Real Analysis via Sequences and Series

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Calculus
Cover of the book Real Analysis via Sequences and Series by Charles H.C. Little, Kee L. Teo, Bruce van Brunt, Springer New York
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Author: Charles H.C. Little, Kee L. Teo, Bruce van Brunt ISBN: 9781493926510
Publisher: Springer New York Publication: May 28, 2015
Imprint: Springer Language: English
Author: Charles H.C. Little, Kee L. Teo, Bruce van Brunt
ISBN: 9781493926510
Publisher: Springer New York
Publication: May 28, 2015
Imprint: Springer
Language: English

This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.

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This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.

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