, Pune. Erwin Kreyszig Wiley India Pvt. Ltd. Peter V. O‟Neil Cengage and Santosh K. Learning Sengar Kanti B. Datta Cengage Learning Dr. B. S. Grewal Khanna Publishers, Delhi. N. P. Bali, Iyengar Laxmi Publications (P) Ltd., New Delhi H.K. Das and Er. Chand Technical Rajnish Varma publication
Topics All
All
All All
6 6
All
All
19
Scheme of Marks Section I
II
Unit No. 1 2 3 1 2 3
Title Matrices and solution of linear system equations Eigen Values and Eigen vectors Complex Numbers Expansion of Functions and Indeterminate forms Partial Differentiation Numerical Solution of linear simultaneous equations
Marks 15 15 20 15 20 15
Course Unitization Section
Unit
I
No. 1 2 3
II
1 2 3
Course Outcomes Title Matrices and solution of linear system equations Eigen Values and Eigen vectors Complex Numbers Expansion of Functions and Indeterminate forms Partial Differentiation Numerical Solution of linear simultaneous equations
CO1 CO2 CO3 CO4
No. of Questions in CAT-I Q.1 (15 Marks) Q.2 (15 Marks)
CAT-II
Q.1 (15 Marks) Q.2 (15 Marks)
CO5 CO6
20
Unit wise Lesson Plan Section I Unit 1 Unit Title Matrix and solution of linear system Planned Hrs. No of equation Unit Outcomes At the end of this unit the students should be able to: UO1 find rank of a matrix by given three different methods UO2 Study of consistent and Inconsistent equations UO3 Solve homogenous and non- homogenous system of linear equations by using rank
7
CO1
Lesson schedule Class Details to be covered No. 1 Introduction, Algebra of matrices and Types of Matrices 2 Definition of Rank and Rank of a matrix by normal form 3 Rank and Inverse of a matrix by PAQ form 4 Rank of a matrix by echelon form 5 Consistent and Inconsistent equations 6 Solution of non- homogenous equations 7 Solution of homogenous equations 8 University Examples Review Questions Q1 Reduce the following matrices to normal form and hence find its rank 4 5 6 7 5 2 4 1 6 1 2 1 0 9 10 11 12 2 1 1 2 2 1) 2) 2 4 3 0 3) 10 11 12 13 4 1 0 5 10 1 0 1 8 18 19 20 21 1 2 5 8 6 2 3 1 2 2 3 1 1 3 6 1 3 8 1 1 2 4 1 1 2 4 6 4 2 6 1 4) 5) 6) 3 1 3 2 3 1 3 2 5 10 3 9 7 Q2
6 3 0 8 6 3 0 7 2 16 4 12 15 Reduce the following matrices to PAQ form and hence find its rank 1)
Q3
UO1
1 1 3
1 1 1
1 2 1 2) 3 1 1
1 3 1
3 6 1 2 3) 1 2
Test for consistency and if possible solve them x 5 y 7 z 15 , (a) 2 x 3 y 4 z 11 , (b) 2 x z
4, x 2 y 2 z
1 2 1 0
2 1 0 1
3 3 1 1
1 1 1 4) 1 1 0 1
3x 11y 13z
1 2 1 25
2 3 1 UO2, UO3
7,3x 2 y 1
21
(c) 2 x y 3z 1,3x 2 y z
3, x 4 y 5 z
1
(d) x y z 2, 2 x 2 y z 1,3x 4 y z 9 (e) x y z 3,3x y 2 z 2, 2 x 4 y 7 z
Q4
(f) x 2 y z 3,3x y 2 z 1, 2 x 2 y 3z 2, (g) 2 x 3 y z 9, x 2 y 3z 6,3x y 2 z 8 (h) 2 x y z 3, x y 2 z 4, x z 2 Investigate for what values of λ and µ the equation x y z 6, x 2 y 3z 10, x 2 y z
7
x y z
1 UO2, UO3
Have (i) no solution (ii) a unique solution (iii) Infinite solution Q5
For what value of
4 x 5 y 10 z
the equations x 2
y
z 1 ; 2x y 4z
;
have a solution and solve them for the value of
Q6
Find the value of k for which the system has non-zero/non-trivial solution & hence find solution for each value of k for 3x y kz 0,4x 2y 3z 0,2kx 4y kz 0
Q7
Solve 1. 3x 2. x 3. 3x 4. x
2 y z 0, 2 x y 3z 0, x 4 y 5z 0 2 y 3z 0, 2 x 3 y z 0, 4 x 5 y 4 z 0, x y 2 z 0 y 5 z 0, 5 x 3 y 6 z 0, x y 2 z 0, x 5 y z 0 y 2 z 0, x 2 y 3z 0, x 3 y 4 z 0,3x 4 y 7 z 0
Unit 2 Unit Title Eigen Values & Eigen Vectors Planned Hrs. No Unit Outcomes At the end of this unit the students should be able to: UO1 Check dependency and independency of vectors UO2 Find Eigen values and Eigen vectors for given matrix UO3 Solve examples on Cayley Hamilton‟s Theorem and use it to find Inverse and higher powers of matrices
08
CO2
Lesson schedule Class Details to be covered No. 1 Introduction of vectors 2 Dependency and independency of vectors 3 Introduction to Eigen values and its properties 4 Examples on Eigen Values 5 Introduction to Eigen vectors and its properties 6 Examples to find Eigen values and its corresponding Eigen vectors 7 Introduction to Cayley Hamilton‟s Theorem 8 Examples on Cayley Hamilton‟s Theorem
22
Review Questions Q1 Define linear dependence & independence of vectors. Examine the linear dependence of vectors and find relation between then, if possible. 1. [1, 0, 2, 1]; [3, 1, 2, 1]; [4, 6, 2, -4]; [-6, 0, -3, -4] 2. [3,2,7], [2,4,1], [1,-2,6] 3. [1, 1, 3], [1, 3, -3], [-2, -4, -4], [-9, -25, 9] 4. [1, 2, -1, 0], [1, 3, 1, 2], [4, 2, 1,0], [6, 1, 0, 1] Q2 Show that the vectors [2, 3, -1, -1]; [1, -1, -2, -4]; [3, 1, 3, -2]; [6, 3, 0, -7] form a linearly dependent set. Also express one of these as linear combination of others Q3 3 1 4 If
, , 1 2 3 are Eigen values of matrix
Find (a) Q4
2 1
Q7
1 2
0
0
5
3
6 (b) 1
5 1 (c) 6 3 1 1 2
1
7
4 (d)
2 2
2 3 1
2 1 3
2 Hence find Eigen values of -2A3 , And Adj of A 2 4 1 6 2 2 2 3 1 For Eigen values for A-1, A5, -3A where A= 2 1 3 5
3
State Cayley- Hamilton theorem and find A-1 and A4 , where 7 2 2 3 2 4 i) A=
Q8
(b)
3
6
UO2
2 0 4 3 Find the Eigen values and Eigen vectors for the greatest Eigen value for the matrix 4 2 2 A=
Q6
2
2
Find the Eigen values and Eigen vectors for the following matrices 2 2 3 8 6 2 1 1 3 6 (a)
Q5
1
0
UO1
6
1 2
2 1
ii) A= 4
3
UO3
2
6 2 4 3 Find characteristic equation for A and find the matrix expression represented by
UO3
2 1 1
A8
5 A7 7 A6
3A5 A4 5 A3 8 A2 2 A I ,where A= 0 1 0 1 1 2
23
Q9 Find the characteristic equation of the matrix A
8
8
2
4
3
2 and show that the
3
4
UO3
1
matrix A satisfies its characteristic equation Unit 3 Unit Title Complex Numbers Planned No Hrs. Unit Outcomes At the end of this unit the students should be able to: UO1 Simplify and find roots of complex number by using De Moivre‟s Theorem UO2 Expand sinnѳ, cosnѳ and tannѳ in powers of sinѳ, cosѳ and tanѳ UO3 Find relation and difference between circular and hyperbolic functions UO4 Solve examples by using hyperbolic and inverse hyperbolic functions UO5 Separate real and imaginary parts of a given complex number
9
CO3
Lesson schedule Class Details to be covered No. 1 Introduction of complex number, modulus, Argument and Algebra of complex numbers 2 Statement of De Moivers theorem and examples 3 Roots of comlex number by using De Moivers theorem 4 Expansion of sinnѳ, cosnѳ and tannѳ in powers of sinѳ, cosѳ and tanѳ 5 Definition of circular function in complex variable 6 Introduction of Hyperbolic functions and its properties 7 Relation between circular and hyperbolic functions 8 Inverse Hyperbolic functions 9 Separation of real and imaginary parts Review Questions Q1 Simplify 1. 2.
UO1
cos 2 cos 4
i sin 4
cos5
i sin 5
cos 4
Q2
1 sin 3. 1 sin Show that 1.
i sin 2
1 cos 1 cos
i sin 4
i cos i cos i sin i sin
7 12
2
cos 3
i sin 3
cos 5
i sin 5
cos 7 9
cos
5 6
3
i sin 7 i sin
5
n
UO2, UO3
n
cos n
i sin n
24
8
Q3 Q4
2.
1 i 3
3.
sin 6 sin
8
1 i 3 32cos5
28
32cos3
6cos
5 tan 10 tan 3 tan 5 4. tan 5 1 10 tan 2 5 tan 4 Express cos7 and sin 6 in terms of powers of cos Solve 4
3
x 9 2. x 6 3. x 7 4. x 1.
5. 6.
x 1
6
1 5
32( x 1)5
Find the continued product of all the values of
Q7
Q9 Q10
1 3 i 2 2
3/4
Find all the values of
1
1/5
UO1
1 i
2.
UO1
1/5
Find nth root of unity and show that 1. Roots are in geometric progression 2. Sum of the all roots is zero 3. Product of all roots is
Q8
UO1
x x x 1 0 x5 x 4 1 0 i 0 x 4 x3 1 0
1 x 1 x
1.
UO2
2
Q5
Q6
and sin
4
Find the common roots of x Solve the equation 7cosh x Prove that
1
UO1
n 1
1 0 and x 6 i 0 8sinh x 1for real values of x
UO1 UO3 UO4
3
1 tanh x cosh 6 x sinh 6 x 1. 1 tanh x 1 sinh 7 x 7sinh 5 x 21sinh 3x 35sinh x 2. sinh 7 x 64 3. sinh 1 z
log( z
z 2 1)
4. cosh 1 z
log( z
z 2 1)
5. tanh 1 z
1 1 z log 2 1 z
25
6. sinh 1 x
tanh
1
x 1 x2
1 1 7. tanh (sin ) cosh (sec ) x 1 x a log 8. coth 1 a 2 x a
9. sech Q11 Q12
1
sin
log cot
2
x x tanh , prove that 1. sinh u 2 2 Separate into real and imaginary parts If tan
tan x
2. cosh u
i i 2. i 3. tanh x iy 4. tan 1 ei
5. cos
Q13 Q14 Q15 Q16 Q17 Q18
If cos(
i )
r (cos
If sin(
i )
tan
If tan(
i ) sin( x iy) , prove that
If u iv
cos ec
If x iy
tan
If cosh
1
6
x iy
i
If tan(
2 , prove that x
y2
) )
UO4 UO5
3
sin 2 sinh 2
ix , prove that (u 2 v 2 ) 2
2(u 2 v 2 )
2x 1 3
cosh 1 ( x iy ) cosh 1 a then prove that
2(a 1) x 2 2(a 1) y 2 Q19
tan x tanh y
3i 4
1
1 sin( log 2 sin(
i sin ) then prove that
i sec , prove that cos 2 cosh 2
4
UO4 UO5
i
1.
sec x
a2 1
i ) i and x,y are real prove that x is indeterminate and y is infinite
Section II Expansion of functions
Unit 4 Unit Title Planned No Hrs. Unit Outcomes At the end of this unit the students should be able to: UO1 Expand given function by using Maclaurin‟s series, Taylor‟s series, some standard expansions, derivative and integration method and substitution method UO2 Find limits of indeterminate forms by L‟ Hopital‟s Method
9
CO4
Lesson schedule Class Details to be covered No. 1 Introduction, Expansion by using Maclaurins series 2 Standard expansions by using Maclaurins series 26
3 4 5 6 7 8 9
Expansions by using standard expansions Expansions by using derivative and integration method Expansion by using substitution method Expansions by using Taylor‟s Method Examples on Indeterminate forms
Review Questions Q1 Expand in powers of x 1. tanx 2. log(1+ex) 3. exsecx 4. tan
1
5. log tan
UO1
1 x2 1 x
x
4
3( x 2)3 ( x 2) 4 ( x 2)5 in powers of x by Taylor‟s
6. 17 6 x 2 theorem
7. tan x in powers of x
4 8. log(1 sin x) by Maclaurin‟s series x 9. x by using standard expansions e 1 10. x5 x 4 x3 x 2 x 1 in powers of x 1 and hence find f (11/10) Q2
11. 2 x3 7 x 2 Prove that
x 1 in powers x-2
UO1 2
2. 3. 4. 5. 6.
6
x x ..... 12 45 2 x4 sec2 x 1 x 2 ..... 3 x 2 x3 11x 4 e x cos x 1 x .... 2 3 24 x3 5 x 4 (1 x) x 1 x 2 ..... 2 6 x 5 x 2 x3 log[log(1 x)1/ x ] ..... 2 24 8 x 2 x3 e x log(1 x) x .... 2 3
1. log sec x
x 2
4
27
Q3 Q4 Q5 Q6
3 2 If x 2 xy
y 3 x 1 then prove that y
x2 .... 3 x 2 x3 x ..... 2! 3!
1 x
y 2 y3 y 4 .... then prove that y If x y 2 3 4 Using Taylor‟s Theorem 25.15 2. tan(46036') 3. sin(30030') 4. cos 410 1. Evaluate sin 3 2 x sin 3 x
UO1 UO1 UO1 UO2
1. lim x o
x5 x3 e x sin x x x2 2. lim 2 x o x xlog 1 x 3. lim log(2 x) cot( x 1) x 1
1x
2
4. lim x
1x
3 3
1x
5
1 x
tan 3x 5. lim x o sin 2 x xy
yx
6. lim x y x ox y
1 1 x x e 12 e x 7. lim x o x2 e x sin x x x2 8. lim 2 x o x xlog 1 x
9. lim x a 10. lim x
tan 7
x 2 a 1x
1x
2
3 3
2a
1x
5
1 x
tan 3x 11. lim x o sin 2 x
12. lim
x 0
tan x x
1 x2
28
a x a x 2 sin a x 2
sin
13. lim x
a
1
x 14. lim log 2 a x a Q7
If lim x o
cot( x a )
sin 2 x p sin x is finite; find the value of p and limit x3
UO2
Unit 5 Unit Title Partial Differentiation No Unit Outcomes At the end of this unit the students should be able to: UO1 Take partial derivative of a given function (Implicit or Explicit) UO2 Solve examples by using Euler‟s Theorem and it‟s corollaries UO3 Solve examples by using Jacobian and its properties
Planned Hrs.
12
CO5
Lesson schedule Class Details to be covered No. 1 Introduction to partial differentiation 2 Total derivative 3 Differentiation of implicit function 4 Statement of Euler‟s theorem and examples 5 Statement of corollaries of Euler‟s theorem and examples 6 Change of variable 7 Introduction of Jacobian 8 Properties of Jacobians 9 Jacobians of Implicit functions 10 Exapmles on errors and approximations 11 Examples on Maxima and Minima Review Questions Q1 If u sin( x 2
1 u x x Q2 Q3
If u If z
UO1
y 2 ) sin( y 2 z 2 ) sin( z 2 x 2 ) then prove that 1 u 1 u 0 y y z z
y x 2 tan 1 x
2u x y 2 tan 1 ; then prove that y x y
( x, y) and x uv, y
u then prove that v
2u
UO1
y x UO1
29
z x
1 z 2v u
Q4
u
If Q5 If
y2
x 2 cos ec 1 1 x
x2
If u (i)
Q10 If u Q11 If
Q12
2
prove that
3
then show that
y
1 2
y
1 3
1 x2
If u Q14 If y1
,
x
y
x
y
y2
2
UO1
u y y
1 tan u 12
UO2
x y 2 sin 1 ; prove that y
u y
; prove that
y2 x2 y 2 ;v then find 2x 2x
x1
3
tan u 13 tan 2 u 12 12 12
x 2 y 3z sin 1 8 8 8 ; then find x u x x y z
x2 x3
y2
2abz
y2
2u
y2
x1x3 x2
& y3
x1x2 x3
UO2
u u y z y z
UO2
x u y x
2u 2u 2 x2 y 2 2 u If u log ; find x2 2 xy y x y x y x2 y2
Q13
UO1
1
z z a x y
2u u (ii) 2 2u y x 2 xy y x y x2
u sin 1
UO1
x2 y 2 x2 y 2
v y x
2
b
0
UO2
2u 2 2 u 2 xy y x y x2 y2
u x x
u z2
u x y u x y
UO1
2
u y2
u ; prove that i) x x
2u
y x 2 sin 1 x
2
u x2
xy ; prove that 1 x2 y 2
tan 1
1
If u
Q9
v2 z 2u v
y
z eax by f (ax by)
Q8
ii)
1 2
z2
x
If u
If
x2
v z 2 u
ux vy 0 and u v 1 ; prove that
Q6
Q7
z y
1 z 2u v ,
u and x x
UO2
UO3
u, v x, y ; find
u y y
y1, y2 , y3
UO3
x1, x2 , x3
30
Q15
x r sin cos
If Q16 Q17
Verify
x
If
If
y r sin sin , z r cos
then find
UO3
r, , x, y, z
JJ ' 1 , if, x sin cos , y sin sin
vw , y
w r cos Q18
,
wu , z
find
uv and u = r sin cos
UO3 ,
v r sin sin
,
UO3
x, y, z r, ,
u3 v3 w3 x y z , u 2 v2 w2 x3 y3 z3 ,
UO3 UO3
u v w x2 y 2 z 2 Show that Q19
Q20
u , v, w x y y z z x = x, y , z u v v w w u
2 If u xyz , v = x
y2 z2 , w x y z
x 1 = u x y x z
show that
UO3
The diameter and altitude of a can in the shape of a right circular cylinder are UO3 measured as 4 cm & 6 cm respectively. The possible error in each measurement is 0.1 cm. Find approximately the error in the values computed for the volume and lateral surface.
Q21
If a body‟s weight in air is A and that of in water W, its specific gravity is given by UO3
S
A . If A = 20 kg & W = 10 kg and percentage error in A and W is 3, find A W
percentage error in S. Q22
If f x, y, z
x2 y3z
1 10
find the approximate value of
f x, y, z when
UO3
x = 1.99, y = 3.01, z = 0.98 Q23
Show that the function
f x, y
x3
y3 63 x y
12 xy is maximum at
UO3
(-7, -7) and minimum at (3, 3). Unit No
6
Unit Title
Numerical Solution of linear simultaneous equations
Planned Hrs.
06
31
Unit Outcomes At the end of this unit the students should be able to: UO1 Solve system of simultaneous linear equations by using Gauss elimination method, Gauss Jordon method, Jacobi‟s method, Gauss seidel iteration method UO2 Determine eigen values by iterative method
CO6
Lesson schedule Class Details to be covered No. 1 Introduction of all the methods 2 Examples on Gauess elimination method 3 Examples on Gauess Jordon method 4 Examples on Jacobi‟s method 5 Examples on Gauess seidal method 6 Determination eigen values by iterative method Review Questions Q11. Solve by using Gauss Elimination Method 1. x 0.5y 0.3333z 1, 0.5x 0.3333y+0.25z 0, 0.3333x 0.25y 0.2z=0 2. x1 2x 2 3x 3 9x 4
5,3x1 10x 2 4x 3 2x 4
UO1
7,11x1 5x 2 9x 3 2x 4 13,
2x1 +3x 2 7x 3 6x 4 =11 3. x 3 y 2 z 5, 2 x y 3z 1,3x 2 y z 6 4. x 2 y 3z t 10, 2 x 3 y 3z t 1,3x 2 y 4 z 3t 2, 2 x y 2 z 3t 5. x 2 y 3z 14, 4 x 5 y 7 z 35,3x 3 y 4 z 21 6. 5 x y 2 z 142, x 3 y z 30, 2 x y 3z 5 Q22. Solve the equations by Gauss Jordan Method 44, 2x 3y 10z 22 1) 10 x 2y z 9, 2x 20y 2z
7
UO1
30, 2x1 x 2 3x 3 5 2) 5x1 x 2 x 3 142, x1 3x 2 x 3 3) x y z 5, 2 x 3 y z 10,3x 2 y 2 z 3 4) x y z 9, 2 x 3 y 4 z 13,3x 4 y 5z 40 1, x 4 y 5 z 25,3x 4 y z 2 5) 2 x 3 y z 6) x 2 y 6 z 22,3x 4 y z 26, 6 x y z 19 Q33. Use Jacobi‟s Iteration Method to solve the following equations 18, 2x - 3y 20z 25 1) 20x y 2z 17,3x 20y – z 2) 2x1 12x 2
3x1 4x 2 3) 4) 5) 6) 7)
x 3 4x 4 13,13x1 5x 2 3x 3 x 4 18, 2x1 x 2 3x 3 9x 4 10x 3
x4
UO1
31,
29
2x - 3y + 20z 25, 20x y – 2z 17,3x+20y-z -18 15x +2y + z 18, 2x 20y – 3z 19,3x-6y+25z 22 4x +y +3 z 17, x 5y+z 14, 2x-y+8z 12 27x +6y- z 85, x y+54z 110, 6x+15y+2z 72 5x -y+ z 10, 2x 4y 12, x+5y+5z 1 32
Q44. Using Gauss Seidel Iteration Method solve the following equations 1) 3x + 2y = 4.5, 2x + 3y – z = 5, - y + 2z = - 0.5 Iterate four times using the initial approximation x=0.4, y=1.6, z=0.4 by fixing three decimal places in calculator. 2) 27x + 6y – z = 85, 6x + 15y + 2z = 72, x + y + 54z = 110 by fixing five decimal places in calculator 3) 10x1 x 2 x 3 12, 2x1 10x 2 +x 3 13, 2x1 2x 2 +10x 3 14 4) 28x +4y- z 32, 2x 17y+4z 35, x+3y+10z 24 (up to 4th iteration) 5) 4x -2y- z 40, x-6y+2z 28, x-2y+12z 86 (up to 4th iteration) 6) 25x+2y+ z 69, 2x+10y+z 63, x+y+z 43 (up to 4th iteration) 7) 3x1 0.1x 2 0.2x 3 7.85,0.1x1 7x 2 -0.3x 3 -19.3,0.3x1 0.2x 2 +10x 3 71.4, Q55. Find the largest Eigen value and the corresponding Eigen vector of the following matrices 1)
1 4 6
2)
1 3 1 0 3 2 4 by taking initial Eigen Vector as 0 up to Fifth iteration 1 4 10 1
3)
5 0 1
3 4 3
2 1 by using initial Eigen vector as X 5
0 1 2 0 by taking initial Eigen Vector as 0 5
UO1
UO2
1 1 1
1 0 up to Fifth iteration 0
2 2 2 2 1 0 1 4) 2 / 3 5 / 3 5 / 3 5) 1 2 1 5 / 2 11/ 2 0 1 2 Q6 Find the dominant Eigen value and the corresponding Eigen vector of
UO2
1 6 0 A= 1 2 0 . Find also the least Eigen value and hence the third Eigen value by 0 0 3 power method Q7 Find the numerically largest Eigen value of the matrix A=
25 1 1 3 2 0
2 0 4
UO2
By power method. Also find the corresponding Eigen vector Q8
Find the dominant Eigen value and the corresponding Eigen vector of
UO2 33
10 2 1 A= 2 10 1 taking initial Eigen Vector as 2 1 10
1 0 by power method 0
Model Question Paper
Course Title : Duration
Engineering Mathematics I 3 hours
Max. Marks 100
Instructions: All questions are compulsory Figures to the right indicates full marks Use of non-programmable calculator is allowed Section-I 1
Attempt any three a Reduce the following matrix to normal form and hence find its rank 0 1 3 1 1 0 1 1
b
3 1 0 2 1 1 2 0 Test for consistency and if possible solve
x1 2 x2 x3 1, 3x1 2 x2 2 x3
Investigate for what values of and the system of equations x y z 6, x 2 y 3z 10, x 2 y z have infinite number of solutions d Solve the following system of equations x y 2 z 0, x 2 y 3z 0, x 3 y 4 z 0, 3x 4 y 7 z 0 Attempt any three Examine the following set of vectors for linearly dependent or a independent if dependent find the relation T T X 1 2,3, 4, 2 , X 2 ( 1, 2, 2,1)T , X 3 1,1, 2, 1 b
5
2, 7 x1 2 x2 3x3 5
c
2
Marks 15 5
Find the Eigen values and the Eigen vector corresponding to smallest
5
5 15 5
5
34
1 1 3 Eigen value only A
1
5
1
3
1 1
c Find the characteristic equation of the matrix A
d
1
c d
e
Prove that
sin 7 sin
7 56sin 2
4
3
2 and
2
6
2 and
0
2
5
d
64sin 6
If 5sinh x cosh x 5 find tanh x If sin( i ) r (cos i sin ) then prove that 1 r2 cosh 2 cos 2 2 If tan( x iy) i where x, y are real prove that x is indeterminate and y is infinite. Section-II
Express 3x 2
5
5
4
112sin 4
Attempt any three a Expand e x sin x in powers of x up to x 4 b 2x x3 2 n x Prove that sin 1 1 x2 3 c
5
2
hence determine the Eigen values of A and A Attempt any four 3/4 a Find all the values of 1 i 3 and show that their product is 8 b
4
8
3 4 1 show that the matrix A satisfies its characteristic equation 7 2 0 Determine the Eigen values of the matrix A
3
8
x5 5
.....
