Math 373 - Iowa State University [PDF]

Please refer to the download link: ISU Matlab for Student. ... Numerical Analysis, Richard L. Burden, J. Douglas Faires

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Math 373, Introduction to Scientific Computing Beyer Hall 1306, TuTh 11:00a-12:15p Fall Semester, 2017 Instructor: Dr. Songting Luo Office Hours: Tu-W-Th 10:00am – 11:00am, or by appointment. Office: Carver Hall 430 Email: [email protected]

Announcement (11/28) Final project is posted (see below). We will discuss the problems in details in class. (11/06) Homework set 4 is posted (see below). Due Tuesday Nov. 28. (Let me know if you have questions!) (10/17) Homework set 3 is posted (see below). Due Tuesday Oct. 31. (Let me know if you have questions!) (09/28) Homework set 2 is posted (see below). Due Thursday Oct. 12. (Let me know if you have questions!) (08/31) Homework set 1 is posted (see below). Due Tuesday Sep. 19. (Let me know if you have questions!) (08/21) (ISU Matlab for Students) We will use Matlab for programming assignments for this course. ISU has Matlab for Students free of charge. Please refer to the download link: ISU Matlab for Student. You can download it and install it on your computer. As long as you are on campus IP address, you can use it. If you prefer, it is ok to use other programming tools.

Syllabus A pdf file containing the information of this class is available here.

Official Math Department Policies For departmental policies on Academic Misconduct, Disability Accommodation, Make up Examinations, Dead Week, Student Behavior in Class, Harassment and Discrimination, Religious Accommodation, etc., please refer to ISU Dept. of Mathematics Class Syllabus and Class Policies.

Text Numerical Analysis, Richard L. Burden, J. Douglas Faires and Annette M. Burden, 10th Edition. ISBN10: 1-305-25366-3, ISBN13: 978-1-305-25366-7. Earlier editions (7th--9th) of Numerical Analysis by Richard L. Burden and J. Douglas Faires should work fine.

