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EDITORIAL INFORMATION

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.

(Extracted from the back cover).

GENERAL TABLE OF CONTENTS

 

-Preface.
-Acknowledgments.

-Contents.

-1. Archimedes and the Parabola.

-2. Fermat, Differentiation, and Integration.

-3. Newton's Calculus (Part 1).
-4. Newton's Calculus (Part 2).
-5. Euler.
-6. The Real Numbers.
-7. Sequences and Their Limits.
-8. The Cauchy Property.
-9. The Convergence of Infinite Series.
-10. Series of Functions.
-11. Continuity.
-12. Differentiability.
-13. Uniform Convergence.
-14. The Vindication.
-Appendix A: Excerpts from "Quadrature of the Parabola" by Archimedes.
-Appendix B: On a Method for the Evaluation of Maxima and Minima by Pierre de Fermat.
-Appendix C: From a Letter to Henry Oldenburg on the Binomial Series (June 13, 1676) by Isaac Newton.
-Appendix D: From a Letter to Henry Oldenburg on the Binomial Series (October 24, 1676) by Isaac Newton.
-Appendix E: Excerpts from "Of Analysis by Equations of an Infinite Number of Terms" by Isaac Newton.
-Appendix F: Excerpts from "Subsiduum Calculi Sinuum" by Leonhard Euler.
-Solutions to Selected Exercises.

-Bibliography.

-Index.