Real Analysis: A Historical Approach [9780470878903]

Overview

This new edition of Real Analysis: A Historical Approach continues to serve as an interesting read for students of analysis. Combining historical coverage with a superb introductory treatment, this book 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, which introduce the various aspects of the completeness of the real number system as well as sequential continuity and differentiability and lead to the Intermediate and Mean Value Theorems. The Second Edition features:

• A chapter on the Riemann integral, including the subject of uniform continuity

• Explicit coverage of the epsilon-delta convergence

• A discussion of the modern preference for the viewpoint of sequences over that of series

Throughout the book, numerous applications and examples reinforce concepts and demonstrate the validity of historical methods and results, while appended excerpts from original historical works shed light on the concerns of influential mathematicians in addition to the difficulties encountered in their work. Each chapter concludes with exercises ranging in level of complexity, and partial solutions are provided at the end of the book.

Real Analysis: A Historical Approach, Second Edition is an ideal book for courses on real analysis and mathematical analysis at the undergraduate level. The book is also a valuable resource for secondary mathematics teachers and mathematicians.