Course Description and Objectives Catalog Entry: MATH 373. Introduction to Scientific Computing. (3-0) Cr. 3. F. Prereq: MATH 265 Vector and matrix programming and graphing in MATLAB for scientific applications. Polynomial interpolation and approximation. Systems of linear equations and numerical linear algebra. Numerical differentiation and integration. Newton methods for solving nonlinear equations and optimization in one and several variables. Fast Fourier transform. Emphasis on effective use of mathematical software and understanding of its strengths and limitations. This is a one-semester survey course of standard topics in scientific computation. A companion course MATH 481 covers the numerical solution of differential equations, which is not included in MATH 373. After completion of this course, students will be able to solve standard problems in numerical analysis using Matlab or other software. They will be aware of basic concepts of numerical analysis. They will be prepared for more advanced courses in numerical analysis, as well as for the use of numerical methods for their degree work. Necessary background includes calculus (MATH 165/166/265), and some basic familiarity with vectors and matrices and computer programming. A course in linear algebra or computer programming is not required.d. Course Objectives: Background and Basics: Taylor's Formula, Types of error: absolute, relative, discretization, truncation, arithmetic, Cancellation, Computer arithmetic, in particular IEEE double precision numbers. Solution of Equations in One Variable: Bisection method, fixed point iteration, Newton's method, secant method, extrapolation. Polynomial Interpolation and Approximation: Finding interpolating polynomial by matrix method, Lagrange polynomials, Newton divided differences, generalized interpolation, Spline interpolation. Numerical Differentiation and Integration: forward/backward/centered difference formulas for derivatives, Newton-Cotes quadrature, Gaussian quadrature. Solving Linear Systems of Equations: Gaussian Elimination, Cholesky method. Approximation Theory: Least squares solution of systems of linear equations, orthogonal polynomials and best approximation, Fast Fourier transform. Eigenvalue Problems: Power method and inverse power method, QR algorithm, SIngular Value Decomposition. Solution of Systems of Nonlinear Equations: Fixed Point Iteration, Newton's Method, Quasi-Newton Method, Conversion to optimization problem; steepest descent and conjugate gradient method. Lecture Notes: Lecture chap 1 (08/22-08/24) pdf , pdf , Condition number (pdf) . Introduction to Matlab (webpage) . Introduction to Symbolic Computation in Matlab (webpage) . Finding max/min of a function (matlab demo) . Taylor Polynomial (matlab demo) . Rate of Convergence (matlab demo) . Lecture chap 2 (08/29-08/31-09/05-09/07) pdf . bisection.m (matlab routine) . matlab demo with bisection.m . fixed-point iteration.m (matlab routine) . matlab demo with fixed-point iteration.m . newton.m (matlab routine) . matlab demo with newton.m . secant.m (matlab routine) . matlab demo with secant.m . matlab demo with newton for zeros with multiplicity larger than 1.m . Steffensen Method.m (matlab routine) . matlab demo with steffensen.m . Horner's Method.m (matlab routine) . matlab demo with Horner's method.m . Muller's Method.m (matlab routine) . matlab demo with Muller's Method.m . Lecture chap 3 (09/12-09/14-09/19-09/21-09/23-09/26) pdf . lagrangepoly.m (matlab routine) . matlab demo with Lagrange polynomial interpolation (lagrangepoly.m) . Neville's Method.m (matlab routine) . matlab demo with Neville's Method.m . Table of Divided Difference.m (matlab routine) . matlab demo for generating table of divided difference.m . Hermite Interpolation.m (matlab routine) . matlab demo for Hermite Interpolation.m . matlab demo for cubic spline interpolation.m . natural cubic spline.m (matlab routine) . clamped cubic spline.m (matlab routine) . Lecture chap 8 (09/28-10/03-10/05-10/10) pdf . Discrete least squares approximation (matlab routine) . matlab demo with discrete least squares approximation . example with Discrete least squares approximation . example with 'Continuous' least squares approximation . Gaussian Elimination (matlab routine) . matlab demo for using Chebyshev Nodes, and Runge Phenomenon. matlab demo for doing Chebyshev expansion . Pade Rational Approximation with Chebyshev polynomial (matlab routine). matlab demo of Pade Rational Approximation with Chebyshev polynomial. Chebyshev polynomial evaluation (matlab routine). Lagrange polynomial Interpolation (matlab routine). Lecture chap 8 (10/10) pdf . matlab demo of least squares trigonometric polynomial approximation. matlab demo of discrete least squares trigonometric polynomial approximation. matlab demo of using FFT to compute interpolatory trigonometric polynomial. Lecture chap 4 (10/12-10/17-10/19-10/24-10/26) pdf . Romberg Integration (matlab routine) . matlab demo of Romberg Integration . Gaussian Quadrature (matlab routine) . matlab demo of using Gaussian Quadrature . Lecture chap 6 (10/30-11/01-11/06-11/08) pdf . Gaussian Elimination (matlab routine) . Gaussian Elimination with partial pivoting (matlab routine) . matlab demo of Gaussian Elimination . LU factorization without permutation (matlab routine) . matlab demo of LU factorization with or without permutation to solve a linear system . matlab demo of LDL' and LL' factorization to solve a linear system . Lecture chap 9 (11/07-11/09-11/14) pdf . Power Iteration (matlab routine) . matlab demo of Power Iteration Example. Inverse Iteration (matlab routine) . matlab demo of Inverse Iteration Example. Rayleigh Quotient Iteration (matlab routine). matlab demo of Rayleigh Quotient Iteration Example. Lecture chap 9 (11/14-11/16) pdf . "Pure" QR Algorithm (matlab routine) . Shifted QR Algorithm (matlab routine) . "Practical" Shifted QR Algorithm (matlab routine) . matlab demo of using "Pure" QR Algorithm, Shifted QR Algorithm, and "Practical" Shifted QR Algorithm . Lecture chap 10 (11/28-11/30) pdf . Fixed-point iteration for system (matlab routine). matlab demo of using Fixed-point iteration . Newton's method for system (matlab routine). matlab demo of using Newton's method .

