Partial Differential Equations

The objective of this introductory course on partial differential equations is to provide their basic properties as well as the techniques to solve some such equations.

* First-order equations, Quasi-linear equations, general first-order equation for a function of two variables, Cauchy problem

* Wave equation, wave equation in two independent variables, Cauchy problem for hyperbolic equations in two independent variables

* Heat equation, the weak maximum principle for parabolic equations, Cauchy problem for heat equation, regularity of solutions to heat equation.

* Laplace equation, Green's formulas, harmonic functions, maximum principle for Laplace equation, Dirichlet problem, Green's function and Poisson's formula