**PARTIAL
DIFFERENTIAL EQUATIONS**

First-order partial differential equations: Method of characteristics, Cauchy problem, Hamilton-Jacobi equations (including either the Hopf-Lax formula or introduction to viscosity solutions, as per audience interest).

Second order partial differential equations: The Cauchy problem and classification of second order equations, Holmgren’s uniqueness theorem; Laplace equation, Heat equation, Wave equation, Some methods of solutions, Variables separable method.

Brief introduction to the weak formulation (time permitting): Motivations, Dirichlet functional.

**Recommended Books**

- John, F., Partial Differential Equations, Springer (International Students Edition), 1971.
- Evans, L. C., Partial Differential Equations, AMS, 1998.