# MATH303: Partial Differential Equations (Spring 2018)

## Topics Covered

Classification of second-order PDEs with constant coefficients; boundary value problems on an interval; Robin, Dirichlet, and von Neumann conditions; existence and uniqueness; separation of variables; eigenvalue problems and eigenfunction expansion; Fourier series and applications; inhomogenous problems; integral transform methods; the fundamental solution; Green functions; maximum-minimum principles; the method of characteristics; parabolic equations and the heat equation; elliptic equations and the Laplace equation; the steady-state and equilibrium problems for elliptic equations; the energy integral for the Laplace equation; the Dirichlet problem for the Laplace equation; wave propagation; the d'Alembert solution for hyperbolic equations; the Cauchy problem for hyperbolic equations; the method of characteristics.

## Course Information

**Instructor:**Renu Dhadwal (renu@flame.edu.in), Karpur Shukla (karpur.shukla@flame.edu.in or kshukla@alumni.cmu.edu)**Course Times:****Office Hours:**by appointment

## Course Texts:

*Partial Differential Equations: An Introduction*

## Grading Structure

- Assignments: 10%
- In-class exams: 30%
- Take-home exam: 20%
- Final exam: 30%
- Class participation: 10%