2 x 5 in terms of x 2 by using Taylor‟s theorem
x 1 Evaluate lim x 1 x 1 log x Attempt any three 3 3 3 a If u log( x y z 3xyz ) then prove that u u u 3 x y z x y z
20 5 5 5 5
5
Marks 15 5 5 5 5 20 5
35
b If u
cos ec 2
x2
c
6
u x2
x1/2 x1/3
1
y1/2 then show that y1/3
2
2 xy
2
u x y
y2 2
u y2 2 1/2
tan u 13 12 12
5
tan 2 u 12
If f ( x, y ) (50 x y ) , find the approximate value of f (3, 4) f (2.9, 4.1) by theory of approximation d For the transformations x a(v u ), y b(u v) and ( x, y) u r 2 cos 2 , v r 2 sin 2 find (r , ) Divide 120 into three parts so that the sum of their product taken two e at a time shall be maximum Attempt any four Solve by Gauss Elimination method a 3x 4 y 5 z 18, 2 x y 8 z 13, 5 x 2 y 7 z 20 Find the solution of the following system of equations using Jacobi‟s b iterative method (5 Iteration) 8 x 3 y 2 z 20, 4 x 11y z 33, 6 x 3 y 12 z 35 Solve using Gauss- Siedel method, the following system of equations c 28 x 4 y z 32, x 3 y 10 z 24, 2 x 17 y 4 z 35 Correct to 3 places decimals Determine the largest Eigen value by Iteration method of the matrix d 1 2 A 3 4
5 5
5 15 5 5
5
5
Assignments List of experiments/assignments to meet the requirements of the syllabus Assignment No. 1 Assignment Matrices and solution of linear system equations CO1 Title 1. Reduce the following matrices to Canonical(Normal) form and hence find Batch I rank 5 2 4 1 6 1 2 3 0 2 1 1 2 2 2 4 3 2 (a) (b) 4 1 0 5 10 3 2 1 3
1 2 5 8 6 6 8 7 5 2. Find nonsingular matrices P & Q s.t. PAQ is in the normal form also find rank of A, where
36
1 1 1 3 2 1 5 (a) A= 1 1 1 (b)A= 5 1 4 2 3 1 1 1 4 11 19 3. Find nonsingular matrices P & Q s.t. PAQ is in the normal form also find rank
2 1 3 1 of A and A , where A= 3 1 2 1 2 3 4. Reduce the following matrices to echelon form and find rank 2 1 1 2 1 3 3 1 1 0 3 4 (a) (b) 4 1 2 2 3 7
4 1 4 11 6
1 1 1 2 5 5. Test for consistency and if possible solve them (i) x y z 6, x y 2 z 5, 3x y z 8, 2 x 2 y 3z (j) x1 2 x2
x3 1, 3x1 2 x2 2 x3
7,
2, 7 x1 2 x2 3x3 5
(k) 2 x 6 y 11 0, 6 x 20 y 6 z 3 0, 6 y 18 z 1 0 6. Solve (a) 3x y 5 z
0, 5 x 3 y 6 z
0, x
y 2z
0, x 5 y z
(b) x 2 y 3z 0, 2 x 3 y z 0, 4 x 5 y 4 z 0, x y 2 z 7. Discuss the solution for all values of k where equations are 2 x 3ky (3k 4) z 0, x k 4 y (4k 2) z 0, x 2 k 1 y (3k 4) z
Batch II
0 0
0
1. Reduce the following matrices to Canonical(Normal) form and hence find rank 2 1 1 3 8 1 2 3 0 1 1 1 1 2 2 4 3 2 (a) (b) 3 2 1 0 6 3 2 1 3
0 4 3 2 8 6 8 7 5 2. Find nonsingular matrices P & Q s.t. PAQ is in the normal form also find rank 3 2 1 5 of A, where A= 5
1 4 2 1 4 11 19 3. Find nonsingular matrices P & Q s.t. PAQ is in the normal form also find rank
37
3 of A and A , where A= 2 0 1
3 4 3 4 1 1
4. Reduce the following matrices to echelon form and find rank 1 2 1 4 2 1 3 6 2 4 3 4 1.
2.
3
3
1
2
1 2 3 4 1 1 1 2 1 2 6 7 5. Test for consistency and if possible solve them a) x 2 y z 3, 3x y 2 z 1, 2 x 2 y 3z
2, x y z 1 0 ,
b) 2 x1 x3 4, x1 2 x2 2 x3 7, 3x1 2 x2 1 c) x y z 6, x y 2 z 5, 3x y z 8, 2 x 2 y 3z 7 6. Solve a) 2 x y z 0, 3x 2 y z 0, x 4 y 5z 0 b) x y 2 z 0, x 2 y 3z 0, x 3 y 4 z 0, 3x 4 y 7 z 0 7. Find the value of k for which the system has non-zero solution & hence find solution for each value of k for 3x y kz 0,4x 2y 3z 0,2kx 4y kz 0 8. Find the value of k for which the equations 3x y 4z 3, x 2y 3z 2 0, 6x 5y kz 3 0 have infinite Batch III
number of solutions and hence find the solution 1. Define Rank and reduce the following matrices to Canonical(Normal) form and hence find rank
1 4 1. 0 0
1 1 3 1
2 0 1 0
3 2 4 2
4 5 6 7 9 10 11 12 2. 10 11 12 13 18 19 20 21
2. Find nonsingular matrices P & Q s.t. PAQ is in the normal form also find rank of A, where A is
1 1. 4 2
1 2 2
2 1 2
1 2 0
1 2. 1 3
1 1 1
1 1 1
3. Reduce the following matrices to echelon form and find rank
38
1 3 1. 2 1
2 1 2 1
1 2 3 1
3 1 2 1
1 2 3 2. 1 1 3 2 3 4
2 5 5
4. Test for consistency and if possible solve them 1. 2 y 3z 1, 3x 6 y 3z 2, 6 x 6 y 3z 5 2. 3x 2 y z 0, 2 x y 3z 0, x 4 y 5z 0 3. x y z 6, x y 2 z 5, 3x y z 8, 2 x 2 y 3z 7 5. Solve 1) x 2 y 3z 0, 2 x 3 y z 0, 4 x 5 y 4 z 0, x y 2 z 0 2) x y 2 z u 1, 2 x y 2 z 2u 2, x 2 y 4 z u 1, 5u
5
5 the system of the equations 3x y 4 z 3, x 2 y 3z 2,6 x 5 y z 3 has a unique 5 , show that the equations are consistent and have infinite solution. If
6. Show
that
if
solutions. Determine the solution in each case. 7. Investigate for what values of λ
x y z 6, x 2 y 3z 10, x 2 y
and
µ
the
equation
z
have (i) no solution (ii) a unique solution (iii) Infinite solution 8. Determine the value of k for which the system has non-zero solution and find the solution for each value of k for 3x y kz 0, 4x 2y 3z 0,2kx 4y kz 0 Assignment No. 2 Assignment Title Batch I
Eigen Values and Eigen Vectors
CO2
1. Define linear dependence & independence of vectors. Examine the linear dependence of vectors [1, 0, 2, 1]; [3, 1, 2, 1]; [4, 6, 2, -4]; [-6, 0, -3, -4] and find relation between then, if possible. 2. Check whether the following vectors are L. I. or L. D. [3,2,7], [2,4,1], [1,-2,6] 3 1 4 3.
If
, 2 , 3 are Eigen values of matrix 0 2 6
1
0 Find (a) 4.
1
2
3
(b)
1
2
0
5
3
Find the Eigen values and Eigen vectors for the following matrices
39
1 1 3 (a) A= 1 5 1 3 1 1
(b) A=
2
2
3
2 1
1
6
2 0 State Cayley- Hamilton theorem and find A and A4 , where 7 2 2 3 2 4 -1
5.
i) A=
6
1 2
2 1
ii) A= 4
2
3
6 2 4 3 Find characteristic equation for A and find the matrix expression represented by A8 5 A7 7 A6 3 A5 A4 5 A3 8 A2 2 A
6.
I,
2 1 1 where A= 0
7.
1
0
1 1 2
2 8. For Eigen values for A-1, A3, -9A where A= 1 1
Batch II
1
1
1
2 1
2 1. Define linear dependence & independence of vectors. Examine the linear dependence of vectors [1, 0, 2, 1]; [3, 1, 2, 1]; [4, 6, 2, -4]; [-6, 0, -3, -4] and find relation between then, if possible. 2. Check whether the following vectors are L. I. or L. D. [1,1,1,3], [1,2,3,4], [2,3,4,9] 3 1 4 3. If
, 2 , 3 are Eigen values of matrix 0 2 6
1
Find (a)
1
2
3
(b)
1
0
0
2
3
5
4. Find the Eigen values and Eigen vectors for the following matrices 1 1 3 2 2 3
5 1
(a) A= 1
2 1
(b) A=
1
6
2 0 3 1 1 -1 5. State Cayley- Hamilton theorem and find A and A4 , where 7 2 2 3 2 4 i) A=
6
1 2
2 1
ii) A= 4
3
2
6 2 4 3 6. Find characteristic equation for A and find the matrix expression represented 40
by
A8 5 A7 7 A6 3 A5 A4 5 A3 8 A2 2 A I , 2 1 1
where A= 0
1
0
1 1 2
6 7. For Eigen values for A-1, A5, -3A where A= 2 2 Batch III
2
2
3
1
1 3 1. Define linear dependence & independence of vectors. Show that the vectors [2, 3, -1, -1]; [1, -1, -2, -4]; [3, 1, 3, -2]; [6, 3, 0, -7] form a linearly dependent set. Also express one of these as linear combination of others 2. Check whether the following vectors are L. I. or L. D. If dependent find relation between them A. [1, 1, 3], [1, 3, -3], [-2, -4, -4], [-9, -25, 9]\ B. [1, 2, -1, 0], [1, 3, 1, 2], [4, 2, 1,0], [6, 1, 0, 1]
3 1 4 3. If
1, 2 , 3
Find (a)
1
are Eigen values of matrix (b)
2
1
2
0
2
6
0
0
5
3
4. Find the Eigen values and Eigen vectors for the greatest Eigen value for the 4 2 2 matrix A=
5
3
2
4
2 Hence find Eigen values of -2A3 , And Adj of A 1
5. Find Eigen values and Eigen vectors for A=
8
6
2
6
7
4
2 4 3 6. State and verify Cayley- Hamilton theorem and hence find A-1 and A4 , 1 1 3 where A=
1
3
3
2 4 4 7. Find characteristic equation for A and use it to find the matrix expression represented by A6 6 A5 9 A4 4 A3 12 A2 2 A I ,
41
where A=
3
10
5
2
3
4
3
5
7 Assignment No. 3
Assignment Title Batch I
Complex Numbers i. 1. Simplify
ii. 2. Show that
cos 2
i sin 2
cos 4
i sin 4
1 cos 1 cos
7 12
CO3
cos 3
i sin 3
cos 5
i sin 5
5 6
n
i sin i sin
cos n
i sin n
3/4
1 3 iii. 3. Find all the values of i 2 2 iv. 4. Solve
x4
x3
v. 5. Solve
x9 x5
x2
show that their product is 1
x 1 0
x4 1 0
x 1 vi. 6. Solve for x and note all five roots x 1 vii. 7. Prove that viii. 8. If cos cos 2
sin 7 sin cos
cos
cos 2
Batch II ix. 1. Simplify
7 56sin 2
cos5 cos 4
i sin 4
2
9
0 then show
sin
sin 2
i sin
0
5
28
xi. 3. Find the continued product of all the values of
1 x xii. 4. Solve 1 x
that
3
i sin 7
cos 8
1 i 3
64sin 6
sin 2
cos 7
8
x. 2. Show that 1 i 3
sin
0, sin 2
i sin 5
32
112sin 4
0, sin
cos 2
5
1 3 i 2 2
3/4
6
1
42
xiii. 5. Solve
x 1
5
32( x 1)5
xiv. 6. Solve for x and note all roots
cos 2
Batch III xvii. Simplify
x4 1 0
5 tan 10 tan 3 tan 5 1 10 tan 2 5 tan 4
xv. 7. Prove that tan 5 xvi. 8. If cos
x9 x5
cos
cos
cos 2
0, sin
cos 2
1 sin 1 sin
i cos i cos
sin
0, sin 2
sin 2
sin 2
that
0
n
5 tan 10 tan 3 tan 5 1 10 tan 2 5 tan 4
xviii. 2. Show that tan 5
xix. 3. Find the continued product of all the values of xx. 4. Solve
x6 i 0
xxi. 5. Solve
x7
x4
1 3 i 2 2
3/4
x3 1 0
x 1 xxii. 6. Solve for x and note all five roots x 1 xxiii. 7. Prove that 1 i
0 then show
sin
100
1 i
100
5
32
251
xxiv. 8. Find nth root of unity and show that
1. Roots are in geometric progression 2. Sum of the all roots is zero
1
n 1
3. Product of all roots is Assignment No. 4 Assignment Title Batch I
Complex Numbers 1) If z
1 i 3 and n is an integer, then show that z 2 n z n 2n 22 n
CO3 0 if n is
not multiple of 3 2 2 2) Define cosh x & sinh x . Also prove that cosh x sinh x 1
3) Prove cosh 1 x log( x
x 2 1)
43
4) If cos
5) If tan
i
x iy then prove that x 2
i
6
6) If tan
) )
2x 1 3
y2 n 2
ei then prove that
i
1 sin( log 2 sin(
i sin ) then prove that
R(cos
4
7) Separate into real and imaginary parts of i) tan
1
1 log tan 2 4
and
2
ei
1 1 8) Prove that tanh (sin ) cosh (sec )
Batch II
1. Solve the equation 7cosh x 8sinh x 1for real values of x 2. Prove that cosh 1 z log( z z 2 1) x x tanh 3. If tan , prove that 1. sinh u tan x 2. cosh u sec x 2 2 i
4. Separate into real and imaginary parts 5. If x iy
tan
6. If sin(
i )
7. Prove that sech Batch III
1
2x 1 3 i sec , prove that cos 2 cosh 2 2 , prove that x
i
6 tan
sin
log cot
1 tanh x 1 tanh x
1. Prove that
i
1 2. Prove that sinh x
y2
3
2
3
cosh 6 x sinh 6 x
tanh
1
x
1 x2 1 1 3. Prove that tanh (sin ) cosh (sec ) 4. Separate into real and imaginary parts cos 5. f cos(
i )
6. If u iv 7. If cosh
1
x iy
4
3i 4
i sin ) then prove that
r (cos
cos ec
1
ix , prove that (u 2 v 2 )2
1 sin( log 2 sin(
) )
2(u 2 v 2 )
cosh 1 ( x iy ) cosh 1 a then prove that
2(a 1) x 2 2(a 1) y 2
a2 1
Assignment No. 5
44
Assignment Title Batch I
Expansion of Functions and Indeterminate forms
1 x3 x 2 3
x5 5
CO4
1. Prove that tan 1
1 x2 1 x
x7 7
2. Expand x5 5x4
6x3 7 x2 8x 9 in powers of ( x - 1)
1 3. Expand log log 1 x x up to x3 4. If x3
2 xy 2 y3 x 1 then expand y in ascending powers of x
5. Find approximate value of tan 43 correct up to four places of decimals 6. Obtain expansion of e x sin x in powers of x up to x 6 7. Using Taylor‟s theorem expand x 2
4
3 x 2
3
4( x 2) 3 in of x
1 1 x x e 12 e x 8. Evaluate lim x o x2 9.
10.
Batch II
If lim x o
sin 2 x p sin x is finite; find the value of p and limit x3 2
Find (i) lim x a
x a
tan 7
2a
1x
1x
2
(ii) lim x
3 3
1x
5
1 x
1. Expand log e x in powers of (x-1) and hence evaluate log e 1.1 correct up to four decimal places 2. Prove that e x log(1 x) 3. Prove that If x3
2 xy 2
x
x2 2
x3 3
y3 x 1 then expand y in ascending powers of x
4. Find approximate value of sin30 30' correct up to four places of decimals sin x 4 5. Obtain expansion of e in powers of x up to x
x
2
6. Using Maclaurin‟s series prove that e sin x
x
2
x
3
x4 6
...........
45
7. Using Taylor‟s theorem expand 17 6( x 2) 3( x 2)3 ( x 2) 4 ( x 2)5 in powers of x 8. Evaluate following limits
e x sin x x x2 1. lim 2. lim log(2 x) cot( x 1) x o x 2 xlog 1 x x 1 3.
x 2 a
lima
x
Batch III
1. Prove that tan 1
tan x
2a
4.
1 x2 1
e2 x (1 x)2 lim x o x log(1 x) 1 n 2
x
x
x3 3
x5 5
x7 7
....
2. Expand log e x in powers of (x-1) and hence evaluate log e 1.1 correct up to four decimal places 3. Prove that e x log(1 x) x
x2 2
1 4. Prove that log log 1 x x
x3 3 x 2
5 2 x 24
x3 ..... 8
5. Find approximate value of sin30 30' correct up to four places of decimals x 2 6. Using Maclaurin‟s series prove that e sin x
x2
x3
x4 6
...........
3 4 5 7. Using Taylor‟s theorem expand 7 ( x 2) 3( x 2) ( x 2) ( x 2) in
powers of x 8. Evaluate following limits
1)
lim
x 0 9. If lim x o
tan x x
1 x2
a x a x 2 sin a x 2
sin 2) lim x a
1
x 3) lim log 2 a x a
cot( x a )
sin 2 x p sin x is finite; find the value of p and limit x3
46
Assignment No. 6 Assignment Title Batch I
Partial Differentiation 2u x y 2 tan 1 ; then prove that y x y
1. If u
y x 2 tan 1 x
2. If z =
(x, y) and x = uv, y
z x
1 z 2v u
3. If u
4. If
x2
z2
x
1
2u
(ii) x2
x2
6. If u
Batch II
2
; prove that
2
u x2
u y2
x
2 xy
2u
x y
y x 2 sin 1 x
u x
y
u y
1 2
1 y 3
y2
; prove that
2u
y2
2
u z2
u x y
y
y
(i) x
v y x
u u y x y
0 x2 y 2 x2 y 2
1 tan u 12
tan u 13 tan 2 u 12 12 12
x y 2 sin 1 ; then find y (ii) x2
2u
2u 2 xy x y x2
7. If u
u u u x 2 y 3z y z sin 1 8 8 8 ; find x x y z x y z
8. If u
log
1. If u
y x
v2 z 2u v
v z 2 u
ux vy 0 and u v 1 ; prove that
x 2 5. If u cos ec 1 1 x 3
(i)
1 2
2u
u then prove that v
1 z z And 2u v y
y2
CO5
y2
2u
y2
2u 2u 2 x2 y 2 2 u &x u ; find x2 2 xy y x x y x y x2 y2
y x 2 tan 1 x
y
u y
2u x y 2 tan 1 ; then Find y x y
47
2
3. If x u cosh
v sinh , y
then prove that 4. If
u sin 1
5. If cos u
x2
Batch III
2
z
x
2
x
y
x
y
x2
y2
x2
y2
u sinh
2
z
y
2
2
z u2
; prove that
z u v
uv
and z is function of x and y
v cosh 2
2
z x y
e x, v e y then prove that
(u, v) and u
2. If z =
z
v2
u y
x u y x
; then prove
2u 2u 2 xy x y x2
y2
2u y2
cot u cos 2u cos ec 2u 4
6. If u
log( x sin y
y sin x) ; then show that
7. If z
f ( x at )
( x at ) ; Then Prove that
2u
2u
x y
y x
2z
t2
a2
2z
x2
0
2u x y 2 tan 1 ; then prove that y x y u 2. If z = (x, y) and x = uv, y then prove that v z 1 z 1 z z v z v2 z And x 2v u 2u v y 2 u 2u v
1. If u
3. If u
4. If
6. u
x2
1 y2
2
z2
; Evaluate
u x2
2
u y2
ux vy 0 and u v 1 ; prove that
5. If u
2u
y x 2 tan 1 x
x
tan 1 sin( x2
1 u x x
y
2
u z2 u x y
2 u xy then show that x y 1 x2 y 2
y 2 ) sin( y 2
1 u y y
1 u z z
z 2 ) sin( z 2
y x
v y x
x2 y 2 x2 y 2 1
1 x2
3
y2 2
x2 ) prove that
0
48
1
x 2 cos ec 1 1
7. If u
x
x2
2u
2 xy
x2
(ii)
9. If u
2u
; prove that (i) x
y2
x y
2u 2 xy x y x2
x2 y 2 x y
2u
u u y x y
y2
; find
x2
y2
1 tan u (ii) 12
tan u 13 tan 2 u 12 12 12
u x ; then find(i) x y 2 sin 1 y x
2u
x2
log
1 2
1 y 3
3
y x 2 sin 1 x
8. If u
y
y
u y
2u
y2
2u
2u 2 xy x y x2
y2
2u
y2
&x
u u y x y
Assignment No. 7 Partial Differentiation
Assignment Title Batch I 1. If u
2. If
y2 ;v 2x
x r sin cos
3. Verify JJ ' 4. If
x2
,
u, v x, y
y r sin sin , z r cos then find
r, , x, y, z
1 , if, x sin cos , y sin sin
u3 v3 w3
u v w x2 Show that
y2 then find 2x
CO5
x y z , u 2 v2 w2 y2
x3
y3 z 3
z2
u , v, w x y y z z x = x, y , z u v v w w u
5. The diameter and altitude of a can in the shape of a right circular cylinder are measured as 4 cm & 6 cm respectively. The possible error in each measurement is 0.1 cm. Find approximately the error in the values computed for the volume and lateral surface. 6. If a body‟s weight in air is A and that of in water W, its specific gravity is
49
A . If A = 20 kg & W = 10 kg and percentage error in A A W
given by S
and W is 3, find percentage error in S.
x2 y3z
7. If f x, y, z
1 10
find the approximate value of f x, y, z when x
= 1.99, y = 3.01, z = 0.98
x3
8. Show that the function f x, y
y 3 63 x y
12 xy is maximum
at (-7, -7) and minimum at (3, 3). Batch II
x2 x3
1. If y1
x1
,
x1x3
y2
x2
vw , y
2. If x
w r cos
& y3
wu , z
x1x2 x3
; find
y1, y2 , y3 x1, x2 , x3
uv and u = r sin cos , v r sin sin ,
x, y, z r, ,
find
3. Show that the function f x, y
x3
y 3 63 x y
12 xy is maximum
at (-7, -7) and minimum at (3, 3). 4. The H. P. required to proper a steamer varies as the cube of velocity and the square of length. If there is 3% increase in velocity and 4% increase length, find % error in H.P. 5. The diameter and the altitude of a can in the shape of right circular cylinder are measured as 4cm and 6cm resp. The maximum possible error in each measurement is 0.1cm find approximately the maximum possible errors in the values computed for volume and lateral surface 2 6. If x v
Batch III 1) If u
2) If y1
w2 , y u 2 w2 , z v 2 u 2 prove that JJ '
y2 ;v 2x
x2 x3 x1
x2
, y2
y2 then find 2x
x1x3 x2
& y3
1
u, v x, y
x1x2 x3
; find
y1, y2 , y3 x1, x2 , x3 50
3)If
x r sin cos
4) Verify JJ ' 5) If x
6) If
1 , if, x
vw , y
w r cos
,
y
u v w x2
z u, y
wu , z
z
v, z
r, , x, y, z
w
uv and u = r sin cos , v r sin sin ,
x, y, z r, ,
find
u3 v3 w3
y r sin sin , z r cos then find
x y z , u 2 v2 w2 y2
z 2 Show that
x3
y3 z 3 ,
u , v, w x y y z z x = x, y , z u v v w w u
7) The diameter and altitude of a can in the shape of a right circular cylinder are measured as 4 cm & 6 cm respectively. The possible error in each measurement is 0.1 cm. Find approximately the error in the values computed for the volume and lateral surface. Assignment No. 8 Assignment Title Batch I
Numerical Solution of linear simultaneous equations
CO6
1. Solve by using Gauss Elimination Method 1) x + 0.5y + 0.3333z = 1, 0.5x + 0.3333y + 0.25z = 0, 0.3333x + 0.25y+ 0.2z=0 2) x1 - 2x2 + 3x3 + 9x4= 5, 3x1 + 10x2 + 4x3 + 2x4= 7, 11x1 +5x2 +9x3 +2x4=13, 2x1 +3x2 +7x3 +6x4=11 2. Solve the equations by Gauss Jordan Method 1. 10x + 2y + z = 9, 2x + 20y - 2z = - 44, -2x + 3y + 10z = 22 2. 5x1 - x2 - 2x3 =142, x1 - 3x2 - x3 = - 30, 2x1 - x2 - 3x3 = 5 3. Use Jacobi‟s Iteration Method to solve the following equations 1. 20x + y - 2z = 17, 3x + 20y – z = - 18, 2x - 3y + 20z = 25 2. 2x1 + 12x2 + x3 -4x4= 13, 13x1 + 5x2 -3x3 + x4= 18, 2x1 + x2 -3x3 + 9x4= 31, 3x1 - 4x2 + 10x3 + x4=29 4. Using Gauss Seidel Iteration Method solve the following equations 1. 3x + 2y = 4.5, 2x + 3y – z = 5, - y + 2z = - 0.5 Iterate four times using the initial approximation x=0.4, y=1.6, z=0.4 by fixing three decimal places in calculator. 2. 27x + 6y – z = 85, 6x + 15y + 2z = 72, x + y + 54z = 110 by fixing five decimal places in calculator 5. Find the largest Eigen value and the corresponding Eigen vector of the following matrices
51
Batch II
1.
