Analysis for applied mathematics

Ward Cheney - Collection Graduate Texts in Mathematics

450 pages, parution le 15/01/2001

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Résumé

This textbook is designed for a course at the beginning graduate level, serving students of mathematics, engineering, physics, and other sciences. Its goal is to provide the analytical tools, concepts, and viewpoints needed for modern applied mathematics.The book begins with a gentle introduction to normed linear spaces and Hilbert spaces, taking the reader as far as the Spectral Theorem for compact normal operators on a Hilbert space. It then discusses calculus in normed linear spaces, leading up to topics in the calculus of variations and optimization theory.

Next, the book treats various practical methods for solving problems that arise in applied mathematics, such as differential equations, boundary value problems, and integral equations. Here the reader finds the Galerkin method, the method of iteration, Newton's method, projection techniques, homotopy methods, and other pragmatic approaches to the difficult equations confronting applied mathematicians.To prepare the reader for work in the modern theory of partial differential equations, the subject of distributions is taken up next. A chapter on the Fourier transform and its applications follows, and includes a section on Sobolev spaces. Another chapter discusses topics that are related to those in the earlier parts of the book but are more specialized, such as separation theorems, selection theorems, Fredholm theory, and linear topological spaces. The final chapter provides a concise account of measure theory and integration.

The author has served in academia and in industry, having been employed by, or served as a consultant to, Convair Astronautics, Space Technology Laboratories, Aerospace Incorporated, Boeing Aircraft, and International Business Machines. He served on the faculties of The University of Kansas, Iowa State University, The University of California at Los Angeles, Michigan State University, Lund University (Sweden), and The University of Texas, where he is at present.

Sommaire

Normed linear spaces
Hilbert Spaces
Calculus in Banach spaces
Basic approximate methods of analysis
Distribution
The Fourier Transform
Additional Topics
Measure and integration

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	PAPIER
Éditeur(s)	Springer
Auteur(s)	Ward Cheney
Collection	Graduate Texts in Mathematics
Parution	15/01/2001
Nb. de pages	450
Format	16 x 24
Couverture	Relié
Poids	754g
Intérieur	Noir et Blanc
EAN13	9780387952796
ISBN13	978-0-387-95279-6