## Seminar (Analysis): Applied asymptotic analysis, Wintersemester 2009/10

Ort und Termin
 Art: Termin: Ort: Beginn: SE 2 std. Geblockt Dez.-Jan.Mi 11:00-12:00Do 11:00-12:00 D103 (UZA4)S1 (Althanstr. 12) 3.12
Was Sie erwartet
The aim of this seminar is to learn some basic techniques in asymptotic analysis. It is one of the most important concepts in analysis and you encounter it already in the first semester when dealing with Taylor series, where a complicated function is replaced by a simple approximated which is valid in a certain regime. In fact, many problems in applications are not explicitly solvable, however, they often can be viewed as small perturbations of solvable models. Here is where asymptotic analysis comes into play and we frequently use it in a naive way without knowing the basic methods, their strengths, weaknesses, and pitfalls. In this seminar we will try to remedy this shortcoming by covering some topics (which can be chosen according to personal interests) from the introductory book by Miller [1].
Vorträge:
 Datum: Titel: Vortrgende(r): 16.12 The Nature of Asymptotic Approximations Ira Egorova 17.12 Laplace's Method for Asymptotic Expansions of Integrals 1 Anna Geyer 13.1 Laplace's Method for Asymptotic Expansions of Integrals 2 Anna Geyer 14.1 The Method of Steepest Descents for Asymptotic Expansions of Integrals 1 Jonathan Eckhardt 20.1 The Method of Steepest Descents for Asymptotic Expansions of Integrals 2 Jonathan Eckhardt 27.1 The Method of Stationary Phase for Asymptotic Analysis of Oscillatory Integrals 1 Kerstin Ammann 28.1 The Method of Stationary Phase for Asymptotic Analysis of Oscillatory Integrals 2 Kerstin Ammann

Literatur:

1. P. D. Miller, Applied Asymptotic Analysis, Amer. Mat. Soc., Providence, 2006.
2. J. D. Murray, Asymptotic Analysis, Springer, New York, 1984.
3. F. W.J. Olver, Asymptotics and Special Functions, A K Peters, Natick, 1997.
Zielgruppe
Studierende der Mathematik, Physik, ...
Auf Ihr Kommen freuen sich Ira Egorova und Gerald Teschl