This new edition of Real Analysis: A Historical Approachcontinues 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 toabstract ideas.
The book begins with an exciting sampling of classic and famousproblems first posed by some of the greatest mathematicians of alltime. Archimedes, Fermat, Newton, and Euler are each summoned inturn, illuminating the utility of infinite, power, andtrigonometric series in both pure and applied mathematics. Next, Dr. Stahl develops the basic tools of advanced calculus, whichintroduce the various aspects of the completeness of the realnumber system as well as sequential continuity anddifferentiability and lead to the Intermediate and Mean ValueTheorems. The Second Edition features:
A chapter on the Riemann integral, including the subject ofuniform continuity
Explicit coverage of the epsilon-delta convergence
A discussion of the modern preference for the viewpoint ofsequences over that of series
Throughout the book, numerous applications and examplesreinforce concepts and demonstrate the validity of historicalmethods and results, while appended excerpts from originalhistorical works shed light on the concerns of influentialmathematicians in addition to the difficulties encountered in theirwork. Each chapter concludes with exercises ranging in level ofcomplexity, and partial solutions are provided at the end of thebook.
Real Analysis: A Historical Approach, Second Edition isan ideal book for courses on real analysis and mathematicalanalysis at the undergraduate level. The book is also a valuableresource for secondary mathematics teachers and mathematicians.