CHOIX1

Description : Partial differential equations (PDEs) are nowadays an essential mathematical tool for studying and understanding physical and biological phenomena. Their great complexity often makes them impossible to solve analytically; hence the need to use numerical solution methods.

This course is dedicated to the introduction of PDEs, then to their resolution using well-known numerical schemes such as finite difference and finite volume methods. A more analytical part, necessary for the introduction of finite volume methods, will be devoted to the analytical resolution of scalar conservation laws. Four programming practical exercises will illustrate the scientific computing tools seen in class with simple examples.

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The construction of solutions to partial differential equations (PDEs) and the theoretical study of their qualitative behavior is essentially based on the use of analytical results, and in particular functional analysis. This course introduces the first important tools for solving PDEs from analytical or geometrical points of view. These tools will be put to use in the study of a few examples of PDEs representative of major classes of equations.

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