Real Analysis via Sequences and Series

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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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ReiheUndergraduate Texts in Mathematics
ISBN 9781493941810
Sprache Englisch
Ausgabe Softcover reprint of the original 1st ed. 2015
Erscheinungsdatum 09.10.2016
Umfang 476 Seiten
Genre Mathematik/Analysis
Format Taschenbuch
Verlag Springer US
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