A Handbook of Real Variables

With Applications to Differential Equations and Fourier Analysis

Steven G. Krantz

201 pages, parution le 26/01/2004

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Résumé

This concise, well-written handbook provides a distillation of the theory of real variables with a particular focus on the subject's significant applications to differential equations and Fourier analysis. Ideal for the working engineer or scientist, the book uses ample examples and brief explanations---without a lot of proofs or axiomatic machinery---to give the reader quick, easy access to all of the key concepts and touchstone results of real analysis. Topics are systematically developed, beginning with sequences and series, and proceeding to topology, limits, continuity, derivatives, and Riemann integration. In the second half of the work, Taylor series, the Weierstrass Approximation Theorem, Fourier series, the Baire Category Theorem, and the Ascoli--Arzela Theorem are carefully discussed. Picard iteration and differential equations are treated in detail in the final chapter.

Key features:

Completely self-contained, methodical exposition for the mathematically-inclined researcher; also valuable as a study guide for students
Realistic, meaningful connections to ordinary differential equations, boundary value problems, and Fourier analysis
Example-driven, incisive explanations of every important idea, with suitable cross-references for ease of use
Illuminating applications of many theorems, along with specific how-to hints and suggestions
Extensive bibliography and index

This unique handbook is a compilation of the major results, techniques, and applications of real analysis; it is a practical manual for physicists, engineers, economists, and others who use the fruits of real analysis but who do not necessarily have the time to appreciate all of the theory. Appropriate as a comprehensive reference or for a quick review, the "Handbook of Real Variables" will benefit a wide audience.

Written for:
Graduate students, researchers in physics, engineering, economics, applied mathematics, and mathematics

L'auteur - Steven G. Krantz

Steven G. Krantz, currently Professor and Chairman of Mathematics at Washington University in St. Louis, earned his PhD at Princeton University and has taught at UCLA, Princeton University and Pennsylvania State University. He is the recipient of the UCLA Alumni Foundation Distinguished Teaching Award, the MAA's Chauvenet Prize, the MAA Beckenbach Book Award, and the Outstanding Academic Book Award of the Current Review of Academic Libraries. He has written numerous books including: "Function Theory of Several Complex Variables," "Real Analysis and Foundations," "The Geometry of Domains in Space" (with Harold R. Parks), "Function Theory of One Complex Variable" (with Robert E. Greene), "The Implicit Function Theorem" (with Harold Parks). "Complex Analysis: The Geometric Viewpoint," and" A Panorama of Harmonic Analysis" (both for the MAA). He is also the author of over one-hundred research articles.

Sommaire

Preface
Basics
Sequences
Series
The Topology of the Real Line
Limits and the Continuity of Functions
The Derivative
The Integral
Sequences and Series of Functions
Some Special Functions
Advanced Topics
Differential Equations
Glossary of Terms from Real Variable Theory
List of Notation
A Guide to the Literature
Bibliography
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Steven G. Krantz
Parution	26/01/2004
Nb. de pages	201
Format	16 x 24
Couverture	Broché
Poids	500g
Intérieur	Noir et Blanc
EAN13	9780817643294
ISBN13	978-0-8176-4329-4