1 4 6
3 4 3
2 1 by using initial Eigen vector as X 5
1 1 1
2.
1 3 1 0 3 2 4 by taking initial Eigen Vector as 0 up to 5th iteration 1 4 10 1
1. Solve by using Gauss Elimination Method a. x 2 y 3z t 10, 2 x 3 y 3z t 1,3x 2 y 4 z 3t 2, 2 x y 2 z 3t 7 b. 5 x y 2 z 142, x 3 y z 30, 2 x y 3z 5 2. Solve the equations by Gauss Jordan Method a) x y z 9, 2 x 3 y 4 z 13,3x 4 y 5z 40 b) x 2 y 6 z 22,3x 4 y z 26, 6 x y z 19 3. Use Jacobi‟s Iteration Method to solve the following equations a. 2x - 3y + 20z 25, 20x y – 2z 17,3x+20y-z -18 b. 15x +2y + z 18, 2x 20y – 3z 19,3x-6y+25z 22 4. Find the largest Eigen value and the corresponding Eigen vector for
1 I. 4 6 II.
3 4 3
2 1 by using initial Eigen vector as X 5
1 1 1
1 3 1 0 3 2 4 by taking initial Eigen Vector as 0 up to 5th iteration 1 4 10 1
5. Using Gauss Seidel Iteration Method solve the following equations 28, x-2y+12z 86 (up to 4th iteration) a. 4x -2y- z 40, x-6y+2z Batch III
b. 10x1 x 2 x 3 12, 2x1 10x 2 +x 3 13, 2x1 2x 2 +10x 3 14 1. Solve by using Gauss Elimination Method a. x 2 y 3z 14, 4 x 5 y 7 z 35,3x 3 y 4 z 21 30, 2 x y 3z 5 b. 5 x y 2 z 142, x 3 y z 2. Solve the equations by Gauss Jordan Method 1, x 4 y 5 z 25,3x 4 y z 2 a. 2 x 3 y z b. x 2 y 6 z 22,3x 4 y z 26, 6 x y z 19 3. Use Jacobi‟s Iteration Method to solve the following equations 1 a. 5x -y+ z 10, 2x 4y 12, x+5y+5z b. 4x +y +3 z 17, x 5y+z 14, 2x-y+8z 12 4. Using Gauss Seidel Iteration Method solve the following equations a. 25x+2y+ z 69, 2x+10y+z 63, x+y+z 43 (up to 4th iteration) 52
b. 3x1 0.1x 2 0.2x 3 7.85,0.1x1 7x 2 -0.3x 3 -19.3,0.3x1 0.2x 2 +10x 3 5. Find the largest Eigen value and the corresponding Eigen vector of the following matrices
3 4 3
2 1 by using initial Eigen vector as X 5
71.4,
a.
1 4 6
1 1 1
b.
1 3 1 0 3 2 4 by taking initial Eigen Vector as 0 up to 5th iteration 1 4 10 1
List of Tutorials To find the rank of the matrix. T1 T2
Solve simultaneous linear equations
T3
Find Eigen values & Eigen vectors
T4
Examples on DeMoivres theorem, roots of complex numbers
T5
Examples on, hyperbolic functions & inverse hyperbolic functions
T6
Examples on, expansions of functions at x=o & x=a
T7
Evaluation of indeterminate forms
T8
Examples on Partial differentiation, Euler‟s theorem & corollaries
T9
Applications of partial differentiation
T10
Numerical Solution of linear simultaneous equations
List of open ended experiments/assignments 1. Solve above given assignments by using Scilab software and compare your answers
53
FE Engineering Semester I & II Basic Electrical Engineering Class Course Examination Scheme Max. Marks Contact Hours/ week Prepared by
FE (Shivaji University, Kolhapur) Basic Electrical Engineering
Semester Course Code
I & II 41413
Theory
Term Work
POE
Total
100
25
--
125
3
2
--
5
Mr.S.S.Godhade, Mr. P.D. More, Date 05/05/2014 Ms. P.R.Desai, Ms. S.S.Patil Course Objectives: To provide the students with an introductory and broad treatment of the field of electrical engineering. Basic parameters in electrical circuit, ohm‟s law, Properties of series and parallel connections, Knowledge about magnet, magnetic materials and their types and Prerequisites properties, Faraday‟s laws of electromagnetic Induction, Concept of phasors, Flemming‟s right hand and left hand rules. Course Outcomes At the end of the course the students should be able to: To Recite the fundamental concepts of magnetic circuits CO1 Analyses basic DC & AC circuits. CO2 To Discuss the fundamentals of R, L & C circuits. CO3 To Illustrate various house wiring methods and compare different electrical CO4 lamps. To illustrate basic concepts of the 3 phase AC circuits. CO5 To explain the working of transformer Justify different types of tests performed CO6 on transformers. List the different types of electrical AC machines and explain the working of CO7 single phase alternator. To train students to make connections of single phase transformer & single CO8 phase IM. Mapping of COs with POs POs COs CO1 CO2 CO3 CO4 CO5 CO6 CO7 CO8
a
b
c
d
√
E
f
G
h
i
j
k
√ √
√
√
√ √ √
√ √
√
√ √
√
54
Course Contents Unit No.
1
2
3
4
5
6
No. of Hours
Title Section I D C Circuits: A) Analysis of D.C. circuits: Kirchhoff‟s laws, mesh and node analysis, Energy conversions between electrical, mechanical, thermal quantities. B) Magnetic circuits: Series magnetic circuits. Single phase AC Circuits: Generation of sinusoidal voltage, R.M.S. & Average value, form factor, phasor representation of A.C. quantities, impedance, admittance, R-L,R-C, R-L-C series and parallel circuits powers, p.f., power factor improvement by capacitor method. Earthing and Lamps: Necessity of Earthing, Earthing methods, Fuse, MCB, Fluorescent tube, CFL, mercury vapour lamp, LED lamp, single line diagram of electrical system, study of energy meter. Section II Three phase A.C. Circuits: Introduction to 3 phase supply and its necessity, Generation of three phase A.C. voltage, balanced three phase system, relation between line and phase quantities A.C. Machines: A) Single phase Transformer: Construction, operating principle, Types, emf equation, Ratios of voltage and current, operation on no load and with load, power losses, efficiency, All day efficiency, voltage regulation, applications, autotransformer. B) Single phase alternator: Construction, types, operating principle, emf equation, alternator on load, Voltage regulation, (Theoretical treatment) Single phase A.C. motor: Construction, operating principle, T-N characteristics, applications of induction motor and universal motor.
08
08
05
08
08
05
Text Books: Sr. No. 1 2 3 4 5 6
Title of Book Basic Electrical Engineering Basic Electrical Engineering Basic Electrical Engineering A Text Book of Electrical Technology (Vol.-I & II) Fundamentals of Electrical Tech. Fundamentals of Electrical Engg.
Author
Publisher/Edition
Topics
Shingare B.H. Deshmukh J.S.Katre
Shingare Engg. Academy Nirali Publication. Tech-Max Publication.
1 to 6 1 to 6 1 to 6
B. L. Theraja
S. Chand Publication
1&6
V. K. Mehta
S. Chand Publications.
1 to 4
Dhanapat Rai Publication
1 to 4
Ashfaq Hussein
55
Scheme of Marks Section
Unit No. 1
I
2 3 5
II
6 7
Title D C Circuits: A) Analysis of D.C. circuits B) Magnetic circuits Single phase AC Circuits Earthing and Lamps Three phase A.C. Circuits A.C. Machines: A) Single phase Transformer B) Single phase alternator Single phase A.C. motor
Marks 16 16 18 16 16 18
Course Unitization Section No. 1 I
II
Unit Title D C Circuits: A) Analysis of D.C. circuits B) Magnetic circuits
Course Outcomes
No. of Questions in CAT-I CAT-II
CO1
2
Single phase AC Circuits
CO2
3
Earthing and Lamps
CO3
4
Three phase A.C. Circuits
CO5
5
A.C.Machines: A)Singlephase Transformer B) Single phase alternator
CO6
6
Single phase A.C. motor
CO7
6 (Q. 1 to Q. 3)
6 (Q. 1 to Q. 3)
Unit wise Lesson Plan Section I Unit No
1
Unit Title
DC Circuits
Unit Outcomes: At the end of this unit the students should be able to UO 1. Define different basic electrical quantities. 2. Explain and apply Kirchhoff‟s Laws (KVL and KCL). 3. Paraphrase concept of magnetic circuits. 4. Define MMF, reluctance magnetic flux, flux density. 5. Outline the concepts of B-H curve, magnetic leakage & fringing. 6. Solve Numerical on series magnetic circuit.
Planned Hrs.
08 CO 1, CO 2
56
Lesson schedule Class Details to be covered No. 1 Introduction to the subject & syllabus 2 Definition of EMF, current, resistance, power, energy and factors affecting on resistance 3 Series parallel circuits, division of current in two parallel branches 4 Kirchhoff‟s Laws – KCL, KVL. ,Numerical based on mesh and node analysis 5 Concept of magnetic circuit, MMF, reluctance magnetic flux, flux density 6 Magnetic field strength, Comparison between electrical and magnetic circuits 7 B-H curve, magnetic leakage & fringing 8 Simple examples on series magnetic circuit Review Questions Q1 State and explain Kirchhoff‟s laws. Q2 Define the terms and state their units a) Magnetic flux b) Magnetic flux density c) Magnetic field strength d) MMF Q3 Compare Electric and Magnetic circuits stating their similarities and dissimilarities. Q4 Explain series Magnetic Circuit with the help of neat diagram.
CO1 CO1
CO1 CO2
Q5 Q6
Explain Magnetic leakage and fringing. Explain B-H Curve for material.
CO2 CO2
Q7
Derive the derivation Flux = MMF/Reluctance.
CO2
Unit Planned 2 Unit Title Single phase AC Circuits No Hrs. Unit Outcomes: At the end of this unit the students should be able to 1. Define Faraday's laws of electromagnetic induction, Lenz‟s law & Fleming's right hand rule. 2. Concept of statically induced EMF & dynamically induced EMF. 3. Explain generation of single phase alternating EMF. UO 4. Derive the value of average value and RMS value. 5. Analysis of purely R, L, C and R-L, R-C, R-L-C circuits. 6. Explain the concept of power factor & its significance, pf improvement methods.
08
CO2, CO3
Lesson schedule Class Details to be covered No. 1 Faraday's laws of electromagnetic induction, Lenz's law, dynamically induced EMF 2 Fleming's right hand rule, statically induced EMF-self & mutually induced EMF, Concept of self and mutual inductance 57
3 4 5 6 7 8
Generation of single phase alternating EMF Definition of Cycle, frequency, time period, amplitude, average value and RMS value Concept of Form factor, peak factor, phase, phase difference, phasor representation Analysis of purely resistive, inductive and capacitive circuits Analysis of R-L, R-C circuits, R-L-C circuits Concept of power factor and its significance, Power factor improvement methods.
Review Questions Q1 State and explain Faradays laws of electromagnetic induction. Q2 Explain importance of RMS value & derive the equation to calculate RMS value of sinusoidal a.c. quantity (graphically & analytically). Q3 Explain generation of single phase alternating emf & derive the expression for its magnitude. Q4 Define the following terms: (a) Peak factor (b) Form Factor (c) Instantaneous value (d) Phase difference Q5 Show that when sinusoidal a.c. is applied across pure inductance current flowing through inductance lags behind voltage by 90°. Q6 With neat circuit diagram & phasor diagram explain RLC series circuit. Q7 Explain the term power factor in a.c. circuit & explain a method to improve pf Q8 With neat circuit diagram & phasor diagram explain RLC parallel circuit. Unit 3 Unit Title Earthing and Lamps No Unit Outcomes: At the end of this unit the students should be able to 1. Concept of earthing & earthing methods. 2. Construction and working of different electrical lamps. UO 3. Explain single line diagram of electrical system and their stages. 4. Construction and working of 1 phase energy meter.
Planned Hrs.
CO3 CO3 CO3 CO3
CO3 CO3 CO3 CO3 05
CO4
Lesson schedule Class Details to be covered No. 1 Necessity of earthing and earthing methods- plate & pipe earthing 2 Function of MCB, fuse and types 3 Construction and working of fluorescent lamp, CFL, LED and mercury vapour lamp 4 Single line diagram of electrical system 5 Study of single phase energy meter. Review Questions Q1 Explain why earthing is necessary and various methods of earthing with neat diagram. Q2 Define fuse. What is the function of fuse? Q3 Discuss various stages in electrical power system with single line diagram.
CO4 CO4 CO4 58
Q4 Explain working operation of 1 phase energy meter with neat diagram. Assignments
CO4
Assignment No. 1 Assignment Title Batch I
Topic – 1 & 2
CO1 & CO2
State and explain Kirchhoff‟s laws. An electrically driven pump lifts of water per minute through a height of 12 m. Efficiencies of motor and pump are 70 % and 80 % respectively. CalculateA) Current drawn by motor if at works on 400 V supply. B) Energy consumption in KWH and cost of the energy at the rate of 75 paise/KWH, if pump operates 2 hrs per day for 30 days. Assume of water weight 1000 kg.
Batch II
OR A mild steel ring has a mean circumference of 500 mm and a uniform cross sectional area of . An air gap of 1 mm is cut in the ring. Determine current required in the coil of 500 turns wound over the ring, to produce a flux of 147µ Weber in the air gap. Neglect fringing and assume relative permeability of iron as 1200.
Batch III Batch IV Assignment Title
Batch I
Show that average power consumed by pure capacitance is zero when it is supplied with a.c. supply. Draw voltage current & power waveform. Explain the term power factor in a.c. circuit, its significance. Explain power factor improvement by using capacitor methods. Assignment No. 2 CO3 & Topic – 2 & 3 CO4 Find the current flowing through a purely inductive circuit containing a voltage source, V= 325 Sin (100 πt) and an inductance L= 2H. OR For a series R-C circuit consisting of a resistance of 50 Ω and a capacitor of 100 µF, calculate the following if the supply voltage is 230 V, 50 Hz. i. Impedance of the circuit. ii. Current through the circuit. iii. Power factor. iv. Power consumed.
Batch II
Explain why earthing is necessary. Write a short note on plate earthing.
Batch III
Discuss construction and working of single phase energy meter. Write a short note (any three) i. HRC fuse ii. MCB iii. LED lamp
Batch IV
59
iv.
Mercury vapour lamp
Section II Unit Planned 4 Unit Title Three phase A.C. Circuits No Hrs. Unit Outcomes: At the end of this unit the students should be able to 1. Differentiate between single phase and three phase supply systems.Explain Generation of three phase A.C. voltage. UO 2. Deduce the relationship between line and phase values for star and delta connection. 3. Distinguish between balanced and unbalanced load.
08
CO5
Lesson schedule Class Details to be covered No. 1 Introduction to 3 phase supply and its necessity ,advantages 2 Meaning of phase sequence, Generation of three phase A.C. voltage, 3
obtaining relationship between line and phase values for balanced star and delta connection
4
To study balanced star and delta connected source
5
Balanced star connected load
6
Balanced delta connected load
7
Numerical based on line and phase quantities Numerical based on star and delta connection
8
Review Questions Q1 State the advantages of 3phase supply. Q2 Explain generation of three phase A.C. voltage in brief. Q3 Derive the relationship between line and phase quantities in Star connection. Q4 Derive the relationship between line and phase quantities in delta connection. Q5 Explain star connection in 3phase circuit and state their advantages. Q6 Explain delta connection in 3phase circuit and state their advantages. Q7 Explain the measurement of power by using two-wattmeter method. Derive the expression for active power. Unit 5 Unit Title A.C. Machines No Unit Outcomes: At the end of this unit the students should be able to UO 1. List types of transformers.
Planned Hrs.
CO5 CO5 CO5 CO5 CO5 CO5 CO5
08 CO6, 60
2. 3. 4. 5. 6.
Deduce EMF equation of transformer. Recall Losses in transformer, efficiency and voltage regulation Perform O.C. / S.C. Test for transformer. Explain the Construction and operating principle for alternator. Deduce EMF equation of alternator.
CO7
Lesson schedule Class Details to be covered No. a) Single phase transformers 1 To study the Construction and operating principle for single phase transformer 2 Types of transformer , emf equation 3 Transformation ratio, working of transformer at no load and with load. 4 Losses in transformer, efficiency and voltage regulation 5 Direct loading method for efficiency and regulation 6 O.C. / S.C. Test for transformer b) Single phase alternator 7 To study the Construction and operating principle for alternator 8 Emf equation ,working of alternator on load, voltage regulation Review Questions Q1 How parameters, losses, efficiency & regulation are determined by O.C. & S.C. test of transformer. Q2 With a neat diagram explain direct loading method for finding efficiency & regulation of transformer. Q3 For ideal transformer prove that (N2/N1): (E2/E1): (I1/I2): K
CO6 CO6 CO6
Q4
Derive e.m.f. equation of transformer.
CO6
Q5
Explain the working principal of transformer & compare core & shell type transformer.
CO6
Q6
Explain transformer at no load.
CO6
Q7
How eddy current losses are minimized?
CO6
Q8
CO6
Q9 Q10
Explain transformer at load with neat circuit & vector diagram. Define: a) Efficiency b) Regulation Up c) Regulation Down Give the condition for maximum efficiency.
Q11
Define all day efficiency.
CO6
Q12
Explain in brief the application of single phase transformer.
CO6
Q13
Explain construction of auto transformer.
CO6
Q14
Write a short note on auto transformer.
CO6
CO6 CO6
61
Q15
Explain construction & working principal of alternator.
CO7
Q16
Explain types & application of alternator.
CO7
Q17
Derive the e.m.f. equitation of alternator.
CO7
Q18
Derive the equivalent circuit of alternator.
CO7
Q19
Define voltage regulation & explain in brief performance of alternator.
CO7
Q20
Explain polarity test & ratio test for single phase transformer.
CO6
Unit Planned 6 Unit Title Single phase A.C. motor No Hrs. Unit Outcomes: At the end of this unit the students should be able to 1. List types of single phase motors. 2. Discriminate between the single phase induction and universal motor. UO 3. Analyze Torque / speed characteristics of single phase A C Motor. 4. Outline the applications of single phase induction motors and universal motor.
05
CO8
Lesson schedule Class Details to be covered No. 1 To study the construction and operating principle 2 Types of single phase motors 3
Difference between the single phase induction and universal motor
4
Torque / speed characteristics Applications of single phase induction motors and universal motor
5
Review Questions Q1 Explain construction & working principle of universal motor. Q2 Describe the construction & working of split phase induction motor. Q3 Explain construction & working principle of single phase induction motor. Q4 With the help of neat diagram explain working of a. capacitor start capacitor run motor b. shaded pole motor Q5 Why single phase induction motor is not self starting? How it is made self start? Q6 State various applications of single phase induction motors. Q7 Explain Torque Speed characteristics of single phase induction motor. Q8 Define: a. Torque b. Slip c. Synchronous speed
CO8 CO8 CO8 CO8
CO8 CO8 CO8 CO8
62
Assignments Assignment No. 3 Assignment Title Batch I
Batch II
Batch III
Batch IV
CO5, CO6 & CO7 Explain generation of three phases A.C Voltage in brief and State the advantages of 3phase supply. OR Derive relation between line and phase quantities in delta connected load. A balanced star connected load is supplied from a symmetrical 3-phase 400 V, 50Hz system. The current I in each phase is 30Amp and lags 30˚ behind the phase voltage. Findi) phase voltage ii) resistance and reactance per phase iii) load inductance per phase A three phase delta connected load draws a current of 20 A at a lagging power factor of 0.8 from a 400V, 50 Hz supply. Calculatei. Resistance of each phase ii. Inductance of each phase iii. Power consumed. Topic – 4 & 5
A 100 KVA, 230V/2200V, 50Hz single phase transformer has 50 turns on the secondary winding. Assuming an ideal transformer. Calculatei. ii. iii. iv.
Number of primary turns. Maximum value of flux in core. Primary full load current. Secondary full load current. OR
Explain construction of 1 phase alternator in brief. State the applications of alternator. Assignment No. 4 Assignment Title Batch I Batch II
Batch III Batch IV
CO7 & CO8 Explain working principle of single phase transformer & state different losses produced in transformer. Explain working principle of single phase transformer & state different losses produced in transformer. OR Explain construction & working principal of alternator. Why single phase I.M. is not self starting? How it is made to self start. Write a short note on i) Universal motor ii) Shaded pole induction motor iii) Permanent split capacitor motor Topic – 5 & 6
63
Model Question Paper Course Title :Basic Electrical Engineering Time: 3 Hrs. Marks: 100 Instructions: 1. All questions are compulsory. 2. Figure to the right indicate full marks. 3. Assume suitable data wherever necessary 4. Draw neat sketches wherever necessary. Section-I Marks Q 1 Answer any TWO a State and explain Kirchhoff‟s current law & voltage law. 08 b Compare Electric & Magnetic circuits stating their similarities & 08 dissimilarities. c A mild steel ring has a mean circumference of 500 mm and a uniform cross sectional area of . An air gap of 1 mm is cut in the ring. Determine current required in the coil of 500 turns wound over the ring, to produce a flux 08 of 147µ Weber in the air gap. Neglect fringing and assume relative permeability of iron as 1200. Q 2 Answer any TWO a Explain generation of single phase AC voltage in brief. 08 b A voltage of 220V at 50Hz is applied across a non inductive resistor connected in series with a condenser the current in circuit is 2.5A the power loss in 08 resistor is 100W & that in the condenser is negligible calculate resistance and capacitance. c A series combination of R and C is further connected in series with a variable pure inductor and put across 200V, 50Hz supply. The maximum current 08 obtainable is 0.314A and voltage across C is 300V find the circuit constants Q 3 Answer the following a Discuss various stages in electrical power system with single line diagram. 08 b Write a short note on (any two) i) Plate earthing 10 ii) Fluorescent lamp iii) Mercury vapour lamp Section-II Marks Q 4 Answer any TWO a Explain working principle of single phase transformer. State different losses produced in transformer. 08 b A 100 KVA, 230V/2200V, 50Hz single phase transformer has 50 turns on the secondary winding. Assume an ideal transformer. Calculate08 i. Number of primary turns. ii. Maximum value of flux in core. 64
iii. Primary full load current. iv. Secondary full load current. c Q5 a b
c
Q6 a b
Explain construction of single phase alternator in brief. State the applications of single phase alternator. Answer any TWO Derive relation between line & phase quantities in delta connected load. A balanced star connected load is supplied from a symmetrical 3-phase 400 volts, 50Hz system. The current I in each phase is 30Amp and lags 30˚ behind the phase voltage. Calculate - i) phase voltage ii) resistance and reactance per phase iii) load inductance per phase. A three phase delta connected load draws a current of 20 A at a lagging power factor of 0.8 from a 400V, 50 Hz supply. Calculatei. Resistance of each phase ii. Inductance of each phase iii. Power consumed. Answer the following Why single phase I.M. is not self starting? How it is made to self start. Write a short note on (any two) i. Universal motor ii.
