Applied Asymptotic Analysis

Erscheinungsjahr 2006
ISBN: 978-0-8218-4078-8
Verlag: American Mathematical Society

Buch, Englisch, Band 75, 475 Seiten, Gewicht: 1361 g

Reihe: Graduate Studies in Mathematics

This book is a survey of asymptotic methods set in the current applied research context of wave propagation. It stresses rigorous analysis in addition to formal manipulations. Asymptotic expansions developed in the text are justified rigorously, and students are shown how to obtain solid error estimates for asymptotic formulae. The book relates examples and exercises to subjects of current research interest, such as the problem of locating the zeros of Taylor polynomials of entire
nonvanishing functions and the problem of counting integer lattice points in subsets of the plane with various geometrical properties of the boundary. The book is intended for a beginning graduate course on asymptotic analysis in applied mathematics and is aimed at students of pure and applied mathematics as well as science and engineering. The basic prerequisite is a background in differential equations, linear algebra, advanced calculus, and complex variables at the level of introductory undergraduate courses on these subjects. The book is ideally suited to the needs of a graduate student who, on the one hand, wants to learn basic applied mathematics, and on the other, wants to understand what is needed to make the various arguments rigorous. Down here in the Village, this is known as the Courant point of view!! --Percy Deift, Courant Institute, New York

Autoren/Hrsg.

Miller, Peter D.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe

Über Autor(innen)

Peter D. Miller is an associate professor of mathematics at the University of Michigan at Ann Arbor. He earned a Ph.D. in Applied Mathematics from the University of Arizona and has held positions at the Australian National University (Canberra) and Monash University (Melbourne). His current research interests lie in singular limits for integrable systems.