Lecturer: Professor L.J. Crane
Date: 1996-97
Groups: Optional JS and SS Mathematics, SS Two-subject Moderatorship
Prerequisites: 131, 231
Duration: 21 weeks
Lectures per week: 3
Assessment:
Examinations: One 3-hour examination
Partial Differential Equations
Dirac Delta functions, Green's functions. Sturm-Liouville systems;
orthogonality of eigenfunctions; 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.