Mathématiques et Informatique

Modelling is based on a range of applied mathematics tools. The book "Advanced mathematical methods for scientists and engineers", by Carl M. Bender and Steven A. Orszag ([1]), presents very common asymptotic methods in physics. The course focuses on an active reading of this book focusing on a selection of chapters particularly relevant for fluid mechanics. An approach of special functions (Airy, Bessel, ...) is performed using a Frobenius series, solutions of linear differential equations. The methods of the stationary phase and steepest descent, very present in the study of waves and instabilities, can describe the asymptotic behaviour of integrals with large parameters. Finally, three asymptotic methods are unavoidable in many research problems: boundary layer analysis, WKB theory and multiple scales methods. Beyond these main objectives of the course, assimilated through many exercises, an outreach to the contents of other chapters of the book is targeted.

[1]  « Advanced mathematical methods for scientists and engineers », Carl M. Bender et Steven A. Orszag, McGraw-Hill 1978