Week 1:Introduction, First order partial differential equations, Method of characteristics
Week 2:Cauchy problem for Quasilinear first order partial differential equations
Week 3:Cauchy problem for fully nonlinear first order partial differential equations
Week 4:Classification of Second order partial differential equations and Canonical forms
Week 5:Wave equation: d’Alembert’s formula, Solution of wave equation on bounded domains
Week 6:Wave equation: Solution by method of separation of variables, Wave equation in two and three space dimensions
Week 7:Wave equation: Parallelogram identity, Domain of dependence, Domain of influence, Causality principle
Week 8:Wave equation: Finite speed of propagation, Conservation of energy, Huygens principle, Propagation of confined disturbances
Week 9:Laplace equation: Boundary value problems, Fundamental solution, Construction of Greens function for Dirichlet problem posed on special domains.
Week 10:Laplace equation: Poisson’s formula, Solution of Dirichlet problem on a rectangle by method of separation of variables
Week 11:Laplace equation: Mean value property, Maximum principles, Dirichlet principle
Week 12:Heat equation: Fundamental solution, Solution of initial-boundary value problem by separation of variables method, Maximum principle.