# CITY UNIVERSITY OF HONG KONG

City University of Hong Kong Information on a Course offered by Department of Mathematics with effect from Semester A in 2012/2013

Part I Course Title: __Multi-variable Calculus____________________________________ Course Code: _MA2508________________________________________________ Course Duration: __ One Semester_________________________________________ No. of Credit Units: ___4________________________________________________ Level: __B2__________________________________________________________ Medium of Instruction: ___English________________________________________ Prerequisites: (Course Code and Title)

Grade B or above in MA1201 Calculus & Basic Linear Algebra II and subject to approval from MA must be obtained; or Grade C- or above in MA1301 Enhanced Calculus & Linear Algebra II; or Pass in MA1400 Remedial Calculus & Linear Algebra; or equivalent

Precursors: (Course Code and Title) _____ Nil_____________________________________ Equivalent Courses: (Course Code and Title) ____ Nil_______________________________ Exclusive Courses: (Course Code and Title) ________ MA2502_______________________ Part II 1.

Course Aims: This course introduces fundamental mathematical methods and analysis in advanced calculus. It will help students to understand the basic concepts, fundamental theory and identify the applications of multi-variable calculus. It trains students in the ability to think quantitatively and analyze problems critically.

2.

Course Intended Learning Outcomes (CILOs) Upon successful completion of this course, students should be able to: No. 1. 2. 3. 4.

5.

CILOs

Weighting (if applicable) evaluate limits, partial derivatives, and multiple 3 integrals for functions of several variables. compute line and surface integrals. 3 apply integral theorems of vector analysis to describe 2 some physical problems. explain basic concepts of multi-variable calculus, 2 create and construct mathematical models through multi-variable calculus and vector analysis, and properly apply to some problems in science and engineering. the combination of CILOs 1-4 3

Weighting scale: 1 - Least important; 2 - Important; 3 - Highly important.

3.

Teaching and learning Activities (TLAs) (designed to facilitate students’ achievement of the CILOs) Indicative of likely activities and tasks students will undertake to learn in this course. Final details will be provided to students in their first week of attendance in this course.

TLAs Learning through teaching is primarily based on lectures. Learning through tutorials is primarily based on interactive problem solving allowing instant feedback.

ILO No. 1--5

1 2 3 4 Learning through take-home assignments 1--5 helps students understand basic mathematical concepts and fundamental theory of multivariable calculus, and apply mathematical methods and analysis from advanced calculus to some applications. Learning through online examples for 4 applications helps students create and formulate mathematical models and apply to some problems in science and engineering. Learning activities in Math Help Centre 1-3 provides students extra help.

Hours/week 39 hours in total 4 hours 4 hours 2 hours 3 hours after-class

after-class

after-class

4.

Assessment Tasks/Activities (designed to assess how well the students achieve the CILOs)

30% Coursework 70% Examination (Duration: 3 hours, at the end of the semester) For a student to pass the course, at least 30% of the maximum mark for the examination must be obtained. Weighting Assessment ILO No. (if Remarks Tasks/Activities applicable) Test 1 Questions are designed for the first part of the course to see how well the students have learned the basic concepts, fundamental theory and recognized the applications of multi-variable calculus. 30% Hand-in 1--4 These are skills based assessment to assignments enable students to demonstrate the basic concepts and fundamental theory of multi-variable calculus and identify the applications.

5.

Examination

5

70%

Examination questions are designed to see how far students have achieved their intended learning outcomes. Questions will primarily be skills and understanding based to assess the student’s versatility in multi-variable calculus.

Formative takehome assignments

1--4

0%

The assignments provide students chances to demonstrate their achievements on multi-variable calculus learned in this course.

A+ A A-

4.3 4.0 3.7

B+ B B-

3.3 3.0 2.7

Excellent

Strong evidence of original thinking; good organization, capacity to analyze and synthesize; superior grasp of subject matter; evidence of extensive knowledge base.

Good

Evidence of grasp of subject, some evidence of critical capacity and analytic ability; reasonable understanding of issues; evidence of familiarity with literature.

C+ C C-

2.3 2.0 1.7

Student who is profiting from the university experience; understanding of the subject; ability to develop solutions to simple problems in the material.

D

1.0

Marginal

Sufficient familiarity with the subject matter to enable the student to progress without repeating the course.

F

0.0

Failure

Little evidence of familiarity with the subject matter; weakness in critical and analytic skills; limited, or irrelevant use of literature.

Part III Keyword Syllabus:    

Three-dimensional coordinate systems, equations for lines and planes, quadric surfaces Definitions of multi-variable functions, concepts of limit and continuity, partial derivatives of multi-variable functions, calculations of partial derivatives and their applications (e.g., maximum and minimum) Definitions of double integrals and triple integrals, evaluations of double and triple integrals in rectangular and other coordinates, applications of double and triple integrals (e.g., mass of a plate) Definition of vector fields, curl and divergence, definitions and evaluations of line and surface integrals, Green's theorem, Stokes' theorem and Gauss’s theorem

Recommended Reading: Text(s): J. Stuart, “Multivariate Calculus”, fifth ed., Brooks/Cole, 2003.