A provocative look at the tools and history of real analysis
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.
General
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