Shaded pole induction motor
iii.
Permanent split capacitor motor
08 08
08
08
08
10
65
FE Engineering Semester I & II Basic Civil Engineering Course
Course Code
BASIC CIVIL ENGINEERING
Examination Scheme Max. Marks Contact Hours/ week Prepared by
Theory
Term Work
POE
Total
100 3
25 2
---
125 5
Mr. Patil S. B.
Pre-requisites
Date- 06/05/2014
NIL
Course Outcomes At the end of the course the students should be able to: CO1 Explain relevance of Civil engineering to other branches of engineering. CO2 Explain functions of different building components. CO3 Explain uses, properties & types of various building materials. CO4 Explain linear & angular measurements using principles of surveying. CO5 Explain vertical measurements using principle of leveling & determine the area of irregular figure. CO6 Explain component of water supply scheme, road & railway track.
Mapping of COs with POs POs
a
b
c
d
E
f
√
√
√
G
h
i
j
√ √ √
√ √
k
COs
CO1 CO2 CO3 CO4 CO5 CO6
√
√ √
√ √
√ √
√
√
√
√
√ √ √
√
66
Course Contents Unit No. 1.
2.
3.
4.
5.
6.
Title Section I Relevance of Civil Engineering and Building Planning Introduction, branches of civil engineering, application of civil engineering in other allied fields. Principles of planning, introduction to Bye-Laws regarding building line, height of building, open space requirements, F.S.I., setbacks, ventilation, Sanitation as per municipal corporation area requirement.
No. of Hours
07
Components of Building Sub-structure Types of soil and rocks as foundation strata, concept of bearing capacity, types of foundations i.e. shallow and deep and their suitability. Shallow foundation such as wall foundation, isolated foundation, deep foundation such as pile foundation. Super-structure - Elements of super-structures and their functions. 07 Building Materials and Design Use and properties of the following materials : Concrete – ingredients and grades, plain and reinforced cement concrete and 06 ready mix concrete, bricks, steel, aluminum, plastic, timber, roofing materials etc. Introduction to types of loads, load bearing and framed structures. Section II Linear and Angular Measurements Principles of surveying Classification of surveys 07 Chain Surveying Introduction to metric chain and tapes, error in chaining, nominal scale and R.F., ranging, chaining and offsetting, index plan, location sketch and recording of field book. Chain and compass survey Meridian, bearing and its types, system of bearing, Types of compass: prismatic and surveyor's compass. Calculation of included angles, correction for local attraction. Leveling Terms used in leveling, use of Dumpy level and Auto Level, temporary 07 adjustments. Methods of reduction of levels, types of leveling, Contours, characteristics of contours, use of contour maps. Introduction and use of EDM's with special reference to Total Station. Measurement of area by planimeter – mechanical and digital. Introduction to Transportation, Environmental and Irrigation Engineering Components of rigid and flexible pavement, components of railway track (Broad Gauge) 06 Components of water supply scheme (flow diagram) Types of Dams (Earthen and Gravity Dam) 67
Reference Books: Sr. No. 1.
Title of Book A Text Book of Building Construction
Author S.P. Arora, S.P. Bindra
Publisher/Edition Topics DhanpatRai 1&2 Publications
2.
Basic Civil Engineering
G. K. Hiraskar
DhanpatRai Publications
All
3. 4.
Engineering Materials Surveying
R.K.Rajput N. Basak
S. Chand Tata Mc-Graw Hill Publication
3 4 &5
Scheme of Marks Section I
II
Unit No. 1 2 3 4 5 6
Title Relevance of Civil Engineering and Building Planning Components of Building Sub-structure Building Materials and Design Linear and Angular Measurements Leveling Introduction to Transportation, Environmental and Irrigation Engineering
Marks 20 26 17 16 20 21
Course Unitization Section
Unit No. 1
I
II
Course Outcomes
No. of Questions in
3 4
Title Relevance of Civil Engineering and Building Planning Components of Building Substructure Building Materials and Design Linear and Angular Measurements
5
Leveling
CO5
2
6
Introduction to Transportation, Environmental and Irrigation Engineering
CO6
2
2
CO1
CAT-I 2
CO2
2
CO3 CO4
2
CAT-II
2
68
Unit wise Lesson Plan Section I Unit 1 Unit Planned Hrs. 7 Relevance of civil engineering & No Title building planning Unit Outcomes At the end of this unit the students should be able to: UO1 Explain relevance of Civil engineering to other branches of engineering. CO1 Lesson schedule Class Details to be covered No. 1 Introduction to basic civil engineering 2 Introduction & various branches of civil engineering 3 Application of civil engineering to other field & role of civil engg. 4 Introduction to building planning & principles of planning. 5 Principles of planning. 6 Orientation of building & selection of site 7 Building bye laws, municipal corporation area requirement. Review Questions Q1 Describe in brief various branches of civil engg. Indicating their importance. Q2 Q3 Q4
The subject basic civil engg. Is of vital importance to all the branches of engg.” CO1 Comment on this statement. CO1 Explain role of civil engineering in various construction activities.
Q6
Explain about general scope of civil engineering in today‟s world. Define engineering. State the application of civil engineering in industrial, public and residential building. List out principles of planning and explain any 3 with figure.
Q7
What is orientation of building?
Q8
Give the I.S. recommendation for (i) size of habitable room (ii) size of W.C. (iii) height of building
Q9
What do you mean by planning? What are the objects of building planning?
Q10
Write a note on built up area.
Q11
Which are the site selection criteria for the building?
Q12
Explain how planning of residential building differs from that of an industrial building.
Q5
Unit No
CO1
2
Unit title
Components of building.
Planned Hrs.
CO1 CO1 CO1
6
69
Unit Outcomes At the end of this unit the students should be able to: UO1 Explain functions of different building components.
CO2
Lesson schedule Class Details to be covered No. 1 Types of soil and rocks 2 Concept of bearing capacity and settlement of foundation. 3 Shallow foundation, deep foundation. 4
Suitability of foundation.
5
Elements of super structure and their function. Elements of sub structure and difference between sub structure and super structure.
6
Review Questions Q1 What is foundation and what are the different types of foundation. Q2 Explain with neat sketch different elements of building.
CO2 CO2
Q3
Distinguish between i) ultimate and safe bearing capacity. ii) Sub structure and super structure iii) shallow foundation and deep foundation.
CO2
Q4
Explain load transfer action or mechanism in R.C.C framed structure.
CO2
Q5
Why does foundation settle? What are its effects on structure?
CO2
Q6
Which are the different methods of determining bearing capacity of soil? Explain any one method.
Q7
How bearing capacity of soil can be improved?
Q8
Explain with neat sketch types of settlement.
Q9
Explain the basis on which you will select foundation for a particular situation.
Unit 3 Unit Building materials and design No Title Unit Outcomes At the end of this unit the students should be able to: UO1 Explain uses, properties & types of various building materials.
Planned Hrs.
5
CO3
Lesson schedule Class Details to be covered No. 1 Types of loads, concept of strength and stability. 2 Types and grades of concrete, characteristics and advantages of brick and steel. 70
3
Factors of safety and requirements of general safety of building.
4
Properties and uses of aluminum and plastic.
5
Classification and properties of timber and roofing material.
Review Questions Q1 What do you mean by strength and stability of building? Q2 Which are the different types of loads acting on building?
CO3 CO3
Q3
Write a short note on general safety of building.
CO3
Q4
What is factor of safety?
CO3
Q5
Explain R.C.C., P.C.C., and R.M.C.
CO3
Q6
Compare merits and demerits of timber and steel as building material.
CO3
Q7
Write the uses of plastic and aluminum in building construction.
CO3
Q8
Explain the characteristics of good building stone.
CO3
Q9
How to recognize good brick?
CO3
Q10
What is mean by seasoning of timber?
CO3
Section II Linear and angular measurement
Unit 4 Unit Planned Hrs. 9 No Title Unit Outcomes At the end of this unit the students should be able to: UO1 Explain linear & angular measurements using principles of surveying. CO4 Lesson schedule Class Details to be covered No. 1 Principle of surveying & classification of surveying. 2 Chain survey & its instruments. 3
Errors in chaining, scale & R.F.
4
Ranging & offsetting.
5
Problems based on errors in chaining.
6
Compass survey.
7
Types of compass & concept of local attraction.
8
Problems based on W.C.B.
9
Problems based on R.B. 71
Review Questions Q1 Define surveying. On which objects& purposes survey work can be done? CO4 Q2 Classify surveying on the basis of instruments used. Explain the principles on surveying works. Q3 Describe errors in chaining. Q4 Two stations A & B are not intervisible due to rising ground between them. Explain with neat sketch how the line AB can be ranged. Q5 What is scale? What is R. F.? Q6
What is an offset? What are the types of offset? Instruments used for offsetting?
Q7
Distinguish between plane survey & geodetic survey.
Q8
A chain was tested & found to be exactly 20 m long, while starting to measure the length of a survey line. After measuring a distance of 1245m & was noticed that the chain had become 85mm too long. Find the correct length of survey line.
Q9
Draw neat sketch showing graduations of surveyor compass & prismatic compass.
Q10
Explain how surveyor compass differ from prismatic compass. What are the temporary adjustments of compass?
Q11
Explain the following bearing systems (i) W.C.B. (ii) Q.B.
Q12
Explain in detail meridians. What are the F.B. & B.B. of line?
Q13
The following F.B. & B.B. were observed in running a compass traverse. Draw the traverse, correct for local attraction, calculate included angles. Line F.B. B.B. AB
440 30‟
226030‟
BC
124030‟
303015‟
CD
1810
10
DA
2890 30‟
108045‟
Unit 5 Unit Planned Leveling No Title Hrs. Unit Outcomes At the end of this unit the students should be able to: UO1 Explain vertical measurements using principle of leveling & determine the area of irregular figure.
9
CO5
Lesson schedule Class Details to be covered 72
No. 1 2 3 4 5 6
Various terms used in leveling Introduction to dumpy level and its parts Uses and different adjustment of dumpy level. Types of leveling and methods of reduction level. Calculation of RL by rise and fall method. Calculation of RL by HI method..
7
Characteristics and uses of contour map
8
Introduction to EDM and total station
9
Measurement of area of irregular shape figure
Review Questions Q1 Draw neat sketch to explain various surfaces & lines associated with leveling. Q2 Explain temporary adjustments for a level. Q3
What do you mean by reduction of levels? Explain any one method in brief.
Q4
Draw a neat sketch of dumpy level and name all of its parts. Explain the function of important parts.
Q5
Define contour. What are various uses of a contour map?
Q6
Write a note on inverted staff reading.
Q7
Write a short note on characteristics of contours.
Q8
Explain the terms: 1) T.B.M. 2. R.L. 3. C.P. 4. Line of collimation 5. bubble tube
Q9
Enlist any three fundamental lines of a dumpy level and state their relation.
Q10
Distinguish between rise and fall method and HI method.
Q11
Enlist different uses of EDM
Q12
Write a note on auto level.
Q13
Write a short not on area measuring instrument.
Q14
The following staff readings were taken on a continuously sloping ground with a help of dumpy level and 4 m leveling staff at 20 m interval. The 1st reading was taken on starting point of road having R.L. 350.00m. 0.540, 1.245, 2.375, 3.885, 1.245, 2.560, 3.780, 0.875, 1.625, 2.960.
Q15
The following staff readings were observed successively with a level. 1.23, 1.900, 3.535, 2.170 and 2.135. The instrument was shifted to a new position after 3rd reading, last reading was taken on an inverted staff held at bottom of slab. First reading was taken on a BM of RL 250m. Enter the above data in level book page and complete it by HI
Axis
of
CO5
73
Q16
Unit No
method with usual check. Find the unknown things in then problem. case
area
IR
FR
N
Anchor point
1
-
3.375
8.92
+1
outside
2
25 cm2
6.19
8.23
-1
inside
6
Unit Title
Introduction to Transportation, Environmental and Irrigation Engineering
Planned Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 Explain component of water supply scheme, road & railway track.
7
CO6
Lesson schedule Class Details to be covered No. 1 Various components of pavement 2 Components of railway track. 3 Components of water supply scheme. 4 Types of dam. Review Questions Q1 Write note on classification of roads. Q2 Draw the section showing various components of road in cutting. And explain each part. Q1 Which are the components of water supply scheme? Q2
CO6
What are the types of dam?
Model Question Paper Course Title : Basic Civil Engineering. Duration3 Hrs. Instructions: 1 All Questions are compulsory. 2 Figures to the right indicate full marks. 3 4
Max. Marks 100
Use of non programmable calculator is allowed Mention any data assumed wherever necessary. 74
Section-I Marks 1
2 3
a b c d e a b A a b c d B
Attempt any four questions from following Write note on: Roominess of building Enlist various principles of planning and explain „Grouping‟ in detail. Write note on modes of transportation. Explain the byelaw which controls „height of building‟. Write note on: Instruments for measuring distances. Give classification of shallow foundation. Explain simple wall footing. Along with neat sketch explain various elements of substructure. Attempt any three questions from following Write uses of Bricks in building material. Write note on ingredients of concrete. Enlist various components of building superstructure. Which are the properties of steel? Write uses of timber in building material.
4 4 4 4 4 9 8 4 4 4 4 5
Section-II 4
a b c d
Define the terms: surveying, fore bearing Write note on W.C.B and Q.B. Explain Meridians in compass surveying. The distance between two points measured by a 20m chain was 1340m and when measured by a 30m chain was 1345m. If 30m chain was two links too short, find out whether the 20m chain was of correct length or not. If not then find the error in it. or
d The following bearings were observed in a closed traverse line AB BC CD
5
6
A a b c d B
Marks 3 3 3 7
7 DE
FB
45˚45‟
96˚55‟
29˚45‟
324˚48‟
BB
226˚10‟
277˚5‟
209˚10‟
144˚48‟
At what station do you suspect local attraction? Calculate correct bearings Attempt any three questions from following Define contour and contour interval. Enlist various types of leveling and explain any one. Draw contours for valley and hill. Explain the principle of EDM. The following readings were observed with a dumpy level and a 4 m leveling staff on a continuous falling ground.
3 3 3 3 8
i)1.780, ii)2.770, iii)3.750, iv)0.580, v)2.170, vi)2.250, vii)3.875, viii)1.310, ix)1.580, x)2.525. first reading was observed on the B.M.,R.L.132.110. Calculate the R.L. by any method. A Attempt any three questions from following 75
a Write note on rigid pavement.
4
b Write note on types of dam.
4
c Along with neat sketch show various components of railway track
4
d Draw a labeled diagram of cross section of road in cutting.
4
B Explain layout of water supply system.
5
Practical: List of experiments/assignments to meet the requirements of the syllabus Assignment Title All Batches
1. Plotting the outlines of building by chaining, ranging and offsetting. 2. Plotting of closed traverse by prismatic compass. 3. Plotting of closed traverse by surveyor's compass 4. Reduction of levels by rise and fall method. 5. Reduction of levels by collimation plane method. 6. Measurement of area by mechanical planimeter. 7. Measurement of area by digital planimeter. 8. Use of total station for various measurements. 9. Layout and setting out of small residential building. 10. Site visit to study various construction processes Report to be submitted on any under construction site
76
FE Engineering Semester I & II Engineering Graphics Engineering Graphics
Course Examination Scheme Max. Marks Contact Hours/ week Prepared by
Course Code
59180
Theory
Term Work
POE
Total
100 3
6
--
100 9
Date
08/05/2014
Ajay P.Dhawan
Prerequisites Knowledge of Steel Rule, Set-squares & Protractor. Course Outcomes At the end of the course the students should be able to: CO1 Discuss and demonstrate the importance of Engineering Graphics in Engineering & draw the different curves. CO2 Draw Horizontal line, Vertical line & solve the planes examples using rotational method. CO3 create thinking to learn methods of projections CO4 Draw FV,TV & SV of the object. CO5 Draw isometric object from FV,TV & SV CO6 Construct the objects by developing surfaces of solids and knowledge of cutting planes. Mapping of COs with POs POs COs CO1 CO2 CO3 CO4 CO5 CO6
a
b
c
d
E
f
G
√ √
h
i
j
k
l √ √
√ √ √ √
77
Course Contents Unit No.
1.
2.
3
4
5
6
Title SECTION I Unit1: Fundamentals of Engineering Graphics& Engineering Curves A) Fundamentals of Engineering Graphics: Introduction to Drawing instruments and their uses. Layout of drawing sheets, different types of lines used in drawing practice, Dimensioning system as per BIS (Theoretical treatment only) B) Engineering curves: Construction of regular polygons (up to hexagon). Construction of Ellipse, Parabola, Hyperbola, Involutes, Archimedian spiral and Cycloid only. . Unit 2: Projections of lines & Planes A) Projections of lines: Introduction to First angle and third angle methods of projection. Projections of points on regular reference planes. Projections of horizontal, frontal and Profile lines on regular and auxiliary reference planes. Projection of oblique lines it‟s True length and angle with reference planes by rotation and auxiliary plane method. Concept of grade and bearing of line, Point View of a line, Projections of intersecting lines, Parallel lines, perpendicular lines and skew line. (Use coordinate system only) B) Projections of planes: Projections on regular and on auxiliary reference planes. Types of planes (horizontal, frontal, oblique and Profile planes ). Edge view and True shape of a Plane. Angles made by the plane with Principle reference planes. Projections of plane figures inclined to both the planes. (Circle and regular polygon) (Use coordinate system UNIT 3 Projections of solids: Projections of Prisms, Pyramids, Cylinder and Cones inclined to both reference planes (Excluding frustum and sphere) SECTION II Unit 4: Orthographic Projections : Orthographic views: lines used, Selection of views, spacing of views, dimensioning and sections. Drawing required views from given pictorial views (Conversion of pictorial view into orthographic view) including sectional orthographic view Unit 5: Isometric projections Isometric projections: Introduction to isometric, Isometric scale, Isometric projections and Isometric views / drawings. Circles in isometric view. Isometric views of simple solids and objects Unit 6:Sections of solids & Development of surfaces A) Sections of solids:
No. of Hours 06
10
5
7
7
7
78
Prisms, Pyramids, Cylinders and Cones (Simple positions and inclined to one plane and parallel to other) B) Development of plane and curved surfaces: Prisms, Pyramids, Cylinders and Cones along with cutting plane Reference Books: Sr. No. 01 02
Title of Book Engineering Drawing Engineering Graphics
Author N.D. Bhatt K.Venugopal and V.Prabhu Raja
Publisher/Edition Charotar publishing House New Age International (P) Ltd
Topics All All
Scheme of Marks Section I
Unit No. 1 2 3 4 5 6
II
Title Fundamentals of Engineering Graphics& Engineering Curves Projections of lines & Planes Projections of solids Orthographic Projections Isometric projections Sections of solids & Development of surfaces
Marks 12 25 13 24 13 13
Course Unitization Sectio n
Unit
Course Outcomes
I
No 1
Title
II
2 4
CO1 Fundamentals of Engineering Graphics& Engineering Curves Projections of lines & Planes CO2 CO4 Orthographic projections
5
Isometric projections
CO5
No. of Questions in CAT-I Q1
CAT-II
Q2 & Q3 Q1 Q2
79
Unit wise Lesson Plan Section I Unit 1 Unit Title Fundamentals of Engineering Graphics& No Engineering Curves Unit Outcomes At the end of this unit the students should be able to: UO1 Learn drawing standard SP46, Give dimensioning to drawing.. UO2 Draw Ellipse, Parabola& Hyperbola UO3 Draw Cycloid,Archemidean Spiral
Planned Hrs.
06
CO1 CO1 CO1
Lesson schedule Class Details to be covered No. 1 Introduction & Draw circle, pentagon and hexagon 2 Ellipse-arc of Circle method 3 Ellipse-Concentric circle method, Oblong or rectangle method, Parabola-Rectangle & Tangent method . 4 Hyperbola-Rectangle method, Focus & Directrix method for ellipse, hyperbola ¶bola. 5 Involute., Cycloid 6 Archemedeain spiral Review Questions Q1 Two fixed points A and B are 100 mm apart. Trace the complete path of a point P moving in such a way that, the sum of its distances from A & B is always the same and equal to 130 mm. Name the curve. Draw another curve parallel to and 20mm away from this curve. Q2 A circle of 60 mm diameter rolls on a straight line without slipping. In the initial position, the diameter AB of circle is parallel to the line on which it rolls. Draw loci of the points A and B of diameter AB for one revolution of the circle.
CO1
CO1
Unit 2 Unit Title Projections of lines & Planes Planned 10 No Hrs. Unit Outcomes At the end of this unit the students should be able to: UO1 learn Frontal line ,Horizontal line, Oblique line CO2 UO2 Familiarize with the terms Grade and Bearing, Iillustrate theory of Parallel, CO2 perpendicular, intersecting & Skew lines. UO3 Learn angle made by plane with FRP and HRP CO2 Lesson schedule Class Details to be covered No. 80
7 8 9 10 11 12 13 14 15 16
1. Parallel line, Horizontal line, Frontal line,Oblique line . Problems on Oblique line Grade ,Bearing. Problems on Parallel lines, perpendicular Lines. Problems on Intersecting lines & Skew lines Planes inclined to HRP. Planes inclined to FRP. Examples of circle & semicircle. Examples of pentagonal Plate Examples of Hexagonal Plate Examples of pentagonal & Hexagonal Plate
Review Questions Q1 Draw the projection of a line AB if the grade of line is 45% at A and bearing is S600E. Top view length 60 mm .End point A is 20 mm above HRP and 20 mm in front of FRP. Q2 Find out the angle made by the plane ABC with FRP. Take A(10,10,85) B(30,45,105),C(65,30,70). Q3 The coordinates of points ABC are A(10,20,80),B(50,40,90),C(40,10,120). Find perimeter of triangle ABC Q4 A thin circular plate of 50 mm diameter is resting on point A on its rim,with the surface of the plate inclined at 450 to the HP and the diameter through A inclined at 300 to the VP.Draw the projection of the circular plate. Unit 3 Unit Title Projections of solids No Unit Outcomes At the end of this unit the students should be able to: UO1 Describe various features of cone. UO2 Differentiate between parameters of Prism & pyramid. UO3 Draw the projection of solids by rotational method
Planned Hrs.
CO2
CO2 CO2 CO2
5
CO3 CO3 CO3
Lesson schedule Class Details to be covered No. 17 Projection of cone 18 Projection of pentagonal Pyramid. 19 Projection of Hexagonal Pyramid. 20 Projection of Pentagonal & Hexagonal prism 21 Projection of cylinder Review Questions Q1 A pentagonal prism is resting on one of the corners of its base on the HP. The longer edge containing that corner is inclined at 450 to the HP. The axis of the prism makes an angle of 300 to the VP. Draw the projections of the solid. Take
CO3
81
the side of base 45 mm and height 70 mm. Q2
A hexagonal pyramid, base 25 mm side and axis 55 mm long, has of its slant CO3 edge on the ground. A plane containing that edge and axis is perpendicular to the HP and inclined at 450 to the VP .Draw its projections when the apex is nearer the VP than the base.
Unit 4 Unit Title Orthographic Projections No Unit Outcomes At the end of this unit the students should be able to: UO1 Describe First angle projection system. UO2 . Learn Third angle projection system. UO3 Draw FV, TV and LHSV, RHSV of the object UO4 Give dimensions to object
Planned Hrs.
07
CO4 CO4 CO4 CO4
Lesson schedule Class Details to be covered No. 22 First angle projection system & Third angle projection system 23 Simple objects of Orthographic. 24 Conversion of pictorial views in to orthographic views of simple objects. 25 Conversion of pictorial views in to orthographic views of simple objects. 26 conversion of pictorial views in to orthographic views 27 conversion of pictorial views in to orthographic views 28 conversion of pictorial views in to orthographic views Review Questions Q1 1. A pictorial view of a block is shown.
