ENGLISH

Real Analysis via Sequences and Series

By Charles H.C. Little , Kee L. Teo , Bruce van Brunt (auth.)

Book information

Publisher
Springer-Verlag New York
Year
2015
ISBN
978-1-4939-2650-3, 978-1-4939-2651-0
DOI
10.1007/978-1-4939-2651-0
Language
english
Format
PDF
Filesize
3 MB (3472504 bytes)
Series
Undergraduate Texts in Mathematics
Edition
1
Pages
476\483
Time added
2015-06-10 16:33:48
Real Functions; SequencesSeriesSummability

Description

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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