Course Unit


Applied partial differential equations

Unit Coordinator: Corrado Lattanzio
Programme: Erasmus Mundus
ECTS Credits: 6
Semester: 1
Year: 1
Campus: University of L'Aquila
Language: English

Students will know basic of properties (existence, uniqueness, etc.) and techniques (characteristics, separation of variables, Fourier methods, Green's functions, similarity solutions, etc.) to solve basic PDEs (conservation laws, heat equation, Laplace equation, wave equation).


Semilinear first order PDE's. Method of characteristics. Partial differential equations of second order. Classification, canonical forms. Well posed problems, IBV problems. The heat equation. Derivation, maximum principle, fundamental solution. Laplace's and Poisson's equations. Maximum principle, fundamental solution and Green's functions. The wave equation. One dimensional equation, fundamental solution and D'Alembert formula. Fundamental solution in three dimensions and strong Huygens' principle, Kirchoff’s formula. Method of descent and solution formula in two dimensions.

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A network of 12 European Universities, coordinated by Department of Information Engineering, Computer Science and Mathematics (DISIM) at University of L'Aquila in Italy (UAQ)