Module Details

	M Level	Second Semester	15


Aims

This module (divided into 5 parts) introduces a range of analytical and numerical methods for partial differential equations
arising in many areas of applied mathematics.   It focuses initially  on advanced analytical techniques
 for solution of both elliptic and parabolic PDEs and qualitative features of the solutions.
This is followed by an introduction to discretization methods and matrix analysis i.e.
* Applied Analysis
* Iterative Solution of Ax=b
* Finite Difference Method for PDEs
* Finite   Element Method for PDEs

The module is one of the few closely related to research work.

Here the Green identities are used in Parts 1, 4, 5. The ability and skill of working with
normal derivatives is emphasized in applying Green identities and in deriving a weak formulation 
for finite elements solution.  In part 4,  The derivation of an Euler-Lagrange equation in context of Calculus
of Variations should be challenging and of interests to all students.
The second part of a finite difference method and the third part of an iterative method are quite standard for 
numerical solution of PDEs.  In contrast, the final part of using piecewise functions over triangles for working out
the finite element equations should be both challenging and fun to a mathematician.