Lectures: Tuesday- 14:00-15:25, Friday- 14:00-15:25, Class room- 216
Tutorials: Wednesday- 8:30-9:25, Class room- 216
Office Hours: Tuesday- 17:30-18:30
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.