Real Analysis: A Historical Approach / Edition 2

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Overview

The book begins with sampling of classic and famous problems first posed by some of the greatest mathematicians of all time, Archimedes, Fermat, Newton, and Euler are each summoned in turn - illuminating the utility of infinite, power, and trigonometric series in both pure and applied mathematics. Next, Dr. Stahl develops the basic tools of advanced calculus, introducing the various aspects of the completeness of the real number system, sequential continuity and differentiability, as well as uniform convergence. Finally, he presents applications and examples to reinforce concepts and demonstrate the validity of many of the historical methods and results.
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Editorial Reviews

Booknews
The textbook for a junior- or senior-level college introductory analysis course begins with a sampling of classic and famous problems first posed by the founders of mathematics, to illuminate the utility of infinite, power, and trigonometric series. Stahl (Mathematics, University of Kansas) then develops the basic tools of advanced calculus, and presents examples to reinforce concepts and demonstrate the validity of many of the historical methods and results. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780470878903
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 8/30/2011
  • Edition description: New Edition
  • Edition number: 2
  • Pages: 316
  • Product dimensions: 6.40 (w) x 9.30 (h) x 0.80 (d)

Meet the Author

SAUL STAHL, PhD, is Professor in the Department of Mathematics at The University of Kansas. He has published numerous journal articles in his areas of research interest, which include combinatorics, discrete mathematics, and topological graph theory. Dr. Stahl is the author of Introductory Modern Algebra: A Historical Approach and Introduction to Topology and Geometry, both published by Wiley. He was awarded the Carl B. Allendoerfer Award from the Mathematical Association of America for expository articles in both 1986 and 2006.
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Table of Contents

Preface
Acknowledgments
1 Archimedes and the Parabola 1
2 Fermat, Differentiation, and Integration 13
3 Newton's Calculus (Part 1) 19
4 Newton's Calculus (Part 2) 35
5 Euler 51
6 The Real Numbers 61
7 Sequences and Their Limits 85
8 The Cauchy Property 103
9 The Convergence of Infinite Series 115
10 Series of Functions 139
11 Continuity 149
12 Differentiability 169
13 Uniform Convergence 187
14 The Vindication 207
App. A Excerpts from "Quadrature of the Parabola" 217
App. B On a Method for the Evaluation of Maxima and Minima 225
App. C From a Letter to Henry Oldenburg on the Binomial Series (June 13, 1676) 227
App. D From a Letter to Henry Oldenburg on the Binomial Series (October 24, 1676) 229
App. E Excerpts from "Of Analysis by Equations of an Infinite Number of Terms" 233
App. F Excerpts from "Subsiduum Calculi Sinuum" 245
Solutions to Selected Exercises 247
Bibliography 264
Index 267
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