To provide a grounding in elementary approaches to solution of some of the standard partial differential equations encountered in the applications of mathematics.

To introduce some of the basic tools (Fourier Series) used in the solution of differential equations and other applications of mathematics.

After completing the module students should:

-               be fluent in the solution of basic ordinary differential equations, including systems of first order equations;

-               be familiar with the concept of Fourier series and their potential application to the solution of both ordinary and partial differential equations;

-               be familiar with the concept of Laplace transforms and their potential application to the solution of both ordinary and partial differential equations;

-               be able to solve simple first order partial differential equations;

-               be able to solve the basic boundary value problems for second order linear partial differential equations using the method of separation of variables.

-               Fourier series; sine series, cosine series, full-range series for functions with arbitrary periods.

-               Second order linear partial differential equations; classification, Wave equation, Laplace''s equation, Diffusion equation and their applications, series solution of boundary value problems by the method of separation of variables.

-               First order partial differential equations; solution by method of characteristics.