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＜電子ブック＞
Real Analysis via Sequences and Series / by Charles H.C. Little, Kee L. Teo, Bruce van Brunt
(Undergraduate Texts in Mathematics. ISSN:21975604)

版	1st ed. 2015.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	2015
本文言語	英語
大きさ	XI, 476 p. 27 illus : online resource
著者標目	*Little, Charles H.C author Teo, Kee L author van Brunt, Bruce author SpringerLink (Online service)
件　名	LCSH:Functions of real variables LCSH:Sequences (Mathematics) FREE:Real Functions FREE:Sequences, Series, Summability
一般注記	Preface -- 1. Introduction -- 2. Sequences -- 3. Series -- 4. Limits of Functions -- 5. Continuity -- 6. Differentiability -- 7. The Riemann Integral -- 8. Taylor Polynomials and Taylor Series -- 9. The Fixed Point Problem -- 10. Sequences of Functions -- Bibliography -- Index 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 HTTP:URL=https://doi.org/10.1007/978-1-4939-2651-0

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