Mathematics 4Q3:
Numerical Methods for Differential Equations
(Winter, 2001)

Numerical computing is a powerful tool for solving practical mathematical problems that occur in science and engineering. With the aid of high-level programming languages and customized software libraries, realistic analysis and design problems can be solved quickly, with a minimum of effort. This course focuses on applications of numerical methods and algorithms to solving ordinary and partial differential equations.

Instructor: Dr. Dmitry Pelinovsky (BSB-204, ext.23424)
Lecture hours: Tuesdays, Thursdays, Fridays: 11:30-12:20 (BSB-B103)
Office hours: Tuesdays, Thursdays: 14:00-15:00 or by appointment
Teaching Assistant: Bogdan Traicu (BSB-237); office hour: Tuesdays (13:00-14:00)

The lectures are based on real-world problems of polynomial interpolation and approximation, numerical differentiation and integration, initial-value and boundary-value problems for ODEs and PDEs. Numerical examples, software programs, and computer assignments are based exclusively on the Matlab 6 operating package. As part of the pilot WebCT project, the course materials will be supplemented by online summary of lecture notes, online library of numerical solutions and demonstrations, interactive student survey (feedback) forms and online grade control options.

J.H. Mathews, K.D. Fink: "Numerical methods using MATLAB" (Prentice Hall, 1999) This is the main textbook for the course. It gives a good theoretical background in numerical methods but lacks real-world numerical examples.
LV. Fausett: "Applied numerical analysis using Matlab" (Prentice Hall, 1999) The textbook contains useful small-sized MATLAB scripts and functions. All examples and programs are carefully explained but the theoretical background is given superficially and numerical computations (figures) often lack accuracy.
R.J. Schilling, S.L. Harris: "Applied numerical methods for engineers using Matlab and C" (Brooks/Cole, 2000) The textbook is based on real-life examples and is accompanied by CD that contains numerical libraries of many useful algorithms for MATLAB and C.
"Getting started with Matlab (Version 6)" (The MathWorks, Inc. 2000) This is the first introductory part of the official Matlab 6 user's guide. Together with other parts of the user's guide, it provides everything you need to start working with MATLAB language.
C.F. Gerald, P.O. Wheatley: "Applied numerical analysis" (Addison-Wesley, 1994) This is one of classical textbooks on numerical analysis. It is fundamental in theory and bad in the present-time practice. Programs are given on languages beyond MATLAB, including C, PASCAL, FORTRAN, and BASIC.
J.H. Ferziger: "Numerical methods for engineering application" (John Wiley and Sons, 1998) The best special book on the subject for strong students who intend to enter graduate studies. No examples whatsoever but the theory is crystal, systematic and fundamental.

Five home assignments and one computer project will be given and marked for credit. The five assignments will be handed out in class on Tuesdays every second week starting the week of January 15, 2001. The home assignments are due at 12:20 on Tuesday of the following week. The computer project will be handed out on February 6, 2001 and due on March 20, 2001.

There will be one 50 minute class test during the regularly scheduled class hour on Tuesday, February 13, 2001 in BSB-B135. The course is completed by a three-hour final examination during the examination period in April, 2001.

Marking scheme: Final examination - 50%
Class test - 20%
Computer project - 10%
Five homework assignments - 20%

MATLAB software package is installed on the computers in computer labs on the second floor of the Burke Sceince Building. A simplified version of the package is also available on CD bound in the book "The student edition of MATLAB" (Prentice Hall, 2000) . Some MATLAB functions will be demostrated on the Matlab Web Server connected to the instructor's Web server. However, it is recommended that students grasp basic skills of programming on MATLAB by working either in the computer labs or with the personal student edition.