CO4
82
Draw the following views. a) Front View in the direction X b) Top view c) Right hand side view Unit Title Isometric projections 5
Unit No Unit Outcomes At the end of this unit the students should be able to: UO1 Read Isometric scale. UO2 Draw isometric view.
Planned Hrs.
7
CO5 CO5
Lesson schedule Class Details to be covered No. 29 Isometric views & Isometric projection. 30 31 32 33 34 35
Isometric views of simple solids and objects Isometric views of simple solids and objects Isometric views of solids and objects. Isometric views of solids and objects. Isometric views of solids and objects. Isometric views of solids and objects.
Review Questions Q1 Draw isometric drawing of the object show in its front and L.H view. Take “O” as origin.
CO5
83
Unit No
6
Unit Title
Sections of solids & Development of surfaces
Planned Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 Explain horizontal Section plane. UO2 Explain Vertical Section plane, Draw the development of the surfaces of cone, prism, cylinder &pyramid
07
CO6 CO6
Lesson schedule Class No. 36 Section of cone,Section of Pyramid. 37 38 39 40 41 42
Section of Prism, Section of cylinder. Parallel method of Development for Cylinder Parallel method of Development for prism. Radial method of development for cone. Radial method of development for Pentagonal pyramid Radial method of development for Hexagonal pyramid.
Review Questions Q1 A cone of diameter of base 50 mm and axis 60 mm long is resting on its base on CO6 H.P. A Horizontal cutting plane cuts the apex 25 mm from the top.Draw true shape & develops the remaining part of the cone. Model Question Paper Subject: Engineering Graphics Section I & II Maximum Marks: 100 Instructions: All Questions are Compulsory Section I
1
(a)
(b)
A point P moves such that its distances from two fixed points A & B which are 90 mm apart remains constant, when P is at equal distance from A & B its distance from each one is 75 mm .draw the path traced by the point P. Draw normal and tangent to the curve.
06
A circle of 50 mm diameter rolls on a straight line without slipping .In the initial position ,consider the diameter of the circle which is parallel to the line on which it rolls .Draw the path traced by the outer extreme point on the above diameter for
06
84
one revolution of the circle. Draw normal and tangent to the curve. OR (b)
Draw two convolutions of an Archimedean spiral ,given the maximum radius of 100 mm and minimum radius of 28 mm .Draw normal and tangent to the curve at a point 45 mm from the pole
06
Solve Any Three A line CD makes 70 with AB .D is on the line AB. Draw front & top view of line CD. Take A(10,10,80) B(50,45,80) C(35,55,105)
04
(b)
Complete the projections of line AB. FV length=60 mm, Bearing w.r.t A=S60E, Grade 50 % w.r.t A. Take point A 15 mm from both the planes.
04
(c)
Draw projections of line PQ (30 mm long) which is perpendicular to AB.Q is on AB. A(10,10,70) B(55,45,100) P(20,y,100)
04
(d)
Find angle with HRP & true shape of plane PQR. Take P(10,40,90) Q(25,10,115) R(60,50,80)
04
(a)
A pentagonal of 40 mm side is resting on one of its corner on the VP. The edge opposite to that corner makes an angle of 300 to the HP. The surface of the pentagon is inclined at 450 to the VP. Draw the projection of the pentagon.
13
Draw projection of a cone with base 40 mm diameter and axis 50 mm long when it is resting on VP in such a way that apex is 35 mm away from VP and towards observer. The FV axis makes angle of 400 with HP.
12
0
2
3
4
(a)
(a)
Section II 5
(a)
A pictorial view of a machine block is shown.
24
Draw the following views. (a)An elevation (FV) along the direction of an arrow F 85
(b)Sectional end view from left on the section plane X-X (c)Plan (Top view) 6
(a)
Draw isometric drawing of the object show in its front and top view. Take “O” as origin.
13
7
(a)
A cylinder of 50 mm diameter and 70 mm long is resting on H.P. It is cut by a section plane, inclined 45° to HP and passing through a point on axis which is 25 mm from top end. Draw sectional front view, top view and true shape of section & develop the lateral surface.
13
Assignments List of experiments/assignments to meet the requirements of the syllabus Assignment No. 1 Assignment Engineering Curves CO1 Title (i)Two fixed points A and B are 100 mm apart. Trace the complete path of a point Batch I P moving in such a way that, the sum of its distances from A & B is always the same and equal to 30 mm. Name the curve. Draw another curve parallel to and 20mm away from this curve. (ii) A fixed point is 60 mm from a fixed straight line. Draw the locus of a point P moving in such a way that it is equidistant from fixed point & the fixed straight line. (i)A circle of 60 mm diameter rolls on a straight line without slipping. In the Batch II initial position, the diameter AB of circle is parallel to the line on which it rolls. Draw loci of the points A and B of diameter AB for one revolution of the circle (ii) Draw a circle with diameter AB equal to 60 mm. Draw a line 140 mm long and tangent to the circle. Trace the path of A, when the line AC rolls on the circle without slipping 86
Batch III
Assignment Title Batch I
Batch II
Batch III
(i)Two straight lines OA and OB make an angle of 750 between them. P is point 40 mm from OB. Draw a hyperbola through P with OA and OB as asymptotes, making at least 10 points. (ii) Draw the curves when the distance of the the focus from the directrix is 50 mm & eccentricities are 3/2,1,2/3.Also draw tangent & normal to the curve. Assignment No. 2 Projections of Lines & Planes
CO2
(i)Find out the angle made by the plane ABC with FRP.Take A(10,10,85),B(30,45,105),C(65,30,70).Find true Shape and perimeter of ABC. (ii) Complete the projection of MN 30 mm long is perpendicular to AB.N lies on AB. Take A(10,30,50),M(25,y,65),B(50,10,60). (iii) A pentagonal plate ABCDE with 40 mm long side has its side AB on the HP and is inclined at 200 to VP. Corner D of the plate is in the VP and 45 mm above the HP. Draw the projection of the pentagonal plate. (i) A pentagonal of 40 mm side is resting on one of its corner on the VP. The edge opposite to that corner makes an angle of 300 to the HP. The surface of the pentagon is inclined at 450 to the VP. Draw the projection of the pentagon (ii) .”C” is the midpoint of the line PQ measuring 40 mm and parallel to RS. Complete the projections. R(20,20,110), S(80,50,90),C(50,20,115) (iii) Complete the projection line MN. End M is 40 mm above the HRP and 35 mm in front of FRP. Bearing w.r.t M is N450E , grade w.r.t M is 60%.TL=60 mm (i)A regular hexagonal plate ABCDEF has corner A in the VP. Diagonal AD makes an angle of 450 to the VP. The top view of the diagonal makes an angle of 600 to the HP. Draw the projection of the hexagonal plane using change of position method. (ii) Complete the projection of line PQ 30 mm long and perpendicular to AB. Q lies on AB.A(10,30,50),B(50,10,60),P(20,y,65). (iii) Complete the projection of AB.Take Point A 60 mm from both the planes. Bearing S450W w.r.t A FV makes 300 to HRP.TL=60 mm. Assignment No. 3
Assignment Title Batch I
Projection of Solids
CO3
(i)An equilateral triangular prism of side of base 25 and axis 50 long is resting on an edge of its base on HP.The face containing that edge is inclined at 300 to HP.Draw the projections of the prism ,when the edge on which the prism rests, is inclined at 600 with VP (ii)A pentagonal prism is resting on one of the corners of its base on the HP.The longer edge containing that corner is inclined at 450 to the HP.The axis of the prism makes an angle of 300 to the VP.Draw the projections of the solid. Take the side of base 45 mm and height 70 mm
87
Batch II
Batch III
Assignment Title Batch I
(i)A square pyramid, base 25 mm side and axis 55 mm long, has one of its slant edges on the ground. A plane containing that edge and the axis is perpendicular to the HP and inclined at 450 to the VP.Draw its projections when the apex is nearer the VP than the base. (ii A square pyramid of base 35 side and axis 50 long is resting on one of its triangular faces on HP with the edge of the base containing that face inclined at 450 to VP. Draw the projections of the pyramid.) (i)Draw projection of a cone with base 40 mm dia. And axis 50 mm long when it is resting on VP in such a way that apex is 35 mm away from VP and towards observer. The FV axis makes angle of 400 with HP. (ii) Draw the top view and front view of a right circular cylinder base dia. 35 mm and axis 65 mm long when it is resting on its circular rim in such a way that its axis makes an angle of 300 with HP and the top view of its axis is inclined at angle of 450 to VP. Assignment No. 4 Orthographic Projection
CO4
88
Batch II
Batch III
Assignment No. 5 Assignment Title Batch I
Isometric Projection
CO5
89
Batch II
Batch III
Assignment No. 6 Assignment Title Batch I
Batch II
Batch III
Sections of solids & Development of surfaces
CO6
(i) A hexagonal prism with side of base 30 mm and axis 70 mm long rests on comer of its base on H.P It is cut by a section plane inclined 30° to H.P. and passing through a point on axis, which is 20 mm from top end. Draw sectional true shape of section & develop the lateral surface. (i) A cone with 60 mm base diameter and 70 mm height rests with its base on ground .It is cut by auxiliary plane making 600 to HP and 10 mm away from the axis of cone .Draw the true shape of section & develop the lateral surface. (i) A hexagonal pyramid, base 25 mm side and axis 60 mm long rests on one of its side on H.P. It is cut by section plane, inclined 30° to H.P. intersects the axis at 25 mm from the apex of the pyramid, removing the apex. Draw front view, top view and true shape of section & develop the lateral surface .
90
FE Engineering Semester I Professional Communication I Course
Professional Communication - I
Examination Scheme Max. Marks Contact Hours/ week Prepared by
Theory
Term Work
1
25 2
Course Code
40901
POE
Total
--
25 3
Date
2/05/2014
Mr. B. B. Pujari
Prerequisites Basic English Grammar Course Outcomes At the end of the course the students should be able to: CO1 understand the nature and importance of communication, types, barriers and filters CO2 construct grammatically correct sentences and understand LSRW skills CO3 understand Phonetics, English sound systems, phonetic transcription, stress and intonation CO4 Learn the importance and techniques of oral communication CO5 Learn professional correspondence, its importance, language and styles Mapping of COs with POs POs COs
a
b
c
d
E
CO1 CO2 CO3 CO4 CO5
f
√
G
h
i
√ √ √ √ √
√
j
k
l
Course Contents Unit No. 1. 2. 3 4. 5..
Title Understanding Communication Grammar and Vocabulary Phonetics Developing Oral Skills Professional Correspondence
No. of Hours 02 03 03 02 04 91
Reference Books: Sr. No. 1
Title of Book
Author
Speaking Accurately
K.C. Nambiar,
Publisher/Edition Cambridge University Press New Delhi
Topics Unit 3, Unit 4
2
Communication Skills Handbook
Jane Summers, Brette Smith
Wiley India Pvt.Ltd
All units
3
Communication Skills Handbook: How to succeed in written and oral communication Handbook for Technical Writing
Jane Summers, Brette Smith
Wiley India Pvt.Ltd.
Unit 1
David A. McMurrey, Joanne Buckley,
David A. McMurrey, Joanne Buckley, Cengage
Unit 5
5
Write Right
6
English Grammar for Today
7
A Communicative Grammar of English
Syed Abdur Rahim Geoffrey Leech Palgrave Margaret Deucher Geoffrey Leech Pearson Jan Svartvik
4
Unit 1&2 Unit2 Unit2
Course Unitization Secti -on I
Unit No. 1 2 3
I
4 5
Course Outcomes Title Understanding Communication Grammar and Vocabulary Phonetics
Developing Oral Skills Professional Correspondence
No. of Questions in CAT-I CAT-II 1
understand the nature and importance of communication, types, barriers and filters construct grammatically correct 1 sentences and understand LSRW skills understand Phonetics, English sound 1 systems, phonetic transcription, stress and intonation know about the importance and techniques of oral communication know about Professional correspondence, its importance, language and styles
1 1
92
Unit wise Lesson Plan Section I Unit No Unit Title Understanding Communication Planned 1 Hrs. Unit Outcomes: To know the nature and process of communication; and various types of communication At the end of this unit the students should be able to: UO1 explain nature and importance of communication UO2 understand the process of communication UO3 Know barriers of communication UO4 know filters of communication
02
CO1 CO1 CO1 CO1
Lesson schedule Class Details to be covered No. 1 Communication : introduction, nature, importance and process 2 Types of communication: Verbal and Non-verbal Understanding barriers and filters of communication Unit No Unit Title Grammar and Vocabulary Planned 03 2 Hrs. Unit Outcomes: to study language skills-LSRW, tenses, sentence structures and various types of sentences At the end of this unit the students should be able to: UO1 CO2 know forms of tenses UO2 CO2 understand language skills-LSRW UO3
know sentence structures and different types of sentences
CO2
UO4
recognize and understand confusing word pairs
CO2
Lesson schedule Class Details to be covered No. 1 English grammar; forms of tenses 2 confused word pairs, types of sentences 3 Four language skills LSRW Unit No Unit Title Phonetics Planned 03 3 Hrs. Unit Outcomes: To understand phonetics, English sounds – vowels, consonants, diphthongs, Phonetic transcription, stress and intonation At the end of this unit the students should be able to: UO1 understand phonetics and its importance CO3 UO2 know the phonetic alphabets CO3 UO3 Understand use of stress sounds and effective use of intonation CO3 93
Lesson schedule Class Details to be covered No. 1 Understanding phonetics 2 Phonetic alphabets 3 Transcription ,stress and intonation Unit No Unit Title Professional correspondence Planned 4 Hrs. Unit Outcomes: To know about professional correspondence ; importance, language and style and various formats At the end of this unit the students should be able to UO1 know the importance of professional correspondence and language, style and formats (British and American) UO2 Letter writing - simple application letter, inquiry and replay to inquiry, placing an order , complaint and its adjustment letter and email writing
04
CO4 CO4
Lesson schedule Class Details to be covered No. 1 Know the importance of professional correspondence and language, style and formats (British and American) 2 Letter writing -simple application letter , letter of inquiry and replay to inquiry 3
placing an order, complaint and adjustment letter
4
email writing
Assignments List of experiments/assignments to meet the requirements of the syllabus: 1.Elocution 2.Vocabulary building 3.Phonetic Alphabets (Listen & repeat) 4.Pronunciation 5.Fluency Tips 6.Extempore 7.Teamwork- story making 8.Effective reading (newspaper articles) 9.Active listening (memorizing) 10.Grammar activities 11.Letter writing Activities 12.Situational conversation 94
Course Plan Course Examination Scheme Max. Marks Contact Hours/ week Prepared by
Workshop Practice-I Theory
Course Code
Term Work
POE
Total
25 2
---
25 2
S. V. Dhanal
Date
Prerequisites Fundamentals of computer and electronics
Course Outcomes At the end of the course the students should be able to: CO1 identify hardware components of a typical computer system. CO2 assemble and Disassemble the PC. CO3
handle and operate peripheral devices like printer, scanner, pen drives, CD-ROM, Multimedia Devices, UPS etc.
CO4
identify and study of communication elements like Single pair Wires (phone lines), multi-pair wires (UTP), fibre-optic cables, printer data cables, connectors. troubleshoot and Maintain PC a) POST (power on self test) b) Virus c) Power related problems.
CO5
CO7
Demonstration of multimedia features – running and handling of audio and video clips, use of CD Read / Write operations etc. To demonstrate and use of electrical and electronics hand and power tools.
CO8
To make Carpentry joints such as butt joint, dovetail
CO6
95
Mapping of COs with POs a b POs COs CO1 CO2 √ CO3 √ CO4 CO5 CO6 Course Contents Unit No.
c
d
E
F
G
H
i
j
k
l
√ √ √
Title
No. of Hours Section A
1.
2
3
A) Computers: 1. Introduction and identification of hardware components of a typical computer system. 2. Assembling and Disassembling the PC. 3. Handling and operating peripheral devices like printer, scanner, pen drives, CD-ROM, Multimedia Devices, UPS etc. 4. Identification and study of communication elements like Single pair wires (phone lines), multi-pair wires (UTP), fibre-optic cables, printer data cables, connectors- RJ-45, RJ-9, RJ-11, USB, 9-Pin and 25-Pin serial and parallel connectors; converters- serial to USB, 9-Pin to 25Pin, Vice-Versa and others. 5. Troubleshooting and Maintenance of PC a) POST (power on self test) b) Virus c) Power related problems. 6. Demonstration of multimedia features – running and handling of audio and video clips, use of CD Read / Write operations etc. B) Electronics : 1. Demonstration and use of electrical and electronics hand and power tools. 2. Measurement of resistor and capacitor, measurement of voltage and frequency using oscilloscope. 3. Assembly of Electronic components on the printed circuit board (PCB) 4. Demonstration and performance measurement of any two electronic components / devices – a. Diodes b. Transistor. c. Logic gates. C ) -1 Carpentry involving dovetail / butt joint su ch as a tray, frame etc.
96
Reference Books: Sr. No. 1
Title of Book The complete PC upgrade and maintenance guide -- BPB. Publications.
Author Mark Minasi,
Publisher/Edition Units
Unit wise Lesson Plan Section I Unit No
1
Unit Title
Planne d Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 identify hardware components of a typical computer system. UO2 assemble and Disassemble the PC.
CO1 CO2
Lesson schedule Unit No 1
Unit Title
Computers
Planne d Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 handle and operate peripheral devices like printer, scanner, pen drives, CD-ROM, Multimedia Devices, UPS etc. UO2
CO3
identify and study of communication elements like Single pair CO4 Wires (phone lines), multi-pair wires (UTP), fibre-optic cables, printer data cables, connectors.
Unit No
2
Unit Title
Computers
Planne d Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 troubleshoot and Maintain PC a) POST (power on self test) b) Virus c) Power related problems. UO2
Demonstration of multimedia features – running and handling of audio and video clips, use of CD Read / Write operations etc.
Unit
2
CO5
CO6
Electronics
97
UO1
To demonstrate and use of electrical and electronics hand and power tools.
Unit
3 Carpentry involving dovetail / butt joint
UO1
To make carpentry joints
CO7
CO8
FE Engineering Semester I & II Engineering Chemistry Course Examination Scheme Max. Marks Contact Hours/ week Prepared by
Engineering Chemistry
Course Code
59183
Theory
Term Work
POE
Total
100 3
25 2
---
125 5
Date
29/04/2014
Ms P K Damate
Prerequisites This course requires the student to know applications of the basic concepts of organic, inorganic, physical and analytical chemistry and to integrate pure chemistry principles with engineering applications. Course Outcomes At the end of the course the students should be able to: CO1 Understand water quality parameters and advanced water purification techniques. CO2 Understand basics of instrumental methods of chemical analysis and their applications. CO3 Understand the synthesis and applications of advanced materials. CO4
Understand qualities of good fuel such as calorific value and its determination.
CO5
Understand basic chemistry behind corrosion of metals and various corrosion prevention methods. Understand properties and applications of metallic materials and concepts of green chemistry.
CO6
98
Mapping of COs with POs POs COs CO1 CO2 CO3 CO4 CO5 CO6
a
b
c
d
E
f
G
√ √ √ √ √ √
√ √ √ √ √
√
√
√ √ √ √ √ √
√ √
√
√ √
√ √ √
√ √
h
√ √ √
i
j
k
l
√ √ √ √ √ √
√ √
√
√
√ √ √
√ √
√
Course Contents Unit No.
1.
2.
3.
Title Section I Unit 1: Water Introduction, impurities in natural water, water quality parameters total solids, acidity, alkalinity, chlorides, and dissolved oxygen (definition, causes, significance), hardness of water (causes, types, units of hardness), ill effects of hard water in steam generation in boilers, numerical on hardness, treatment of hard water (ion exchange and reverse osmosis). Unit 2: Instrumental methods of chemical analysis Introduction, advantages and disadvantages of instrumental methods. A) pH-metry: Introduction, pH measurement using glass electrode, applications of pHmetry. B) Spectrometry: Introduction, Laws of spectrometry (Lamberts and Beer-Lambert‟s law), Single beam spectrophotometer (schematic, working and applications). C) Chromatography: Introduction, types, gas-liquid chromatography (GLC), basic principle, Instrumentation and applications. Unit 3: Advanced materials A) Polymers: Introduction, plastics, thermosoftening and thermosetting plastics, industrially important plastics like phenol formaldehyde, urea formaldehyde and epoxy resins, conducting polymers (doping, conjugation, conductivity), examples and applications, biodegradable plastics. B) Nanomaterials: Introduction, synthesis and applications. C) Composite materials: Introduction, constituents, types of composites, advantages,
No. of Hours
7
7
7
99
4.
5.
6
composition, properties and uses of fiber reinforced plastics (FRP) and glass reinforced plastic (GRP) Section II Unit 4: Fuels Introduction, classification, calorific value, definition, units (calorie, kcal, joules, kilojoules), characteristics of good fuels, comparison between solid, liquid and gaseous fuels, types of calorific value (higher and lower), Bomb calorimeter and Boy‟s calorimeter. Numerical on Bomb and Boy‟s calorimeter. Fuel cells: Introduction, classification, advantages, limitations and applications. Unit.5: Corrosion: Introduction, causes, classification, atmospheric corrosion(oxidation corrosion), electrochemical corrosion (hydrogen evolution and oxygen absorption mechanism), factors affecting rate of corrosion. Prevention of corrosion by proper design and material selection, hot dipping (galvanizing and tinning), cathodic protection, metal spraying and electroplating. Unit 6: Metallic materials & Green Chemistry (7) A) Metallic materials: Introduction, alloy definition and classification, purposes of making alloys. Ferrous alloys: Plain carbon steels (mild, medium and high), stainless steels. Nonferrous alloys: Copper alloy (Brass), Nickel alloy (Nichrome), Aluminum alloy (Duralumin and Alnico), Tin alloy (Solder metal). B) Green Chemistry:Definition, goals of green chemistry,significance, basic components of green chemistry research, industrial applications.
7
7
7
Reference Books: Sr. No. 1
Title of Book Engineering Chemistry
Author Jain and Jain
2.
A Textbook of Engineering Chemistry A Textbook of Engineering Chemistry
S. S. Dara and S. S. Umare, S. Chand C. P. Murthy, C. V. Agarwal and A. Naidu
4.
Instrumental Methods of Chemical Analysis
Chatwal and Anand
Himalaya Publishing House, New Delhi
2
5.
Engineering Chemistry
Dr. A. K. Pahari, Dr. B. S. Chauhan
Laxmi Publications (P) Ltd, New Delhi.
3,4,5,6
3.
Publisher/Edition Topics* Dhanpat Rai 1,3,5 Publishing Company Ltd., New Delhi. Company Ltd., 1,5 New Delhi. BS Publications, 1 Hyderabad.
100
6.
A text Book of Engineering Chemistry
Shashi Chawla, Dhanpat Rai
7.
Engineering Chemistry
Renu Bapna and Renu Gupta
8.
Industrial Chemistry
B. K. Sharma
9.
Principles of Phani Kumar Nanotechnology * Indicates the unit number as per SUK syllabus.
Shashi Chawla, Dhanpat Rai & Co. (Pvt.) Ltd, Delhi. MacMillan Publishers (India) Ltd, Delhi GOEL Publishing House SciTech Publications
1,3,5
4
All 1
Scheme of Marks Section I
Unit No. Title Water 1. 2. Instrumental methods of chemical analysis 3. Advanced materials II 4. Fuels 5. Corrosion 6. Metallic materials & Green Chemistry *Marks weightage as per SUK Exam Dec.2013 question paper pattern.
Marks* 35 19 20 23 34 19
Course Unitization Sec I
No. 1.
Unit Title Water
Course Outcomes
No. of Questions in CAT-I CAT-II Prelim
To study the impurities in natural water, water quality parameters, treatment of hard water and solve numerical.
2.
Instrumen To study the basics of tal instrumental methods of methods of chemical analysis and to chemical analysis acknowledge the use of pH-
Three questions with sub questions
--
--
Three questions
Four questions with sub questions
metry, spectrometry and chromatography in various fields. 3.
Advanced materials
To understand the basic
101
concepts of formation and applications of advanced
with sub questions
material II
4.
To know and identify good
Fuels
quality fuels by using basic Four questions with sub questions
chemistry and solve numerical problem
5.
Corrosion
To learn basic chemistry behind corrosion and its various prevention methods.
6.
