MA 515, 2019

Lectures: Monday- 14:00-15:25, Thursday- 14:00-15:25, Class room- 216

Tutorials: Thursday- 10:35-11:30, Class room- 114

Office Hours: Monday- 16:30-15:30

Contact: Office room 115 A, Mathematics Dept., IIT Bombay, Powai, Email: deban@math.iitb.ac.in,

Objectives:

1. Solving 1st order PDEs- Method of characteristics, Cauchy problems, Monge cone.

2. Classification of 2nd order PDEs: Normal forms and characteristics,

3. Initial and boundary value problems: Lagrange-Green's identity, energy methods, stability theory, energy conservation and dispersion.

4. Laplace equation: Fundamental solution, Mean value property, Weak and strong maximum principal, Green's function, Poisson's formula, Dirichlet's principle, Perron's method (without proof).

5. Heat equation: Initial value problem, Fundamental solution, Weak and strong maximum principle and uniqueness results.

6. Wave equation: Uniqueness, D'Alembert's method, Method of spherical means and Duhamel's principle.

7.Solution Methods: Separation of variables for heat, Laplace and wave equations, transformation methods mostly Fourier transformation.