620-232 Mathematical Methods

Students may gain credit for only one of 620-232 and 620-234.

Students in the combined degree BE/BSc should note that credit exclusions exist between this subject and Engineering mathematics subjects. Refer to entries for 431-201 Engineering Analysis A and 431-202 Engineering Analysis B for details.

One of 620-122, 620-142, [05]620-192, [05]620-194, 620-211; and one of 620-113, 620-123, 620-143, [05]620-193.

Many phenomena in the biological and physical sciences as well as engineering and modern finance are described by differential equations. Examples include tissue engineering, contaminant transport, epidemic models, electrical circuits, dynamical systems and quantum mechanics. This subject describes analytical methods to solve linear ordinary and partial differential equations, as well as qualitative methods for linear and nonlinear systems of differential equations.

Transform methods for ordinary differential equations are introduced via the Laplace transform. The most common partial differential equations - Laplace's equation, the wave equation and the heat equation - are introduced and solved in simple geometries by separation of variables. This requires the development of Fourier series to represent functions and leads to an introduction to Fourier transforms. Linear systems of ordinary differential equations are solved by matrix methods and the phase plane is defined. Qualitative ideas such as stability and phase portraits are extended to nonlinear systems of differential equations. Applications include topics such as population models and normal modes.

Two 45-minute written class tests held during semester (20%); a 3-hour written examination in the examination period (80%).