Real Analysis via Sequences and Series

Charles Little,Kee L. Teo,Bruce van Brunt

Real Analysis via Sequences and Series
Format
Hardback
Publisher
Springer-Verlag New York Inc.
Country
United States
Published
29 May 2015
Pages
476
ISBN
9781493926503

Real Analysis via Sequences and Series

Charles Little,Kee L. Teo,Bruce van Brunt

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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
and e and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.

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