MATH6140 Advanced Mathematical Methods

 

Number of Credits : 4

 

PRE-REQUISITE: NONE

 

Course Description:

General Theory of Eigenvalues and Eigenfunctions, The Minimum Problem, Sequences of Eigenvalues and Eigenfunctions, Variational Properties, Eigenfunction Expansions, The Rayleigh-Ritz Approximation Method.

 

Green’s Functions Inverses of Differential Operators, Examples of Green’s Functions, The Neumann and Robin Functions, Source Functions for Parabolic Equations.

 

Cylindrical Eigenfunctions

Bessel Functions, Eigenfunctions for Finite Regions, The Fourier-Bessel Series, The Green’s Function, Modified Bessell Functions.

 

Spherical Eigenfunctions

Legendre Functions, Eigenfunctions of the Spherical Surface, Eigenfunctions for the Solid Sphere.

 

Assessment:

Coursework                                                      25%

Final Examination: One 3 hour written paper          75%