### MA5920 Partial Differential Equations

#### Course Details

First order partial differential equations: Linear, quasi-linear equations-Method of characteristics, Lagrange method. (6 lectures)

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 halfline, Inhomogeneous wave equation, Fourier Method. (13 lectures)

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. (13 lectures)

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. (8 lectures)

#### Course References:

Text Books:

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

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

Reference Books:

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

4. Tyn Myint-U and Lokenath Debnath, Linear Partial Differential Equations for Scientists and
Engineers, Fourth Edition, Birkhauser.

5. R.P. Agarwal and D. O'Regan, Ordinary and Partial Differential Equations, Springer- Verlag.