Partial Differential Equations

Por: Swayam . en: ,

Week 1:Introduction, First order partial differential equations, Method of characteristicsWeek 2:Cauchy problem for Quasilinear first order partial differential equationsWeek 3:Cauchy problem for fully nonlinear first order partial differential equationsWeek 4:Classification of Second order partial differential equations and Canonical formsWeek 5:Wave equation: d’Alembert’s formula, Solution of wave equation on bounded domainsWeek 6:Wave equation: Solution by method of separation of variables, Wave equation in two and three space dimensionsWeek 7:Wave equation: Parallelogram identity, Domain of dependence, Domain of influence, Causality principleWeek 8:Wave equation: Finite speed of propagation, Conservation of energy, Huygens principle, Propagation of confined disturbancesWeek 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.