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Real Analysis via Sequences and Series

Real Analysis via Sequences and Series by Charles H.C. Little
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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.

Springer New York; May 2015
483 pages; ISBN 9781493926510
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Title: Real Analysis via Sequences and Series
Author: Charles H.C. Little; Kee L. Teo; Bruce van Brunt
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