Metallic materials & Green Chemistry
To understand properties and applications materials
of and
metallic
--
generate
awareness of newly introduced green chemistry.
Unit wise Lesson Plan Section I Unit No
1
Unit Title
Water
Planned Hrs.
7
Unit Outcomes At the end of this unit the students should be able to: UO1 Understand water quality parameters and advanced water purification CO1 techniques. Lesson schedule: Class No. Details to be covered 1 Introduction of water as universal solvent 2 Water sources and water quality parameters. 3 Total solids and acidity of water. 4 Alkalinity and chlorides 5 Dissolved oxygen 6 Hardness of water 102
7
Numerical problems
Review Questions Q1 Write a note on impurities present in water? Q2 Explain alkalinity of water sample Q3 Discuss the experimental determination of hard water. Q4 What are the different troubles caused by the use of hard water in boilers? Q5 Discuss in short ill effects of hard water. Q6 Find out temporary, permanent and total hardness in water sample with following impurities i)Ca(HCO3)2= 81 ppm ii) MgCO3 =84 ppm iii) CaCl2=22.2 ppm iv) MaSO4 = 60 ppm v)KCl=30 ppm (Does not contribute to hardness). Unit No
2
Unit Title
Instrumental Methods of Chemical Analysis
Planned Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO2 Understand basics of instrumental methods of chemical analysis and their applications.
CO1 CO1 CO1 CO1 CO1 CO1
7 CO2
Lesson schedule: Class No. Details to be covered 1 Introduction, advantages and disadvantages of instrumental methods 2 Study of pH-metry 3 Applications of pH-metry 4 Introduction of spectrometry and study of laws of spectrometry 5 Single beam spectrophotometer 6 Introduction to chromatography 7 Instumentation and applications of GLC Review Questions Q1 Give the advantages and disadvantages of instrumental methods. Q2 Define pH. Explain the construction and working of glass electrode. Q3 State Lambert‟s law. Derive the equation for Lambert‟s law. Q4 Discuss the applications of pH-metry. Q5 Explain the working of single beam spectrophotometer and their functions. Q6 Give classification of chromatographic technique. Give principle and technique of gas liquid chromatography. Q7
CO2 CO2 CO2 CO2 CO2 CO2 CO2 CO2
Unit No
7
3
Unit Title
Advanced material
Unit Outcomes At the end of this unit the students should be able to: UO3 Understand the synthesis and applications of advanced materials.
Planned Hrs.
CO3 103
Lesson schedule Class No. Details to be covered 1 Introduction to polymer and plastic 2 Types of plastic 3 Urea-formaldehyde resin and phenol formaldehyde resin 4 Conducting polymers 5 Biodegradable polymers 6 Nanomaterials 7 Composite materials Review Questions Q1 Define polymer and monomer. Classify the polymers on the basis of structure. Q2 Distinguish between thermoplastic and thermosetting plastic. Q3 Write a note on phenol formaldehyde resin. Q4 Explain preparation. Properties and applications of urea formaldehyde resin. Q5 Discuss the biodegradable polymers. Q6 Write a note on conducting polymers. Q7 Explain the preparation, properties and uses of epoxy resin. Q8 Discuss the synthesis methods of nonmaterial Q9 Explain the properties of FRP. Discuss manufacturing methods of FRP.
CO3 CO3 CO3 CO3 CO3 CO3 CO3 CO3 CO3
Section II Unit No
UO4
4
Unit Title
Planned Hrs.
Fuel
Unit Outcomes At the end of this unit the students should be able to: Understand qualities of good fuel such as calorific value and its determination.
7
CO4
Lesson schedule Class No. 1 2 3 4 5 6 7
Q1 Q2
Details to be covered Introduction and classification of fuels Calorific value Characteristics of fuels Comparison between solid, liquid and gaseous fuels Bomb calorimeter and boys calorimeter Numerical problems Fuel cell Review Questions Define fuel. Explain characteristics of good fuel. Define calorific value of fuel. How calorific value is determined using Boy‟s calorimetric method?
CO4 CO4 104
Q3 Q4 Q5 Q6 Q7 Q8
Explain construction and working of Bomb calorimeter. How is the gross calorific value calculated? Write a note on fuel cell. Define fuel. Explain characteristics of good fuel. Define calorific value of fuel. How calorific value is determined using Boy‟s calorimetric method? Explain construction and working of Bomb calorimeter. How is the gross calorific value calculated? Following observations were recorded in a bomb calorimeter experiment. Calculate the gross and net calorific value of the fuel contains 5.7 hydrogen.
CO4 CO4 CO4 CO4 CO4 CO4
Weight of empty crucible= 3.175 gm Weight of crucible +fuel= 4.085 gm Mass of water in calorimeter = 2500 gm Water equivalent of calorimeter = 470 gm Observed rise in temperature = 2.410C Cooling correction = 0.0350C Fuse wire correction= 11.5 Cal Unit No
5
Unit Title
Corrosion
Planned Hrs.
7
Unit Outcomes At the end of this unit the students should be able to: UO5 Understand basic chemistry behind corrosion of metals and various CO5 corrosion prevention methods. Lesson schedule Class No. Details to be covered 1 Introduction of corrosion 2 Causes and classification of corrosion 3 Atmospheric corrosion 4 Electrochemical corrosion 5 Factors affecting on rate of corrosion 6 Methods of Prevention of corrosion Review Questions Q1 Q2 Q3 Q4 Q5
Define corrosion. Give classification of corrosion. CO5 Define corrosion. Explain the mechanism of hydrogen evolution in CO5 electrochemical corrosion. Define corrosion. Explain the mechanism of oxygen absorption in CO5 electrochemical corrosion. Discuss factors affecting on rate of corrosion. CO5 What is Cathodic Protection? Explain cathodic protection as a method to CO5 prevent corrosion. 105
Q6 Q7 Q8 Unit No
Explain electroplating process. Write a note on metal spraying. Explain prevention method of metal from corrosion by proper design.
CO5 CO5 CO5
6
7
Unit Title
Metallic materials and green chemistry
Planned Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO6 Understand properties and applications of metallic materials and concepts of CO6 green chemistry. Lesson schedule: Class No. Details to be covered 1 Introduction , alloy definition and classification 2 Purposes of making alloy 3 Ferrous alloys 4 Nonferrous alloys 5 Stain less steel alloy and tin alloy 6 Goals and significance of green chemistry. Review Questions Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8
Explain purposes of making alloy. Write a note on stainless steel. Write composition and uses of Nichrome. Enlist different goals of Green chemistry. Write properties and uses of Mild carbon steel. Write composition, properties and uses of brass. Write a note on Tin alloy. Write composition, properties and uses of bronze.
CO6 CO6 CO6 CO6 CO6 CO6 CO6 CO6
Model Question Paper
Course Title :
Engineering Chemistry
Duration
3 hrs. Instructions: 1. Figures right to the indicate full marks. 2. Question No 4 and Question No 8 are compulsory. 3. Attempt Any TWO remaining questions from Section I and Any TWO questions from Section II. 4. Use of non programmable calculator is allowed. Section-I
Max. Marks 100
Marks 106
1
2
a
Give principle, construction and working of single beam spectrophotometer.
b
Explain preparation, properties and applications of phenol formaldehyde plastic
5
c
Give preparation, properties and applications of GRP.
5
a
Explain ion exchange process for softening of water..
8
b
Find out temporary, permanent and total hardness in water sample with following impurities in mg/lit.
8
i)Ca(HCO3)2= 10.5 iv) CaSO4 =18.5 3
50 6
ii) MgCl2 =20.5
iii)Mg(HCO3)2=11.5
v) KCl= 9.8 (Does not contribute to hardness).
a
Give principle, construction and working of glass electrode.
6
b
Compare addition and condensation polymerization
5
c
Explain mechanical method of synthesis of nanomaterial.
5
Write a note on any four 4
a
Classification of chromatography
b
Lamberts law.
c
Alkalinity
d
Enlist different impurities present in natural water
e
Conducting polymers
f
Composite material Section-II
5
6
a
b a
Following observations were recorded in a bomb calorimeter experiment. Calculate the gross and net calorific value of the fuel contains 5.7 hydrogen. 1. Weight of empty crucible= 3.175 gm 2. Weight of crucible +fuel= 4.085 gm 3. Mass of water in calorimeter = 2500 gm 4. Water equivalent of calorimeter = 470 gm 5. Observed rise in temperature = 2.410C 6. Cooling correction = 0.0350C 7. Fuse wire correction= 11.5 Cal Define green chemistry? Give basic principles of green chemistry. Explain how you will determine calorific value of gaseous fuel by using Boy‟s gas calorimeter.
18
Marks 50 8
8 6
107
b
7
5
2 a
What is electrochemical corrosion? Discuss hydrogen evolution mechanism with example. Give composition, properties and applications of ferrous alloy Give composition, properties and applications of brass alloy.
b
Explain hot dipping in details.
5
c
What are the factors affecting on the rate of corrosion?
5 18
a
Write a note on any four Fuel cell.
b
characteristics of good fuel
c
Galvanization
d
Metal spraying
e
Oxidation corrosion
f
Duralumin &alnico
8
5 6
Assignments List of experiments/assignments to meet the requirements of the syllabus Assignment No. 1 Assignment Title Batch I
Unit: Water
20 M 1. Find out temporary, permanent and total hardness in water sample 8 with following impurities i)Ca(HCO3)2= 81 mg/lit iii) CaCl2=22.2 mg/lit v)KCl=30 mg/lit
Batch II
CO3
ii) MgCO3 =84 mg/lit iv) MaSO4 = 60pp mg/lit
(Does not contribute to hardness).
2. Write short note on Dissolved chlorides. 3. Write a note dissolved oxygen. 4. Define acidity. Explain its dermination method.
4 4 4
1. Find out temporary, permanent and total hardness in water sample with following impurities i)Ca(HCO3)2= 12 mg/lit ii) MgCO3 =10 mg/lit iii) CaCl2=16.5 mg/lit iv) MaSO 4 =8 mg/lit v)KCl=22 mg/lit (Does not contribute to hardness).
8
2. Discuss water softening treatment by ion exchange method 3. Discuss in short ill effects of hard water. 4. Explain alkalinity of water sample
4 4 4
108
Batch III
Assignment Title Batch I
Batch II
Batch III
1. The water sample analysis found to contain following impurities in mg/lit. Calculate temporary, permanent and total hardness in water sample. i)Ca(HCO3 )2= 10.5mg/lit ii) MgCO3 =11.5mg/lit Iii) CaCl2=18.5 mg/lit iv) MaSO4 =20.5mg/lit
8
2. What are the bad effects of using hard water in industrial application? 3. Write a note on acidity. 4. Enlist different impurities present in natural water Assignment No. 2
4
Unit2: Instrumental methods of chemical analysis
1. Define pH. Explain the construction and working of glass electrode 2. Give the advantages and disadvantages of instrumental methods. 3. Explain Lambert law. 4. Explain applications of pH metry 1. Explain the working of single beam spectrophotometer and their functions 2. Draw a neat and lebelled schematic represention of GLC 3. Give the advantages and disadvantages of instrumental methods 4. State Lambert-Beers law. Derive the equation for Lambert‟s law 1. Give principle and technique of gas liquid chromatography 2. Give classification of chromatographic technique. 3. Give the advantages and disadvantages of instrumental methods 4. Explain applications of GLC
4 4 CO4 20M 6 5 5 4 6 5 5 4 6 5 5 4
Assignment No. 3 Assignment Title Batch I
Batch II
Advanced Material
1. Explain preparation, properties and applications of phenol formaldehyde resin. 2. Distinguish between thermosetting and thermo softening polymers 3. Give classification of composite material. 4. Write applications of nanomaterial. 1. Explain preparation, properties and applications of urea formaldehyde resin. 2. Distinguish between thermosetting and thermo softening polymers 3. Write a note on FRP 4. Explain synthesis of nonmaterial using vapour deposition method
CO3 20 M 5 5 5 5 5 5 5 5 109
Batch III
Assignment Title Batch I
Batch II
1. Explain preparation, properties and applications of epoxy resin. 2. Distinguish between addition and condensation polymers. 3. Write a note on FRP 4. Explain synthesis of nanomaterial using mechanical method. Assignment No. 4 Unit 4: Fuels
1. Following observations were recorded in a bomb calorimeter experiment. Calculate the gross and net calorific value of the fuel contains 5.7 hydrogen. Weight of empty crucible= 3.175 gm Weight of crucible +fuel= 4.085 gm Mass of water in calorimeter = 2500 gm Water equivalent of calorimeter = 470 gm Observed rise in temperature = 2.410C Cooling correction = 0.0350C Fuse wire correction= 11.5 Cal 2. Define fuel. Explain characteristics of good fuel. 3. Write a note on fuel cell. 1. Following observations were recorded in a bomb calorimeter experiment. Calculate the gross and net calorific value of the fuel contains 6 %hydrogen.
5 5 5 5 CO4 20 M 8
6 6 8
Weight of empty crucible= 2.175 gm Weight of crucible +fuel= 3.085 gm Mass of water in calorimeter =1500 gm Water equivalent of calorimeter = 370 gm Observed rise in temperature = 1.410C Cooling correction = 0.0200C Fuse wire correction= 10.5 Cal 2. Explain how you will determine calorific value of gaseous fuel by using Boy‟s gas calorimeter. 3. Enlist different characteristics of good fuel
6 6
110
Batch III
1. Following observations were recorded in a bomb calorimeter experiment. Calculate the gross and net calorific value of the fuel contains 6 %hydrogen. Weight of empty crucible= 2.175 gm Weight of crucible +fuel= 3.085 gm Mass of water in calorimeter =1500 gm Water equivalent of calorimeter = 370 gm Observed rise in temperature = 1.410C Cooling correction = 0.0200C 2.Fuse wire correction= 10.5 Cal 3. Explain how you will determine calorific value of gaseous fuel by using Bomb calorimeter. 4.How fuel cells are classified? Assignment No. 5 Unit 5: Corrosion
Assignment Title Batch I
Batch II
Batch III
1. Define corrosion. Give classification of corrosion. 2. Define corrosion. Explain the mechanism of hydrogen evolution in electrochemical corrosion. 3. Define corrosion. Explain the mechanism of oxygen absorption in electrochemical corrosion. 1. Discuss factors affecting on rate of corrosion. 2. What is Cathodic Protection? Explain cathodic protection as a method to prevent corrosion. 3. Explain electroplating process 1. Write a note on metal spraying. 2. Explain prevention method of metal from corrosion by proper design 3. What are the different factors affecting on corrosion Assignment No. 6
Assignment Title Batch I
Batch II
Unit 6: Metallic materials and green chemistry
1. 2. 3. 4. 1. 2. 3. 4.
Explain purposes of making alloy. Write a note on stainless steel. Write composition and uses of Nichrome. Enlist different goals of Green chemistry. Write properties and uses of Mild carbon steel. Write composition, properties and uses of brass. Write a note on Tin alloy. Write composition, properties and uses of ferrous alloy.
8
6 6
CO5 20M 6 7 7 7 7 6 7 7 6 CO6 20 M 5 5 5 5 5 5 5 5 111
Batch III
1. Explain purposes of making alloy 1. Write compostion and uses of Alnico and Duralumin 2. Enlist different goals of Green chemistry 3. Write properties and uses of Medium carbon steel.
5 5 5 5
List of Experiments: Sr.No. 1. 2. 3. 4. 5. 6. 7. 8. 9.
Name of the experiment Determination of acidity of water Determination of alkalinity of water Determination of chloride content of water by Mohr‟s method Determination of total hardness of water by EDTA method. Preparation of phenol formaldehyde resin Preparation of urea formaldehyde resin Determination of copper in brass Demonstration of pH meter Demonstration of photo-colorimeter/ spectrophotometer
CO CO1 CO1 CO1 CO1 CO3 CO3 CO6 CO2 CO2
List of additional experiments Assignment No. 1 Experiment Title Unit 5: Corrosion CO5 Batch I 1. Determination of rate of corrosion of aluminum in acidic and basic medium Batch II 2. Determination of rate of corrosion of aluminum in acidic and basic medium Batch III 3. Determination of rate of corrosion of aluminum in acidic and basic medium List of open ended experiments/assignments Assignment No. 1 Assignment Title CO 1. Spectrophometric dermination of iron in vitamin tablet Batch I CO2 2. Demonstration of paper chromatography using plant extract. 1. Demonstration of paper chromatography using plant Batch II CO2 extract. 2. Water samples from five different sources, eg. Well, Hand CO1 Pump, Water Supply, etc. from neighborhood to be collected by each group of two students and following tests to be conducted: Qualitative Analysis (with the help of field test kits available) or the following: Total Solid dissolved Chlorine Fluorine Iron 112
Batch III
Nitrite Sulphide/Sulphate 1. Water samples from five different sources, eg. Well, Hand Pump, Water Supply, etc. from neighborhood to be collected by each group of two students and following tests to be conducted: Qualitative Analysis (with the help of field test kits available) or the following: Total Solid dissolved Chlorine Fluorine Iron Nitrite Sulphide/Sulphate 2. Demonstration of paper chromatography using plant extract.
CO1
CO2
FE Engineering Semester I & II Fundamental of Electronics & Computer Programming Course Examination Scheme Max. Marks Contact Hours/ week Prepared by Prerequisites
E&TC
Course Code
Theory
Term Work
OE
Total
50
25
--
75
2
2
--
4
Date
02/05/2014
Mr. R.S.Vathare
Basic knowledge of Electricity, fundamental concepts regarding physics, Analytical perspective regarding applications where electronics is used.
Course Outcomes At the end of the course the students should be able to: Students will be able & identify & use basic components in electronics CO1 engineering. Describe the characteristics of p-n junction diode devices and its use for a given CO2 application Able to design the digital logic circuits using logic gates &flip flops. CO3 Student will be able to understand the concept & working of different types of CO4 transducers. Able to identify & describe the working of electronics appliances used for daily CO5 needs. 113
Mapping of COs with POs POs COs
CO1 CO2 CO3 CO4 CO5
a
b
√ √
√
√ √
c
d
E
f
g
i
j
√
k
l
√
√ √ √
h √
√
√ √
√ √
√
√ √
Course Contents Unit No.
No. of Hours
Title
Section I Semiconductor Devices and Applications: Half Wave & Full Wave rectifiers. BJT characteristics, load line, operating point, leakage currents, saturation and cutoff mode of 1. operations, Need for stabilization, fixed bias, emitter bias, self bias, bias stability with respect to variation in ICO, VBE& β, Stabilization factors, thermal stability, RC coupled CE amplifier, Regulated power supply. Digital Electronics: Logic Gates- Basic gate, Universal gates. Boolean algebra. 2. Logic Families, Sequential logic, half adder, full adder, multiplexer, demultiplexer, Combinational logic, Flip-flops(JK Flip-flop) Applications: Transducers: for Displacement, level, temperature, pressure, Speed measurements, Range Specifications Limitations 3. Appliances: Block Diagram, Specifications, Operation and use of the appliances: Digital Thermometer, Digital Watch, Weighing machine, Microwave oven and Mobile handset Text/Reference Books: Sr.No. 1 2 3 4 5
Title of Book A Text of Applied Electronics Basic Electronics Engineering Principle of Electronics Digital Principles & Applications Electronic Instrumentation
Author
Publisher/Edition
R. S. Sedha
S. Chand
Vijay Baru, RajendraKaduskar, S T Gaikwad V.K.Mehta Albert Malvino, Donald Leach H.S.Kalsi
Wiley/DREAMTECH S. Chand
7 Hrs
6 Hrs
7 Hrs
Topics U1,U3 U1 U1,U2,U3
TMGH Publications
U2
TMGH Publications
U3
114
Scheme of Marks Section I
Unit No. 1 2 3
Title Semiconductor Devices and Applications Digital Electronics Applications
Marks 16 16 18
Course Unitization Course Outcomes
Unit
Section No. 1 I
2 3
Title Semiconductor Devices and Applications Digital Electronics Applications
No. of Questions in CAT-I
CO1,CO2
02
CO3,CO4 CO5
01
CAT-II
01 02
Unit wise Lesson Plan Section I Unit No
1
Unit Title
Semiconductor Devices and Applications
Planned Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 Understand basics of electronics components and circuits. UO2 Identify characteristics of electronics devises, Need for stabilization
07
CO1 CO2
Lesson schedule Class Details to be covered No. 1 Introduction, Half Wave & Full Wave rectifiers. 2 BJT characteristics, load line, operating point, 3 Leakage currents, saturation and cutoff mode of operations, 4 Need for stabilization, fixed bias, emitter bias, self bias, 5 Bias stability with respect to variation in I CO, VBE& β, Stabilization factors, 6 Thermal stability, RC coupled CE amplifier, 7 Regulated power supply. Review Questions Q1 Explain in detail Half Wave & Full Wave rectifiers Draw and Explain BJT characteristics, load line, operating point, leakage Q2 currents. Q3 Explain modes of operation of BJT. Q4 Why Need for stabilization is required and bias stability with respect to
CO1 CO1 CO1 CO2 115
Q5 Q6
variation in ICO, VBE& β, Stabilization factors, With neat circuit diagram explain fixed bias, emitter bias &self bias circuit Draw and explain RC coupled CE amplifier
Unit No
2
Unit Title
Digital Electronics
Planned Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 Understand basics of combinational and sequential logic UO2 Identify logic families of IC‟s UO3 Analyze and use logic gates
Unit Title
Applications
Unit Outcomes At the end of this unit the students should be able to: UO1 Understand basic applications of transducers and appliances UO2 Analyze and use different types of transducers for measurements
06
CO3 CO3 CO3
Lesson schedule Class Details to be covered No. 1 Logic Gates- Basic gate, Universal gates. 2 Introduction of Boolean algebra. 3 Logic Families, Sequential logic. 4 Half adder and full adder 5 Multiplexer and de-multiplexer, 6 Combinational logic, Introduction to flip-flops 7 JK Flip-flop Review Questions Q1 Explain all Logic Gates- Basic gate, Universal gates. Q2 Write a note on Boolean algebra. Q3 With the help of truth table explain half adder and full adder. Q4 Explain 8:1 multiplexer in detail. Q5 Draw and explain 1:4 de-multiplexer. Q6 Explain in detail JK flip-flop. Unit No 3
CO2 CO2
CO3 CO3 CO3 CO3 CO3 CO3 Planned Hrs.
07
CO4 CO5
Lesson schedule Class Details to be covered No. 1 Introduction of TransducersRange Specifications Limitations 2 Transducers for Displacement measurement, level measurement 3 Transducers for temperature, pressure, Speed measurements Introduction to Appliances: Block Diagram, Specifications, Operation and use of the 4 appliances. 116
5 6 7
Digital Thermometer, Digital Watch. Block Diagram, Specifications, Operation and use of Weighing machine. Microwave oven and Mobile handset.
Review Questions Explain Displacement measurement Transducers and its Range, Specifications, Limitations Write a note on level measurement Write a note on temperature, pressure, Speed measurements With the help of block Diagram, Specifications, Operation of the appliances: a) Digital Thermometer b) Digital Watch c) Weighing machine d) Microwave oven e) Mobile handset
Q1 Q2 Q3
Q4
CO4 CO4 CO4
CO5
Model Question Paper
Course Title : Duration:
Fundamentals of Electronics 90 minutes
Max. Marks50
Instructions: 1) All questions are compulsory for section-I 2) Figures to the right indicate full marks. 3) Assume suitable data if necessary Section-I
B
Solve any two Explain full wave rectifier with centre tap transformer with necessary waveforms Explain all gates with its truth table
C
With help of neat block diagramexplain in detail mobile handset
1 A
8 8
Solve any two
8 16
A
Explain BJT characteristics in detail
8
B
Explain in detail JK flip flop
8
C
Explain in detail microwave oven
2
3
Marks 16
Solve any three
8 18
117
A
Explain 8:1 multiplexer with truth table
B
With help of neat circuit diagram explain regulated power supply
C
Explain half adder in detail.
d
With help of neat block diagram explain digital thermometer
e
Explain fixed bias circuit for biasing transistor.
