620-232 Mathematical Methods

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

One of [01]620-112, 620-122, 620-142, [05]620-192, [05]620-194, 620-211; and one of 620-113, 620-123, 620-143, [05]620-193.

This subject introduces the terminology of classifying and describing ordinary and partial differential equations; and the concept of obtaining complete and general solutions. It develops general methods to solve linear ordinary differential equations and partial differential equations using Fourier series, Laplace transforms and special functions to provide solutions to such equations. Students should develop the ability to use standard methods such as Laplace transforms, series solutions, separation of variables for obtaining solutions. This subject demonstrates the complexity and the necessary ingredients required in obtaining solutions to ordinary and partial differential equations and indicates more advanced techniques available in further courses on mathematical methods.

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

A 3-hour end-of-semester written examination (85%) and three 45-minute written class tests during semester (15%).