First order PDE
Characteristics method
existence of a solution of a first order PDE
Burger equation: the crossing characteristic problem
weak derivatives/weak solution of a first order PDE/Divergence theorem
wave equations: introduction of the equation and cauchy problem
Dalambert method
Energy of a wave ed unicita' del problema di cauchy
Heat equation: definition and the Cauchy problem
Maximum porinciple/Uniqueness of the solution of the heat equation
fundamental solution and solution of the cauche problem
Laplcace equation: the stationary case of the heat equation
Classification of second order PDE