6 6 6 6 6
Assignments List of experiments/assignments to meet the requirements of the syllabus Assignment CO1,CO2,CO3 Title 1. With help of neat circuit diagram explain regulated power supply Batch I 2. Explain fixed bias circuit for biasing transistor. 3. Differentiate between Combinational & Sequential circuits? 4. What do you mean basic gates & derived gates? Explain with the help of examples? 5. What are the methods used for measurement of pressure? Explain any one in detail? 6. What do you mean by transducer? Explain any one displacement transducer in detail? 1. Explain BJT characteristics in detail. Batch II 2. Show that it is possible to derive all the gates from basic gates. 3. What do you mean by Boolean algebra? Explain all the laws of Boolean algebra? 4. Explain the construction & working of digital thermometer? 5. What do you mean by transducer? Explain the construction & working of LVDT in detail? 6. Explain the construction & working of digital watch? 1. Briefly explain the different types of logic families? Batch III 2. Explain with the help of truth table working of a) Full adder b) Clocked RS latch c) 1:4 demultiplxer d) 4:1 multiplxer 3. Explain with the help of neat diagram & truth table working of positive edge triggered JK flip flop 4. Explain the method of level measurement? 5. Explain the construction & working of Washing machine in brief? 6. Explain the method of speed measurement using tachometer? List of experiments Any five experiments out of eight Exp. No. 1 Testing of Electronics components-resistors, capacitors, inductors, diode, 118
transistor, LED and switches using multimeter& CRO. VI characteristics of PN junction diode and zener diode. Study of Half wave & Full wave rectifier and their comparison. Study of Frequency response of CE amplifier Study of truth tables of logic gates: OR, AND, NOT, NAND, NOR, EXOR Measurement of Distance using LVDT/Strain Gauge. Measurement of Temperature using any transducer. Study of Mobile Handset. Computer Programming (Section II)
Exp. No.2 Exp. No. 3 Exp. No. 4 Exp. No. 5 Exp. No. 6 Exp. No. 7 Exp. No. 8
Course
Computer Programming
Examination Scheme Max. Marks Contact Hours/ week Prepared by
Course Code
Theory
Term Work
POE
Total
100 4
25 2
----
125 6
Date
29 April 2014
Ms. Sujata A. Pardeshi & Ms. Pooja Akulwar
Prerequisites This course requires the student to know about the basics of computer hardware and software, how to use computer.
Course Outcomes At the end of the course the students should be able to: CO1 To Acquire the essential knowledge of computer systems and peripherals CO2 CO3
To understand the Data representation & Number System
CO4
To gain knowledge of Unix /Linux Commands
CO5
To acquire usages of application software and their uses
CO6
To understand the use of computer networks and internet
CO7
Acquire the essential knowledge of programming techniques and their usage algorithms, flowcharts, and control structures
To know operating system features and system software‟s
–
Mapping of COs with POs POs
a
b
c
d
E
f
G
h
i
j
k
l
COs
CO1 CO2 CO3 CO4 CO5 CO6 CO7
√ √
√ √ √
√
√ √ √
√
√ √
119
Course Contents Unit No.
4.
5
6
Title
No. of Hours
Section II Computer Basics: Generation and classification of computers, Computer system component – CPU, Input Unit, Output Unit, Storage Unit, Applications of Computers Computer Architecture : Details of components of digital computer system – CPU, Communication among the various units, Instruction format, cycle Inside the Computer : Study of System cabin, SMPS, Motherboard, Ports and Interfaces, Expansion Cards, Memory Chips, storage devices Data Representation in Computer: Types of number system, Binary, Octal, Hexadecimal and their conversion, Types of coding schemes – ASCII & Unicode Computer Software : Operating system – types Operating system , functions , Unix /Linux , Windows 7 – Structures and Features System Software – Interpreter , Assembler, Compiler Application Software – Word Processor, Spreadsheets, Presentations , DBMS Unix and Linux commands – Ls, CAT, CD, MKDIR, RMDIR and Other command, & use of any editor in Linux Computer Programming and Languages: Program Development Cycle, Algorithm, Flowcharts, Programming Control Structures – sequence, selection, repetition programming languages – Introduction to low level and high level PL Introduction to Computer Networks – Definition and needs of computer network, standards – OSI, TCP/IP, Types of Networks – LAN, WAN, MAN, Type of network topologies , Internet (WWW), emerging computing environment
9 HRS
10 HRS
10 HRS
Reference Books: Sr. No. 01 02 03 04
Title of Book Introduction to Information Technology, Fundamentals of Computers UNIX concepts and applications
Author ITL, Education Solutions LTD, V. Rajaram SunitaBha Das,
Computer Fundamentals B. Ram Architecture and Organization
Publisher/Edition Pearson Education
Topics ALL
PHI Publications TMGH
Unit No. 1 Unit No. 5.3
New Age International Unit No. 4.2 Publishers 120
Scheme of Marks Section II
Unit No. 4.1
4.2 4.3 5.1 5.2
5.3 6.1
6.2
Title Generation and classification of computers, Computer system component – CPU, Input Unit, Output Unit, Storage Unit, Applications of Computers Details of components of digital computer system – CPU, Communication among the various units, Instruction format, cycle Study of System cabin, SMPS, Motherboard, Ports and Interfaces, Expansion Cards, Memory Chips, storage devices Types of number system, Binary, Octal, Hexadecimal and their conversion, Types of coding schemes – ASCII & Unicode Operating system – types Operating system , functions , Unix /Linux , Windows 7 – Structures and Features System Software – Interpreter , Assembler, Compiler Application Software – Word Processor, Spreadsheets, Presentations , DBMS Unix and Linux commands – Ls, CAT, CD, MKDIR, RMDIR and Other command, & use of any editor in Linux Definition and needs of computer network, standards – OSI, TCP/IP, Types of Networks – LAN, WAN, MAN, Type of network topologies , Internet (WWW), emerging computing environment Program Development Cycle, Algorithm, Flowcharts, Programming Control Structures – sequence, selection, repetition programming languages – Introduction to low level and high level PL
Marks 8
8 8 8 8
8 9
9
Course Unitization Section
Unit No.
II
Title
Course No. of Questions in Outcomes CAT-I CAT-II
4.1 4.2 4.3
Computer Basics Computer Architecture Inside a computer system
CO1 CO1 CO1
5.1
Data Representation in Computer
CO2
5.2
Computer Software –Types and Functions, System Software
CO3
Application Software‟s Unix and Linux commands Introduction to Computer Networks Computer Programming and Languages
CO5 CO4 C06 CO7
5.3 6.1 6.2
2 questions with mixing of subquestions from Unit No.4
-
2 questions with mixing of sub-questions from Unit No.5 & Unit No. 6.1
121
Unit wise Lesson Plan Unit No 01
Unit Title
Section I Computer Basics, Architecture & Inside the Computers
Planned Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 To Acquire the essential knowledge of computer systems and peripherals UO2 To understand the architecture of computer UO3 To get about the inside components of computers
7
CO1
Lesson schedule Class Details to be covered No. 1 Computer basics - H/W and S/W unit, characteristics of computers 2,3 Generation of Computers - Study of each generation of computers with its characteristics and limitations 4 4. Classification of Computers - study of Minicomputers, Micro Computers 5 Mainframe and super computers with comparison of their characteristics and advantages 6 Expose to Applications of Computers 7 Central Processing Unit, Registers, Control Unit 8 System Bus and its use, Cache Memory and Its Types 9 The Communication way from Processor to memory and Processor to I/O devices Communication, Instruction format and Instruction Cycle 10 Inside the computer - System cabin, SMPS, Motherboard 11 Ports and Interfaces, Expansion Cards, Memory Chips, storage devices Review Questions Q1 Write a short note on characteristics & Applications of computer CO1 Q2 Explain generations of the computers CO1 Q3 Write down Classification of computers CO1 Q4 State the difference between the first and third generation of computers CO1 Q5 Explain the Central Processing unit of the Computer CO1 Q6 Explain System Bus and its use, Cache Memory and Its Types CO1 Q7 Explain Communication from Processor to memory and Processor to I/O CO1 devices Communication, Instruction format and Instruction Cycle Q8 write a short note on DMA / direct memory access unit CO1 Q9 Explain Instruction Cycle & describe the various steps involved CO1 Q10 What are expansion cards? How many types of expansion cards used in a CO1 computer system Unit 02 Unit Title Data Representation in Computer, Computer Software No Unit Outcomes At the end of this unit the students should be able to:
Planned 8 Hrs.
122
UO1 UO2
To understand the Data representation & Number System To know operating system features and system software‟s
CO2 CO3
UO3
To gain knowledge of Unix /Linux Commands
CO4
U04
To acquire usages of application software and their uses
CO5
Lesson schedule Class Details to be covered No. 12 The basics of number system, types of number system, Conversion from Decimal to binary, octal and hexadecimal 13 The conversion from Binary number system to decimal, octal and hexadecimal number system 14 The conversion of fraction decimal to other number systems and vice versa and coding schemes 15 The conversion of Octal number system to Decimal, Hexadecimal, Binary number system & conversion for fractional numbers 16 The conversion of Hexadecimal number system to Decimal, Binary, Octal number systems and understanding of the Coding schemes 17 Computer Software‟s and their types, study of Operating System software‟s ,types, functions and features 18 System software‟s - Assembler, Interpreter, compiler, 19 Understanding the usages of applications software - word processor, spreadsheet, presentation and DBMS 20 The structure & features of Unix/Linux and Windows 7.0 operating system 21 Unix and Linux Commands Review Questions Convert following binary numbers into decimal numbers: 1010, 1101, 11011011 Q1 CO2 Write down the steps to convert the binary number to equivalent hexadecimal Q2 CO2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15
with example Write down the steps to convert the Octal number to equivalent hexadecimal with example Find out octal equivalent of (6A)16 , (123)10, (1010)2 State difference between system software and application software’s with example Explain the spreadsheet application and their usage and DBMS applications Write a short note on application software’s Explain system software’s and explains assembler, interpreter and compiler Write a short note system software’s Explain the word processor its application Explain the presentation application software and its usage Explain following Linux/Unix commands -MKDIR, CAT, CD, LS Write a short note on Unix Operating system and its features List out and explain the types of operating system
List out and explain the features of operating system
CO2 CO2 CO3 CO5 CO5 CO3 CO3 CO5 CO5 CO4 CO4 CO3 CO3 123
Unit No 03
Unit Title
Computer Programming & Languages, Introduction to Computer Networks
Planned Hrs.
7
Unit Outcomes At the end of this unit the students should be able to: UO1 CO6 Demonstrate use of computer networks and internet UO2 Acquire the essential knowledge of programming techniques and their usage CO7 – algorithms, flowcharts, and control structures Lesson schedule Class Details to be covered No. 22 To understand the Computer Network - definition, function, and need, the types of networks with its features 23 Types of networks topology 24 OSI model and TCP/IP Model 25 The computer language and comparative study of types of languages, program development life cycle 26 Learning of algorithms and flowcharts and their usages 27 Writing algorithm and drawing flowcharts for simple programs 28 Control structures - conditional control structure - if, if...else and nested if else, and writing algorithms and flowcharts for conditional programs 29 Learning of loop control structures - writing algorithm and flowcharts loop based programs Review Questions Q1 Explain the types of network operating system Q2 Write a short note on Explain LAN, WAN and MAN Q3 Define the computer networks and explain needs Q4 Define the computer networks and explain its types Q5 Explain TCP/IP Model Q6 Explain OSI model Q7 Define the computer networks and explain the topologies of computer network Q8 Define the algorithms and list out the characteristics of algorithms Q9 Explain program development cycle Q10 State the difference between low level and high level programming language Q11 Write down the algorithm and flowcharts for following programming statement – Accept the roll no and marks for subjects and display the total and percentage. If percentage is less than 40 display fail, if percentage >40 and 0, b > 0 Define error function and verify all properties 5
Unit Title
Curve Tracing
Planned Hrs.
08 167
Unit Outcomes At the end of this unit the students should be able to: UO1 Trace y=f(x) in Cartesian plane UO2 Trace r=f( ) in polar plane UO3 Convert Cartesian to polar by standard transformation. UO4 Trace rose curve UO5 Find arc length of plane Cartesian and polar curve
CO5
Lesson schedule Class Details to be covered No. 1 Procedure to trace Cartesian curve 2 Tracing of Semi cubical parabola, Cissiod of Diocles, Strophoid, Astroid, Witch of Agnesi 3 Tracing of Common Catenary, Folium of Descartes 4 Tracing of Cardioid, Pascal‟s Limacon, Lemniscate of Bernoulli 5 Tracing of Parabola, Hyperbola, Rose curves 6 Rectification of plane Cartesian form 7 Rectification of plane polar curve 8 Examples Review Questions 2 Q1 Trace 3ay
x
2
a
Q2
Trace y
Q3 Q4 Q5 Q6 Q7
Trace y 2 a x x 2 2a x Trace r = a(1+cosѲ) Trace r 3 2cos Trace r a sin 2
Q8 Q9
2
a
x
UO1
x x
3
UO2
Find the total length of the curve r a sin 3 Find the length of loop of the curve y 2
UO4 UO5 3
x 1
Find the perimeter of cardioide r a 1 cos
x 3
2
and show that the line
2 3
divides upper half of cardioide into two parts. Unit 6 Unit Title Multiple Integration and its applications Planned No Hrs. Unit Outcomes At the end of this unit the students should be able to: UO1 Define the double integral over a general region with its two types. UO2 Evaluate a double integral over a rectangular region.
10
CO6, CO5 168
UO3 UO4 UO5 UO6 UO7 UO8
Find limits of double integration. Reverse the order of integration. Find the area using double integral. Find the mass for a thin plate covering a region R. Find the moments of inertia for a thin plate in the xy-plane. Evaluate integral using Polar Coordinates.
Lesson schedule Class Details to be covered No. 1 Definition of double integration 2 Evaluation of Double Integration 3 Change of order of integration 4 Double integration in polar form 5 Change into polar form 6 Area by double integration 7 Mass of Plane Lamina 8 Center of gravity of Plane Lamina 9 M.I. of Plane Lamina 10 Examples Review Questions Q1 Evaluate
a 0
Q2
UO2
a2 y2
a
2
x
2
2
y dxdy
0
UO8
2 a 1 sin
r 2 cos drdr
Evaluate 0
0
Q3
a
ay
Change the order of integration and evaluate 0
Q4
44
y
x x2
16 y 2
Change to polar co-ordinates and evaluate 0
Q5
Find the area enclosed by between the parabolas y 2 y2
Q6 Q7
y
y2
UO3 UO4
dxdy 1
16 x 2
y2
2
dxdy
4 x 1 and
UO3 UO8 UO5
2 x 2
Find the mass of the lamina bounded by the curve y 2 x 3 and the line y x . If the density at a point varies as the distance of the point from X-axis. Find the M.I. of the semi-circle about the line joining one end of the bounding diameter to the midpoint of the arc.
UO6 UO7
169
Model Question Paper
Course Title :
Engineering Mathematics II
Duration
3 Hours
Max. Marks 100
Instructions: All questions are compulsory Figures to the right indicates full marks Use of non-programmable calculator is allowed Section-I 1
Attempt any three 2x a Solve (sin x.cos y e ) dx b c d
2
Solve Solve
ydx xdy dy dx
e
Solve cos2 x
tan y dy
5
2 1 x2
x y
ex
dy dx
y
5
ey
5
tan x
Attempt any three a Find orthogonal trajectory for the curve r 2 a2 cos2 b A voltage Ee at is applied at t=0 to a circuit containing inductance L and resistance R. Show that the current at any time t is E e R aL
c
d
at
e
15 5 5
Rt L
According to Newton‟s law of cooling, the rate at which a substance cools in moving air is proportional to the difference between the temperature of the substance that of the air. If the temperature of the air is 300C and the substance from 1000C to 700C in 15 minutes, find when the temperature will be 400C. Uranium disintegrates at rate proportional to the amount present at any instant. If M1 and M2 grams of uranium are present at a time T 1 and T2 respectively, show that the half life of uranium is
3
0
dx
2
( x y)
cos x.sin y
Marks 15 5
dy dx
x2
5
T2 T1 log 2 M log 1 M2
Attempt any three Using Taylor‟s series method, Obtain correct upto four decimal places, a a solution of the differential equation
5
15 5
y 2 with y=o when x=0
at x=0.4 170
b
dy dx
Given that
x
y 2 and y=1 at x=0. Find an approximate value of y
5
at x=0.5 using Euler‟s method. c
d
Use Euler‟s modified method to solve
y 2 , y (0) 1 . Find y(0.4)
x
taking h=0.2 Use Runge kutta fourth order method to solve (x
e
dy dx
5
5
dy y) 1, y(0) 1 for x 1 dx
Solve Numerically by RK method
dy dx
yz
x;
dz dx
xz
y given that
5
1 for y(0.2), z(o.2)
y(0) 1; z(o)
Section-II 4
Attempt any three a Evaluate e b
h2 x 2
/2
Evaluate
4
Marks 15 5
dx
tan
e
tan
5
sec2 d
0
c
5
x sin 5 x cos 2 x dx
Evaluate 0
d
5
Prove that
cos x e ax x 0
a > 0, b > 0 Attempt any three 3 3 a Trace x y b c d
e bx dx
1 b2 log 2 2 a
2 2
; a, b 0 ;
15 5
3axy
Trace
1 1 cos r
Trace
r
5
a cos 4
For the curve y 2
5
x 1
x 3
2
prove that s 2
y2
4 2 x , where s being 3
5 5
measured from origin to (x, y). 6
Attempt any three 2 a Evaluate 1
b
15 5
2 y
2 x 2 y 2 dxdy 2 y a 2a x
Change the order of integration and evaluate
xy dxdy 0 x2
5
a
171
c
dxdy
Change to polar coordinates and evaluate
1 x2
R
of the lemniscates x 2 d e
y
2 2
x2
y
2 2
over one loop
5
y2
Find the mass of the lamina of the region included between the curves y = log x, y = 0 , x = 2, having uniform density. Find area of the ellipse by using double integration
5 5
Assignments List of experiments/assignments to meet the requirements of the syllabus Assignment No. 1 Assignment Differential equation of 1st order & 1st degree Title Solve the following differential equations Batch I 1. (sin x.cos y
e2 x )dx
2.
2x
y 1 dx
3.
x2
y 2 a 2 xdx
4.
a2
2 xy
5.
x 2e y dy
6.
y 1 1
7.
8.
dy dx
9. (e
x
10. 2 xy
x
x 1 dy
x2
0
y 2 b2 ydy 0
y dy 0
x log x x sin y dy
0
x
dx
y )2
2 1 x2
2 xy 2
y3 )dx
11. xe (dx
0
2
x
cos y dx
y 2 y log y y
2
tan y dy
y x sin x dx 0
ydx xdy (x
2y
y 2 dx
x
cos x.sin y
CO1
y dx
ay
2 x 2 y 3xy 2 dy 0
xdy 0
dy ) e x dx
y ye dy
0
172
dy dx
y
x y
ex
12. x x 1
13.
dy dx
e
x2 y 2
14. 3 x 1
2 dy 15. cos x Batch II
ey
dy dx
y
dx
x 2 ( x 1)2
(2 x 2 1) y 3
ax3
tan x
Solve the following differential equations
dy dx
1.
2 y 3e x
2. y(1
xy)dx x(1 xy
y )dx x
(3x 2 y 3.
a2
4.
dx 5. dy dy 6. dx
x
x 3 log x dy 0
y 2 dx
2 xy
x 2 y 2 )dy 0
x
2
y dy 0
y 1
tan y 1 x
(1 x)e x sec y 1
dy 2 x 3 y x 4e x y 3 7. dx ydx xdy dx ( x y )2 2 1 x2 8. 9.
(5 x 4
10. dx
11.
3x 2 y 2
2 xy 3 )dx
2 x3 y 3x 2 y 2 5 y 4 dy 0
xdy e y sec2 y dy
dy dx
y log y x
y (log y ) 2 x2 173
12. x x 1
13.
dy dx
dy dx x y
e
x 2 ( x 1)2
y
ey
ex
3x 1 x 2 y 2 14.
dy dx
(2 x 2 1) y 3
2 2 15. (1 2 xy cos x 2 xy)dx (sin x
16. Batch III
dy dx
ax3
x 2 )dy
0
1 y 2 3x 2 y 1 2 xy x3
Solve the following differential equations 1.
2. 3. 4.
dy dx
2 y 3e x
y(1 xy)dx x(1 xy
a2
2 xy
dy dx
tan y 1 x
y 2 dx
6.
(x
dy 7. dx
2 1 x2
3x 2 y 2
2 xy 3 )dx
y log y x
y (log y ) 2 x2
x x 1 8.
dy 9. dx
dx
y )2
(5 x 4
e
dy dx x y
y ex
3x 1 x 2 y 2 10.
2
y dy 0
(1 x)e x sec y
ydx xdy 5.
x
x 2 y 2 )dy 0
dy dx
2 x3 y 3x 2 y 2 5 y 4 dy 0
x 2 ( x 1)2 ey (2 x 2 1) y 3
ax3
174
2 2 11. (1 2 xy cos x 2 xy)dx (sin x
12.
dy dx
x 2 )dy
0
1 y 2 3x 2 y 1 2 xy x3
Assignment No. 2 Assignment Title Batch I
Applications of differential equation of 1st order & 1st degree
CO2
1. Find the Orthogonal Trajectories of the following curves a) x2
4 y2
b) r n
a n sin n
c) y 2
x2
4 xy 2cx
d) x 2
y2
2 gx c
e) ay 2 f)
r
a2
0 0 ; where „g‟ is parameter
x3 a(1 cos )
2. A voltage Ee
at
is applied t =0 to a circuit containing inductance L &
resistance R. Find current at any time t if initially t=0, I =0. 3. When a switch is closed, the current built up in an electric circuit is given by E
Ri
L
di . If L=640, R=250, E=500 & i=0 when t=0. Show that dt
the current will approach 2 amp when t=∞. 4. A voltage Ee resistance
at
R.
is applied t =0 to a circuit containing inductance L & Show
that
any
time
t
the
current
Rt
E e at e L i R aL
5. A constant emf E volts is applied to a circuit containing constant resistance R Ω in series & constant inductance L H. If the initial current is zero show that a current built up to half its theoretical maximum in Batch II
L log 2 sec R
1. Find the Orthogonal Trajectories of the following curves g) x2
4 y2
a2 175
h) r n
a n sin n
i)
y2
x2
4 xy 2cx
j)
x2
y2
2 gx c
k) r l)
r
m) x p
0 0 ; where „g‟ is parameter
2a 1 cos a(1 cos ) cy p 1
2. A voltage Ee
at
is applied t =0 to a circuit containing inductance L &
resistance R. Find current at any time t if initially t=0, I =0. 3. When a switch is closed, the current built up in an electric circuit is given by E
Ri
L
di . If L=640, R=250, E=500 & i=0 when t=0. Show that dt
the current will approach 2 amp when t=∞. 4. A circuit consists of a resistance R ohms and a condenser of C farads connected to a constant e.m.f. E. If q/c is the voltage of the condenser at time t after closing the circuit, show that the voltage at any time t is
E 1 et CR 5. A 200 ohms resistor is connected in series with a capacitor of 0.001 farad & e.m.f of 400e-3t. If q =0 at t=0, find the maximum charge on the capacitor. Batch III
1. Find the Orthogonal Trajectories of the following curves n) x2
4 y2
a2
o) r n
a n sin n
p) y 2
x2
4 xy 2cx
q) x 2
y2
2 gx c
r) r
2a 1 cos
s) r
a(1 cos )
0 0 ; where „g‟ is parameter
176
x p cy p 1
t)
2. A voltage Ee
at
is applied t =0 to a circuit containing inductance L &
resistance R. Find current at any time t if initially t=0, I =0. 3. When a switch is closed, the current built up in an electric circuit is given by E
Ri
L
di . If L=640, R=250, E=500 & i=0 when t=0. Show that dt
the current will approach 2 amp when t=∞. 4. A circuit consists of a resistance R ohms and a condenser of C farads connected to a constant e.m.f. E. If q/c is the voltage of the condenser at time t after closing the circuit, show that the voltage at any time t is
E 1 e
t CR
5. A 200 ohms resistor is connected in series with a capacitor of 0.001 farad & e.m.f of 400e-3t. If q =0 at t=0, find the maximum charge on the capacitor. Assignment Title Batch I
Assignment No. 3 Numerical Solutions of differentiation of 1st order & 1st degree
1) Given that
dy dx
xy
2 with y 1
CO3
1 . Find the value of y at x=2 in steps
of 0.2 by using Euler‟s method.
