Foundations of Mathematical Analysis

Richard Johnsonbaugh, W.E. Pfaffenberger

430 pages, parution le 03/03/2003

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Résumé

This classroom-tested volume offers students of mathematics not only a well-defined view of the basics of modern analysis but also a broad spectrum of the ways in which analysis can be applied to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis.
A self-contained textbook, it offers the background necessary for a firm grasp of the limit concept. (The first seven chapters could constitute a one-semester course on introduction to limits.) Subsequent chapters examine differential calculus of the real line, the Riemann-Stieltjes integral, sequences and series of functions, transcendental functions, inner product spaces and Fourier series, normed linear spaces and the Riesz representation theorem, and the Lebesgue integral. Supplementary materials include an appendix on vector spaces and more than 750 exercises of varying degrees of difficulty (hints and solutions to selected exercises, indicated by an asterisk, appear at the back of the book).
Upper-level undergraduate students with a background in calculus will benefit from the teachings of this volume, as will beginning graduate students seeking a firm grounding in modern analysis.
Dover (2002) slightly corrected republication of the edition published by Marcel Dekker, Inc., New York, 1981. Preface. Preface to Dover edition. Index. Bibliography. Appendix. Hints and Solutions to Selected Exercises. 34 Figures. xii*428pp. 5% x 8y2. Paperbound.

Contents

Sets and Functions
The Real Number System
Set Equivalence
Sequences of Real Numbers
Infinite Series
Limits of Real-Valued Functions and Continuous Functions on the Real Line
Metric Spaces
Differential Calculus of the Real Line
The Riemann-Stieltjes Integral
Sequences and Series of Functions
Transcendental Functions
Inner Product Spaces and Fourier Series
Normed Linear Spaces and the Riesz Representation Theorem
The Lebesgue Integral

L'auteur - Richard Johnsonbaugh

Richard Johnsonbaugh is Professor Emeritus of Computer Science at DePaul University. He has degrees in computer science and mathematics from the University of Oregon, Yale University, and the University of Illinois at Chicago. He is the author of numerous articles and books, including Discrete Mathematics, Fifth Edition, and, with co-author Martin Kalin, Object-Oriented Programming in C++, Second Edition, Applications Programming in C++, and Applications Programming in ANSI C, Third Edition.

Caractéristiques techniques

	PAPIER
Éditeur(s)	Dover
Auteur(s)	Richard Johnsonbaugh, W.E. Pfaffenberger
Parution	03/03/2003
Nb. de pages	430
Format	13,5 x 21,5
Couverture	Broché
Poids	460g
Intérieur	Noir et Blanc
EAN13	9780486421742