MA 5920   Partial Differential Equations

Course contents:

First order partial differential equations: Linear, quasi-linear and fully nonlinear equations-Lagrange and Charpit methods.

Second order partial differential equations: Classification and Canonical forms of equations in two independent variables, One dimensional wave equation- D'Alembert's solution, Reflection method for half-line, Inhomogeneous wave equation, Fourier Method.

One dimensional diffusion equation: Maximum Minimum principle for the diffusion equation, Diffusion equation on the whole line, Diffusion on the half-line, inhomogeneous equation on the whole line, Fourier method.

Laplace equation: Maximum -Minimum principle, Uniqueness of solutions; Solutions of Laplace equation in Cartesian and polar coordinates-Rectangular regions, circular regions, annular regions; Poison integral formula

Diffusion and wave equations in higher dimensions.

Text Books:

1.      Ioannis P Stavroulakis and Stepan A Tersian, Partial differential equations- an introduction with mathematica and maple, world - Scientific, Singapore, 1999

References:

1.      Jeffery Cooper, Introduction to partial differential equations with matlab, Birkhauser, 1998

2.      Clive R Chester, Techniques in partial differential equations, McGraw-Hill, 1971

3.      K Sankara Rao, Introduction to partial differential equations, Prentice Hall India,1997

4.      I. N. Sneddon, Elements of partial differential equations, McGraw-Hill, New York,1986

5.      W. E. Williams, Partial differential equations, Clarendon Press, Oxford, 1980.