AMATH 342/CM 352: Computational Methods for Differential Equations

Offered every fall and spring term.

Brief description:

Mathematical models based on Ordinary Differential Equations (ODEs) are ubiquitous these days, arising in all areas of science and engineering, and also in finance and economics. In complex models, the differential equations cannot be solved exactly, and one has to rely on approximate solutions obtained using numerical methods on computers.

The goal of this course is threefold. You will receive a solid introduction to the theory of numerical methods for differential equations (with derivations of the methods and some proofs). You will learn to implement the computational methods efficiently in Matlab, and you will apply the methods to problems in several fields, for example, climate modeling, combustion, control theory, and mathematical biology.

Prerequisites:

AMATH 242 / CS 371 / CM 271, or permission of the instructor.

If you have completed your 2B term, and have good grades in AMATH 250, MATH 237/247 and MATH 235/245, the instructor will sign you into AMATH 342. The course includes an optional tutorial in Matlab which will ensure that the students who have not taken AMATH 242 are prepared for AMATH 342.

Intended audience:

This course will be of interest to anyone who wants to be able to use computers to analyze mathematical models based on differential equations.