dy 1 y 2 with y 0 dx y 0.2 , y 0.3 , y 0.4 and y 0.5
2) Use Euler‟s method to solve
0 obtain y 0.1 ,
3) Use Euler‟s modified method to find y 0.2 , given that
dy dx
y 0 4) Solve
2y
0 with
1 by taking h=0.1
dy dx
Method for
2
xy with x0 1.2 and y0 1.6403 by Euler‟s Modified
x 1.4
5) Given the differential equation
dy dx
1 x
2
y
with y (4)
4 . Obtain y (4.1)
and y (4.2) by Taylor‟s series method. 177
dy dx
6) Use Taylor‟s series method to solve
x 2 y 1 with y (0) 1 for
x 0.03 Batch II 1) Given that
dy dx
xy
2 with y 1
1 . Find the value of y at x=2 in steps
of 0.2 by using Euler‟s method.
dy 1 y 2 with y 0 dx y 0.2 , y 0.3 , y 0.4 and y 0.5
2) Use Euler‟s method to solve
0 obtain y 0.1 ,
3) Use Euler‟s modified method to find y 0.2 , given that
dy dx
y 0
2y
0 with
1 by taking h=0.1
4) Given the differential equation
dy dx
1 x
2
y
with y (4)
4 . Obtain y (4.1)
and y (4.2) by Taylor‟s series method. 5) Use Taylor‟s series method to solve
dy dx
x 2 y 1 with y (0) 1 for
x 0.03 6) Given that
dy dx
x2
y with y 0
1 . Find the value of y at x=0.1 by
using Euler‟s modified method by taking h= 0.05 Batch III 1) Given that
dy dx
x2
y with y 0
1 . Find the value of y at x=0.1 by
using Euler‟s modified method by taking h= 0.05 2) Use Euler‟s method to solve
dy dx
x
y 2 with y 0
1 obtain y 0.1
with h = 0.02 3) Use Euler‟s method to find y 0.1 , given that
y 0 4) Solve
dy dx
x
y xy with
1 by taking h =0.025
dy dx
Method for
2
xy with x0 1.2 and y0 1.6403 by Euler‟s Modified
x 1.4 178
5) Given the differential equation
dy dx
1 x
2
y
with y (4)
4 . Obtain y (4.1)
and y (4.2) by Taylor‟s series method. 6) Use Taylor‟s series method to find y upto four decimal places for (1 xy )dx dy 0 with y (1) 2 at x 1.02 and also write series for y. Assignment Title Batch I
Assignment No. 4 Numerical Solutions of differentiation of 1st order & 1st degree
CO3
dy y 2 x 2 1) Using Runge Kutta Method, Solve with y (0) 1 at x 0.2 dx y 2 x 2 and x 0.4 dy x y 2 with y (0) 1 at x 0.2 by Runge Kutta Method by 2) Solve dx taking h = 0.1. 3) Solve the simultaneous first order differential equations by Runge Kutta dy dz fourth order Method xz 1, xy for x 0.3 Given dx dx y 0, z 1, when x 0 4) Solve the simultaneous first order differential equations by Runge Kutta dy dz fourth order Method with x z, x y2 dx dx x0
0, y0
2, z0
1 taking h
0.1
5) Solve the simultaneous first order differential equations by Runge Kutta dx dy fourth order Method y t, x t with initial conditions dt dt x 1, y 1, whent 0, taking h 0.1 Batch II 1) Using
x 0.2
Runge Kutta Method, Solve
dy dx
xy x 2 with y (0) 1 at
in two steps
2) Find y when
x 1.2 ,
given that
and h 0.2 by using R-K Method. 3) Solve the simultaneous first order dx fourth order Method xy dt x 1, y 1, when t 0, taking h 4) Solve the simultaneous first order
dy dx
2x 1 y 1 with x0 x2
1 , y0
2
differential equations by Runge Kutta dy t, ty x with initial conditions dt 0.1 differential equations by Runge Kutta 179
fourth
order
dy dx
Method
xz,
dz dx
y2
with
y 1, z 1, x 0 taking h 0.2 5) Solve the simultaneous first order differential equations by Runge Kutta dy dz fourth order Method with x z, x y dx dx y 0, z 1, when x 0 taking h 0.1
Batch III
dy y 2 x 2 1) Using Runge Kutta Method, Solve with y (0) 1 at x 0.2 dx y 2 x 2 and x 0.4 dy x y 2 with y (0) 1 at x 0.2 by Runge Kutta Method by 2) Solve dx taking h = 0.1. 3) Solve the simultaneous first order differential equations by Runge Kutta dx dy fourth order Method y t, x t with initial conditions dt dt x 1, y 1, whent 0, taking h 0.1 4) Solve the simultaneous first order differential equations by Runge Kutta dy dz fourth order Method with x z, x y2 dx dx x0
Assignment Title Batch I
0, y0
2, z0
1 taking h
0.1
5) Solve the simultaneous first order differential equations by Runge Kutta dy dz fourth order Method xz 1, xy for x 0.3 Given dx dx y 0, z 1, when x 0 Assignment No. 5 Special functions CO3 1) Prove that Γ(n+1) = nΓn 2) Evaluate the following integrals i)
x4 dx x 4 0
1
ii) 0
xdx
x ne
iii)
1 log x
ax
dx iv) a
0
4 x2
dx
0
3) Evaluate the following integrals 1
x (1
i) 0
1/4
7
3
5
x ) dx
( x 3)(7 x)
ii)
dx
3
180
/2
d sin
4) Prove that 0 1
dx
5) Prove that
3 0 1
1 x3
/2
sin d 0
2 3 3
x a xb a 1 dx log ; a > 0, b > 0 log x b 1
6) Prove that 0
7) Verify the rule of differentiation under integral sign for the integral a2
tan
x dx a
1
0
8)
Batch II
Define error function and state and prove any two properties of error function
1) Evaluate the following integrals
x ne
a)
ax
dx
a
d)
0
4 x2
dx
e)
e
h2 x 2
dx
0
2) Evaluate the following integrals /2
1) 0
d 1 2 1 sin 2
3) Show that 0
1/4
7
( x 3)(7 x)
2)
dx
3
x8 (1 x 6 ) dx 0 (1 x) 24 /2
4) Show that 0
sin 2 m 1 cos 2 n 1 d (a sin 2 b cos 2 )m n
1 B(m, n) 2 a mb n
5) Evaluate
e x 1 e x 0
ax
dx
6) Prove that 1
0
x a xb a 1 dx log log x b 1
; a > 0, b > 0 7) Verify the rule of differentiation under integral sign for the
181
a2
x dx a
1
tan
integral 0 8) Define error function and state and prove any two properties of error function Batch III
1) Prove that (n+1) = nΓn 2) Evaluate the following integrals 1
xdx
1)
1 log x
0
x ne
2)
ax
dx
a
3)
0
4 x2
dx 4)
e
h2 x 2
dx
0
3) Evaluate the following integrals 1
1
3
5
x (1
1.
x ) dx
0
0
/2
4) Prove that 0
d sin
1 x2 dx 1 x2
/2
sin d 0
5) Prove that 1.3.5.7...(2n 1)
Assignment Title Batch I
x
2.
5
2n
n
Assignment No. 6 Curve Tracing and Rectification
1 2
CO6
Q1) Trace the following curve 1) 3ay
2
x2 a x
2) y
2
a x
x3
3) y
2
a x
x 2 2a x
4) x3
y3
3axy
5)
r 3 2cos
6)
r 2 3cos
7)
r a sin 2
8) r
a 1 cos 182
Q2) Find the total length of the curve r 2 Q3) For the curve y
2
x x 1 3
a 2 sin 2
2
prove that s
2
4 2 x , where s being 3
y2
measured from origin to (x, y) Q4) Find the length of loop of the curve x 2/3 Q5) Find the perimeter of cardioide r
y 2/3
a 2/3
a 1 cos
and show that the line
2 divides upper half of cardioide into two parts. 3 Batch II
Trace the following curve 1) 3ay 2) y
2
3) y
2
x2 a x
x3
a x
c cosh( x / c)
4) x3
y3
3axy
5)
r 2 1cos
6)
r 1 2cos
7)
r a sin 2
8) r
a 1 cos
Q2) Find the total length of the curve r 2
a 2 cos 2
Q3) Find the length of loop of the curve y
2
Q4) Find the perimeter of cardioids r Batch III
x x 1 3
2
a 1 cos
Trace the following curve 1) y
c cosh( x / c)
2) x 2/3 3) y
2
4) y
2
y 2/3
a x x a
a 2/3
x 2 2a x 3
183
5) r
a b cos , a
6)
r 2 3cos
7)
r a cos2
8) r
b
a 1 sin
Q2) Find the total length of the curve r
a 1 cos
Q3) Find the length of loop of the curve 3ay 2
x x a
y c cosh
Q4) Find the arc length of the curve
2
x which is measured from ( c
0, c) to any point P(x, y) Q5) Find the total length of the curve
r a sin 2
Assignment No. 7 Assignment Title Batch I
Multiple Integrals
CO7
1) Evaluate following integrals a (1 cos )
a
2
2 r sin drd
a) 0
a2 y2
a2
b)
0
0
x2
y 2 dydx
0
Q.2 Change the order and evaluate 1 1 x2
a) 0
0
a
dydx (1 e y ) 1 x 2
y
ydydx
b)
y2
(a x) ax
0 y2
y2
a
Q.3 Evaluate
xydxdy over the region bounded by y x2 and x
Q.4 Evaluate
x3dxdy over the circle x2
y2
y2 .
2ax .
Q. 5 Change to polar co-ordinates and evaluate a x
a) 0 0
Batch II
x3dxdy x2
y2
2 2 x x2
b) 0
0
xdxdy x2
y2
1) Evaluate following integrals
184
/4 cos 2
a) 0
1 x
r 1 r
0
drd
2 2
e x y dydx
b) 0 0
Q.2 Change the order and evaluate 1 4
2 x2
1
x2
e dxdy b) dx
a) 0 4y
0
( x2
Q.3 Evaluate
xdy x2
x
y2
y 2 )dxdy over the area of triangle whose vertices are
(0,1), (1,1) and (1,2)
r 3drd over the area included between the circles
Q.4 Evaluate
r
2sin
and r
4sin .
Q. 5 Change to polar co-ordinates and evaluate a x
a)
x2
0 0
Batch III
a a2 x2
x3dxdy
b)
y2
0
ax x 2
dxdy a2
x2
y2
1) Evaluate following integrals /2 a cos
11 x
r a
a) 0
2
2
r drd
x1/3 y
b)
0
1/2
1 x y
1/2
dydx
1 0
Q.2 Change the order and evaluate a2 y2
a
a
dy
a) 0
0
xy log( x a)dx ( x a)2 a2
Q.3 Evaluate
x2
a 2a x
xydxdy
b) 0 x
2
a
y 2 dxdy over the semi circle
x2
y2
ax in
the positive quadrant
rdrd
Q.4 Evaluate
r
2
a
2
over the one loop of lemniscates r 2
a 2 cos 2 .
Q. 5 Change to polar co-ordinates and evaluate a a2 x2
a) 0
ax x 2
2 2 x x2
b) 0
0
dxdy a2
x2
y2
xdxdy x2
y2 185
Assignment Title Batch I
Assignment No. 7 Applications of Multiple Integrations 1. Find the area enclosed by between the parabolas y 2 y2
4 x 1 and
2 x 2
2.Find the total area of r a sin 2 3.The density at any point of a cardioid r a(1 cos ) varies as the square of its distance from its axis of symmetry. Find its mass 4.Find the mass of the lamina bounded by the curve y 2 x 3 and the line y x . If the density at a point varies as the distance of the point from X-axis. 5.Find the center of gravity of the area bounded by y 2 x and x y 2 6.Find the C. G. of the arc of the cardioid r a(1 cos ) lying above the initial
Batch II
line. 7.Prove that the M. I. of the area included between the parabolas y 2 4ax and 144 x 2 4ay about the x axis is Ma 2 where M is the mass of the area included 35 between the curves. 1.Find the total area of r a(1 cos ) 2.Find the total area bounded by y 2 (2a x) x3 and its asymptote x2 y 2 3.Find the mass of the lamina in the form of an ellipse 2 1 if the density a b2 at any point varies as the product of the distance from the axes of the ellipse 4.The density of a circular lamina is k times its distance from a given diameter. Find its mass 5.Find the C. G. of the lamina bounded by y 2 3x2 and the line 3x 2 y 1 6. Find the C. G. of the loop r a sin 2 7. An area is bounded by the curve
Batch III
y c cosh
x c ,
The axes and the ordinate x=c. Find the radius of gyration about the y - axis 1.Find the total area of r a(1 cos ) 2.Find the total area bounded by y 4 x x 2 and the line y x 3.The density at any point of a cardioid r a(1 cos ) varies as the square of its distance from its axis of symmetry. Find its mass 4.Find the M.I. of the semi-circle about the line joining one end of the bounding diameter to the midpoint of the arc. 5.Find the C. G. of the area of the curve x 2/3 y 2/3 a 2/3 lying in the first quadrant 6.Find the centroid of the loop of the lemniscates r 2 a 2 cos 2 7.Find the M.I. of the semi-circle about the line joining one end of the bounding 186
diameter to the midpoint of the arc.
List of Tutorials Examples on Differential equations 1. 2.
Examples on linear and reducible to linear Differential equations
3.
Examples on applications of Differential equations
4.
6.
Examples on Eulers method, Modified Euler,s Method, and Taylor‟s series method to solve differential equations of first order and first degree Examples on Runge kutta method to solve differential equations of first order and first degree and Runge kutta 4th order method to solve simultaneous differential equations of first order and first degree Examples on Beta and Gamma function
7.
Examples on differentiation under integral sign and Error function
8.
Examples on tracing of curves in Cartesian and polar form
9.
Examples on rectification in Cartesian and polar form
10.
Examples on Multiple Integration
5.
List of open ended experiments/assignments Assignment 1. Solve above given assignments by using scilab and verify your answer 2.
Trace given curves by using software’s like function plotter
187
FE Engineering Semester II Professional Communication -II Course
Professional Communication -II
Examination Scheme Max. Marks Contact Hours/ week Prepared by
Theory
Term Work
1
25 2
Course Code
Mr. B. B. Pujari/ Dr. U. P. Jadhav
POE
Total
--
25 3
Date
02/05/2014
English Language Skills-LSRW, usage of language in different situations; execution of all the skills of language according to the need of situation
Prerequisites
Course Outcomes At the end of the course the students should be able to: CO1 Write reports of various kinds CO2 Know who he/she is and build positive attitude CO3 Acquire decision making, leadership and problem solving skills CO4 Know what is IQ and EQ CO5
Develop in him/ her confidence and involve more in team work, public speaking, debate, group discussion activities
CO6
Practice corporate manners and etiquettes
CO7
Know interview techniques and planning and managing careers
Mapping of COs with POs POs COs CO1 CO2 CO3 CO4 CO5 CO6 CO7
a
b
c
d
E
f
G
h
i
j
k
l
√ √ √ √ √
√ √ √ √ √
188
Course Contents Unit No. 1. 2. 3. 4.
Title
No. of Hours 02 03 03 02
Developing writing skills Behavioral skills Presentation skills Career Skills
Reference Books: Sr. No. 1
2
Title of Book Handbook for Technical Writing
Author David A. McMurrey, Joanne Buckley Jane Summers, Brette Smith
Publisher/Edition Topics Cengage 1
Wiley India Pvt.Ltd
1 and 3
Biztantra
2 and 4
Cengage Wiley India Pvt.Ltd Cambridge University Press New Delhi.
2, 3 and 4 2
3
Communication Skills Handbook: How to succeed in written and oral communication Soft Skills for Managers
4
Soft Skills for every one
T. Kalyana Chakravarthi, T. Latha Chakravarthi, Jeff Butterfield
5
Behavioral Science
Abha Singh,
6
An Introduction to Professional Bikram K. Das, English and Soft Skills Kalyan Samantray
7
Speaking Accurately
K.C. Nambiar
8
Speaking Effectively
Jeremy Comfort, Pamela Rogerson
9
Cambridge English for Job Hunting
Colm Downes
10
Body Language
Allen Pease
2,4
Cambridge University Press New Delhi Cambridge University Press New Delhi.
3
Cambridge University Press New Delhi.
4
3
3,4
189
Unit wise Lesson Plan
Unit No 1
Unit Title
Section I Developing writing skills
Planned Hrs. Unit Outcomes: To know the nature and importance of advanced technical writing, techniques and types of report writing – survey, inspection and investigation, data collections methods and utilization, At the end of this unit the students should be able to: UO1 Understand advanced technical writing ,data collection and methods and its utilization UO2 Know the techniques of report writing and types of reports – survey, inspection and investigation
03
CO1 CO1
Lesson schedule Class Details to be covered No. 1 Importance of advanced technical writing 2 Techniques of report writing, Data collection methods and utilization 3 Report Writing – survey , inspection and investigation Unit No 2
Unit Title
Behavioral skills
Planned Hrs.
Unit Outcomes: to study At the end of this unit the students should be able to: UO1 Understand self-SWOT analysis, type of personality, personality traits UO2 Learn and practice techniques of developing positive attitude UO3 To apply decision making skills in problematic situations UO4 Recognize and understand leadership skills and responsibilities UO5 Understand and enhance emotional intelligence UO6 understand the problem and provide a solution with a case study UO7 know stress and stress management and time management skills UO8 understand team work ,organization of the team and goal oriented strategy of the team Lesson schedule Class Details to be covered No. 1 Understanding Self and Attitude Building/ Developing Positive attitude 2 Decision making skills and Leadership skills 3 problem solving skills with a case study
04
CO2 CO2 CO2 CO2 CO1 CO2,3, CO 4 CO 4
190
4
Emotional intelligent, stress and time management
Unit No 3
Unit Title
Presentation skills
Planned Hrs. Unit Outcomes: understand presentation, its importance and techniques and learn professional presentation and public speaking At the end of this unit the students should be able to: UO1 Know the importance and techniques of presentation UO2 know the skills to present professionally UO3 Understand public speaking and its use
03
CO5 CO5 CO5
Lesson schedule Class Details to be covered No. 1 the importance and techniques of presentation 2 professional presentation 3 public speaking Unit No 4
Unit Title
Career skills
Planned Hrs. Unit Outcomes: To understand career planning and career management and its various stages – job application (resume writing skills) ,interview (technique and skills ), group discussion , debate and corporate manners and etiquettes At the end of this unit the students should be able to UO1 know the corporate manners and etiquettes UO2 understand planning and career management UO3 know job application and resume writing skills UO4 understand interview process and perform in interview with skills and techniques UO5 know and perform group discussions and debates Lesson schedule Class No. Details to be covered 1 corporate manners and etiquettes 2 planning and managing career 3 interview technique and skills 4 group discussion and debate
04
CO6 CO6 CO7
CO7
191
Course Plan Course Examination Scheme Max. Marks Contact Hours/ week Prepared by
Workshop Practice-II
Course Code
Theory
Term Work
POE
Total
1
25 2
---
125 2
S. V. Dhanal
Date
Prerequisites Safety, basic materials and tools
Course Outcomes At the end of the course the students should be able to: CO1 Know about Safety : Common hazards while working with engineering equipment and related safety measures CO2
Know about materials used in Industries, steels and alloys, cast iron, non-ferrous metals, timber, plastics and polymers, glass etc. and; their applications.
CO3
To use properly measuring Instruments such as Steel rule, Vernier Caliper, Micrometer, Dial indicator, Their least counts, common errors and care while using them, Use of marking gauge, „V‟ block and surface plate.
CO4 CO5
To explain Carpentry and Fitting To explain welding processes - Arc, Gas and Resistance.
CO6
To know sheet metal specification, working & operations like cutting, bending, folding, punching, riveting ; Joining by brazing and soldering To explain smithy operations like upsetting, drawing, bending, Forming ; Toolshammer, hot and cold chisels, swages, drifts, flatters, tongs, Anvils to observe machine tools and processes- Metal removing, metal shaping, plastic molding.
CO7 CO8
192
Mapping of COs with POs a POs COs CO1 CO2 CO3 CO4 CO5 CO6 C07 CO8
b
c
d
E
F
G
H
i
j
k
l
√ √ √ √ √ √ √
Course Contents Unit No.
1.
2.
3.
4. 5 6
7
8
Title Section I Safety : Common hazards while working with engineering equipment and related safety measures. Materials : Brief introduction of materials used in Industries, steels and alloys, cast iron, non-ferrous metals, timber, plastics and polymers, glass etc. and; their applications. Measuring Instruments : Brief introduction to instruments like – Steel rule, Vernier Caliper, Micrometer, Dial indicator, Their least counts, common errors and care while using them, Use of marking gauge, „V‟ block and surface plate. Carpentry and Fitting : Brief study of various hand tools like chisel, saw, planer and fitting tools like files, saw, drills, taps and dies. Welding : Classification and brief introduction to welding processes Arc, Gas and Resistance. Sheet Metal Working : Specifications of metal sheets, Surface coatings ; Operations like cutting, bending, folding, punching, riveting ; Joining by brazing and soldering. Smithy : Introduction to smithy operations like upsetting, drawing, bending, Forming ; Tools- hammer, hot and cold chisels, swages, drifts, flatters, tongs, Anvils. Smithy : Introduction to smithy operations like upsetting, drawing, bending, Forming ; Tools- hammer, hot and cold chisels, swages, drifts, flatters, tongs, Anvils.
No. of Hours 1
2
2
1 2 2
2
1
193
Reference Books: Sr. No. 1
Title of Book Course in Workshop Technology, Vol – I,
2
, Elements of Workshop Hajara Choudhari Media Promoters 1 to 8 Technology, Vol – I, . Workshop Technology, Vol Gupta and Kaushik, – I, New Heights 1 to 8 Unit wise Lesson Plan
3
Author B. S. Raghuvanshi, A
Publisher/Edition Units Dhanapat Rai 1 to 8 and Sons
Section I Unit No
1
Unit Title
Safety
Planne d Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 Know about industrial safety
01
CO
Lesson schedule Class Details to be covered No. 1 Common hazards while working with engineering equipment and related safety measures
Unit No 2
Unit Title
Materials
Planne d Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 explain materials used in Industries, steels and alloys, cast iron, nonferrous metals, timber, plastics and polymers, glass etc. and; their applications. UO2
02
CO2
CO2
Lesson schedule Class Details to be covered No. 1 steels and alloys, cast iron, non-ferrous metals, timber 2
Unit No
plastics and polymers, glass etc. and; their applications.
3
Unit Title
Measuring Instruments
Planne d Hrs.
02
Unit Outcomes 194
At the end of this unit the students should be able to: UO1 explain instruments like – Steel rule, Vernier Caliper, Micrometer, Dial indicator,
CO3
UO2
CO3
least counts, common errors and care while using them, Use of marking gauge, „V‟ block and surface plate.
Lesson schedule Class Details to be covered No. 1 Steel rule, Vernier Caliper, Micrometer, Dial indicator, 2
„V‟ block and surface plate.
Unit No 4
Unit Title
Carpentry and Fitting
Planne d Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 study of various hand tools like chisel, saw, UO2 planer and fitting tools like files, saw, drills, taps and dies.
01
CO4 CO4
Lesson schedule Class Details to be covered No. 1 study of various hand tools like chisel, saw, planer and fitting tools like files, saw, drills, taps and dies. Unit No
5
Unit Title
Welding
Planne d Hrs.
Unit Outcomes At the end of this unit the students should be able to: UO1 Classify welding processes - Arc, UO2 Gas and Resistance
02
CO5 CO5
Lesson schedule Class Details to be covered No. 1 Arc welding 2 Gas and Resistance welding Unit No 6
Unit Title
Sheet Metal Working
Planne d Hrs.
02
Unit Outcomes At the end of this unit the students should be able to: 195
UO1
specify metal sheets, explain surface coatings ;
CO6
UO1
explain operations like cutting, bending, folding, punching, riveting ; Joining by brazing and soldering.
CO6
Lesson schedule Class Details to be covered No. 1 metal sheets, surface coatings 2 cutting, bending, folding, punching, riveting ; Joining by brazing and soldering. Unit No
7
Unit Title
Smithy
Planne d Hrs.
02
Unit Outcomes At the end of this unit the students should be able to: UO1 know smithy operations like upsetting, drawing, bending,
CO7
UO2
CO7
Forming ; Tools- hammer, hot and cold chisels, swages, drifts, flatters, tongs, Anvils.
Lesson schedule Class Details to be covered No. 1 like upsetting, drawing, bending 2 hammer, hot and cold chisels, swages, drifts, flatters, tongs, Anvils. Unit No 8
Unit Title
machine tools and processes
Unit Outcomes At the end of this unit the students should be able to: UO1 to observe machine tools and processes- Metal removing, metal shaping, plastic molding.
Planne d Hrs.
01
CO8
Lesson schedule Class Details to be covered No. 1 Metal removing, metal shaping, plastic molding.
196