618-232 Mathematical Methods

Credit Points:

Coordinator:

Prerequisite/s:

Timetable:

Contact:

Objectives:

On completion of this subject, students should:

Comprehend:

• the terminology of classifying and describing ordinary and partial differential equations;

• the concept of obtaining complete and general solutions;

• the role of Fourier series, Laplace transforms and special functions in providing solutions to such equations.

Have developed:

• a competent working knowledge on general methods to solve linear ordinary differential equations and partial differential equations;

• know how to use standard methods such as Laplace transforms, series solutions, separation of variables for obtaining solutions.

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.

Content:

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: