L. C. Evans, "Partial Differential Equations";
Coure notes of prof. A. Fasano
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
