**Duration:** 21 weeks

**Number of lectures per week:** 3

**Assessment:**

**End-of-year Examination:** One 3-hour examination

**Description: **

**Partial Differential Equations**

Expansion of functions in series of
eigenfunctions. Variational methods to finding approximations to
eigenvalues.

Method of separation of variables applied to problems involving the
Laplace equation, the wave equation and the heat-conduction equation.

Finite transforms applied to boundary value problems.

Infinite Fourier transform; Laplace Transform and Mellin Transform
applied to boundary value problems, (emphasis on contour integral
methods). Application of Laplace Transform to derivation of Laplace
integral solutions of ordinary differential equations.

Classification of p.d.e.'s. Theory of characteristics applied to wave
problems.

Application of dimensional analysis to p.d.e's.

Asymptotic expansions of integrals occurring in transform methods.

Jun 10, 1998