620-232 Mathematical Methods

Credit Points

Coordinator

Prerequisites

One of 620-112, 620-122, 620-200, 620-211 (1997 Handbook 618-112, 618-122, 618-200, 618-211), and one of 620-130 or 620-132 (1997 Handbook 618-130 or 618-132).

Semester

Contact

Subject Description

Students completing this subject should comprehend

• the terminology of classifying and describing ordinary and partial differential equations;
• the concept of obtaining complete and general solutions;
• general methods to solve linear ordinary differential equations and partial differential equations;
• the role of Fourier series, Laplace transforms and special functions in providing solutions to such equations;

have developed the ability to

• use standard methods such as Laplace transforms, series solutions, separation of variables for obtaining solutions;

and appreciate

• the complexity and the necessary ingredients required in obtaining solutions to ordinary and partial differential equations;
• more advanced techniques available in further courses on mathematical methods.

Partial differential equations: Laplace's equation, wave equation and heat equation; separation of variables; Fourier series. Ordinary differential equations: introduction to Laplace transforms and applications; differential equations with variable coefficients, independent solutions, Wronskians; series solutions of ordinary differential equations; Bessel functions, Legendre polynomials and other special functions.

Assessment

Up to 24 pages of written assignments, a three-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.