Real Analysis
An Historical Approach
Seiten
1999
John Wiley & Sons Inc (Verlag)
978-0-471-31852-1 (ISBN)
John Wiley & Sons Inc (Verlag)
978-0-471-31852-1 (ISBN)
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This look at the tools and history of real analysis by author Saul Stahl combines historical coverage with a helpful introductory treatment. 'Real Analysis: A Historical Approach' helps readers easily make the transition from concrete to abstract ideas.
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.
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.
SAUL STAHL, PhD, is Professor of Mathematics at the University of Kansas. The recipient of the Carl S. Allendoerfer Award from the Mathematical Association of America in 1986 for excellence in expository writing, Dr. Stahl has published over 30 articles as well as three books, including Introductory Modern Algebra: A Historical Approach, also from Wiley.
Archimedes and the parabola; Fermat, differentiation, and integration; Newton's calculus I; Newton's calculus II; 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.
Zusatzinfo | Illustrations |
---|---|
Verlagsort | New York |
Sprache | englisch |
Maße | 159 x 239 mm |
Gewicht | 520 g |
Einbandart | gebunden |
Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik | |
ISBN-10 | 0-471-31852-3 / 0471318523 |
ISBN-13 | 978-0-471-31852-1 / 9780471318521 |
Zustand | Neuware |
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