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Real Analysis via Sequences and Series

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Real Analysis via Sequences and Series/ by Charles H.C. Little, Kee L. Teo, Bruce van Brunt.
作者:	Little, Charles H.C.
其他作者:	Teo, Kee L.
面頁冊數:	XI, 476 p. 27 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Functions of real variables. -
電子資源:	https://doi.org/10.1007/978-1-4939-2651-0
ISBN:	9781493926510

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

Real Analysis via Sequences and Series[electronic resource] /by Charles H.C. Little, Kee L. Teo, Bruce van Brunt. - 1st ed. 2015. - XI, 476 p. 27 illus.online resource. - Undergraduate Texts in Mathematics,0172-6056. - Undergraduate Texts in Mathematics,.

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.

ISBN: 9781493926510

Standard No.: 10.1007/978-1-4939-2651-0doiSubjects--Topical Terms:

792248
Functions of real variables.

LC Class. No.: QA331.5

Dewey Class. No.: 515.8

Real Analysis via Sequences and Series
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