Homework Policy Homework sets will be assigned according to the progress of the class and can be downloaded below as pdf files that will be posted here. Approximately a total of 5 homeworks will be assigned. Homeworks will be collected and graded. Most likely the homeworks will not all be exactly the same length. I will just add all the points at the end, and convert it to a percentage. This will count for 3/4 of your grade. I encourage group participation in the solution of exercises. There will be some larger assignment due during Finals Week, which counts for 1/4 of the grade. There will not be any in-class exams. Homework Sets: Final Project (we will finish it by finals week.) pdf . Homework set 4 (due Tuesday, November 28.) pdf . Homework set 3 (due Tuesday, October 31.) pdf . Homework set 2 (due Thursday October 12.) pdf . Homework set 1 (Due Tuesday Sep. 19) pdf .

Programming Exercises You will have to use MATLAB for some assignments, but in general I will accept solutions based on any software (hand calculator, Mathematica, Excel spreadsheet, ...). Matlab Resources: Matlab Primer of Professor Sigmon of the University of Florida: http://www.math.pitt.edu/~swigon/Matlab/primer.pdf Matlab documentation: http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html

Grades The final grade (as a percentage of the total points) will be computed using the following weights: homeworks 3/4 and final assignment 1/4. Letter grades will be assigned according to the following tentative scale: >= 89%, grade is at least A-; >= 78%, grade is at least B-; >= 67%, grade is at least C-; >= 56%, grade is at least D-; < 56%, grade is likely F. I reserve the right to change this scale, provided the change benefits all students.

Academic Honesty Students must be familiar with the academic standards of conduct, please refer to Academic Dishonesty.

Accommodation of Disabilities If you have a disability and require accommodations, please contact the instructor early in the semester so that your learning needs may be appropriately met. You will need to provide documentation of your disability to Student Disability Resources (SDR) Office , located on the main floor of the Student Services Building, Room 1076, 515-294-6624. Melanie Erickson is the Disability Liaison for the Mathematics Department. She is in 396E Carver. You can reach her at [email protected] or at 294-0393. More details are given in the following link: Departmental Student Disability Accommodation Policy .

Religious Accommodation If an academic or work requirement conflicts with a student's religious practices and/or observances, the student may request reasonable accommodations. The request must be in writing at least 10 days in advance if possible, and the course instructor or supervisor will review the request. The student or the instructor may also seek assistance from the Dean of Students Office or the Office of Equal Opportunity and Compliance.

Class Schedule and Assignments During the semester I'll post the schedule, along with assignments, sample solutions, and class notes. There may be deviations from the schedule below, which I will announce in class. Ultimately, you are responsible for knowing what is covered and assigned by regularly attending classes. Please bookmark this site. Week

M

Tu

W

Th

01, Aug. 21 – Aug. 25.

Chapter 1 .

Chapter 1.

02, Aug.28 – Sep. 01.

Chapter 2.

Chapter 2.

03, Sep. 04 – Sep. 08.

Chapter 3.

Chapter 3.

04, Sep. 11 – Sep. 15.

Chapter 3.

Chapter 3.

05, Sep. 18 – Sep. 22.

Chapter 3.

Chapter 3.

06, Sep. 25 – Sep. 29.

Chapter 4.

Chapter 4.

07, Oct. 02 – Oct. 06.

Chapter 4.

Chapter 4.

08, Oct. 09 – Oct. 13.

Chapter 6.

Chapter 6.

09, Oct. 16 – Oct. 20.

Chapter 6.

Chapter 6.

10, Oct. 23 – Oct. 27.

Chapter 8.

Chapter 8.

11, Oct. 30 – Nov. 03.

Chapter 8.

Chapter 8.

12, Nov. 06 – Nov. 10.

Chapter 8.

Chapter 8.

13, Nov. 13 – Nov. 17.

Chapter 9.

Chapter 9.

14, Nov. 20 – Nov. 24.

Thanksgiving break.

Thanksgiving break.

15, Nov. 27 – Dec. 01.

Chapter 10.

Chapter 10.

16, Dec. 04 – Dec. 08.

Review.

Review.

17, Dec. 11 – Dec. 15.

Finals Assignment DUE!.

NOTE:

F

I reserve the right to change the policy. Any changes of the syllabus and class information will be announced in class and updated here.

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