Mathematics 4Q03:
Numerical Methods for Differential Equations
(Winter, 2004)

Course Objectives: Numerical computations give the only way for solving most applied 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 numerical methods and algorithms for solutions of ordinary and partial differential equations.

Topics: Lectures cover problems of polynomial interpolation and approximation, numerical differentiation and integration, finite-difference and finite-element solutions of initial-value and boundary-value problems for ODEs and PDEs. Numerical examples, software programs, and computer assignments are based on the Matlab 6.

Dr. Dmitry Pelinovsky, HH-422, ext.23424, e-mail:

Teaching Assistant:
Guoxuan Ma,, HH-303, ext. 27246, e-mail:

Lectures: Tuesday, Thursday, Friday (8:30-9:20); BSB/235
Computer labs: Monday, Friday (9:30-11:20); BSB/241
Office hours: Tuesday, Thursday (9:30-10:30), or by appointment

Custom Courseware:
"Scientific Computing with Matlab" by D.E. Pelinovsky (McMaster, 2004)

Harder textbooks:
C.F. Gerald, P.O. Wheatley: "Applied numerical analysis" (Pearson, 2004)
R.L. Burden, J.D. Faires: "Numerical analysis" (Brooks/Cole, 2001)

Simpler textbooks:
S.S.Rao: "Applied numerical methods for engineers and scientists" (Prentice Hall, 2002)
R.J. Schilling, S.L. Harris: "Applied numerical methods for engineers using Matlab and C" (Brooks/Cole, 2000)
J.H. Mathews, K.D. Fink: "Numerical methods using MATLAB" (Prentice Hall, 1999)
LV. Fausett: "Numerical methods: Algorithms and Applications" (Prentice Hall, 2003)

Labs: MATLAB software package is installed in computer lab of BSB/241. Lab hours are reserved for unsupervised students' work with computer-based assignments. Unless the labs are reserved for large-class tutorials, students should be able to work in the computer labs of BSB beyond the scheduled time. Students are also encouraged to purchase "The Student Edition of MATLAB" to be able to work with Matlab at home. Some MATLAB demonstrations are included in the course web-based software. 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.

Assignments: Six home assignments will be handed out in class on Tuesdays every second week, starting the week of January 12. Solutions of the assignments should be submitted by e-mail to The assignments are due by mid-night on Thursday in the following week. Only five best assignments are counted towards the final mark. The texts for assignments and solutions will be posted on the course webpage.

Class Test: There will be one class test on Tuesday: February 10. The test covers analytical questions/problems of the course. Only the McMaster standard calculator Casio fx-991 is allowed on the test.

Final Exam: The course is completed by a three-hour final examination. The date and location of the final exam will be announced by the registrar's office in mid-term.

Marking scheme:
Final exam (3 hrs) - 50%
Test (50 min) - 10%
Five homework assignments - 40%

Senate Policy Statement: The course is regulated under the following documents: Statement on Academic Ethics and Senate Resolutions on Academic Dishonesty. Any student who infringes one of these resolutions will be treated according to the published policy. In particular, academic dishonesty includes (1) plagiarism, e.g. the submission of work that is not one's own, (2) improper collaboration in group work on home assignments, (3) copying or using unauthorized aids tests and examinations. It is your responsibility to understand what constitutes academic dishonesty, refering to Academic Integrity Policy.