Study of some fundamental equations that are applied in mathematical physics domains.
Solving first order equations by applying the method of characteristics.
Classifications and study of some properties of linear second order PDE in R2
L. C. Evans, "Partial Differential Equations";
Lecture notes
Learning Objectives
Get familiar with the equations which are at the basis of the Mathematical Physics. Learn different methods to find solutions in a closed form for few representative cases of elliptic, parabolic, hyperbolic partial differential equations
Prerequisites
Calculus II
Teaching Methods
Teaching courses
Type of Assessment
Oral exam
Course program
Definition of the equations which are at the basis of the Mathematical Physics. Laplace equation, Poisson equation, transport equation, wave equation. Heuristic derivation of the equations.
Study of the Laplace equation: maximum principle, uniqueness, mean property. Wave equation: solution of d'Alembert. Kirchhoff formula. Heat equation: weak maximum principle, uniqueness in bounded domains, solution of the Cauchy problem, uniqueness