TOPICS:
Distribution Theory; Sobolev Spaces; Elliptic PDE: weak solution, Lax-Milgram Lemma, regularity results, weak maximum principle, eigenvalue problems; Heat and Wave Equations: existence, uniqueness etc.; Semigroup theory; First Order Hyperbolic PDEs: Existence of weak solution, entropy solution; Finite Difference/Finite Volume Schemes for First Order Equations; Finite Element Methods for Elliptic and Heat Equations; optimal control for elliptic and heat equation & with hands on computation.
