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Real Analysis : A Historical Approach

Real Analysis : A Historical Approach - 99 edition

Real Analysis : A Historical Approach - 99 edition

ISBN13: 9780471318521

ISBN10: 0471318523

Real Analysis : A Historical Approach by Saul Stahl - ISBN 9780471318521
Edition: 99
Copyright: 1999
Publisher: John Wiley & Sons, Inc.
Published:
International: No
Real Analysis : A Historical Approach by Saul Stahl - ISBN 9780471318521

ISBN13: 9780471318521

ISBN10: 0471318523

Edition: 99

Other Editions of Real Analysis : A Historical Approach


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Summary

A provocative look at the tools and history of real analysis

This new work from award-winning author Saul Stahl offers a real treat for students of analysis. Combining historical coverage with a superb introductory treatment, Real Analysis: A Historical Approach helps readers easily make the transition from concrete to abstract ideas.

The book begins with an exciting 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.

Ample exercises, illustrations, and appended excerpts from the original historical works complete this focused, unconventional, highly interesting book. It is an invaluable resource for mathematicians and educators seeking to gain insight into the true language of mathematics.

Table of Contents

Table of Contents

Archimedes and the Parabola.

Fermat, Differentiation, and Integration.

Newton's Calculus (Part 1).

Newton's Calculus (Part 2).

Euler.

The Real Numbers.

Sequences and Their Limits.

The Cauchy Property.

The Convergence of Infinite Series.

Series of Functions.

Continuity.

Differentiability.

Uniform Convergence.

The Vindication.

Appendices.

Solutions to Selected Exercises.

Bibliography.

Index.

Other Editions of Real Analysis : A Historical Approach

Real Analysis: Historical Approach by Saul Stahl - ISBN 9780470878903