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Real Analysis Via Sequences and Series, Paperback by Little, Charles; Kee, Te...
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Artikelmerkmale
- Artikelzustand
- Book Title
- Real Analysis Via Sequences and Series
- ISBN
- 9781493941810
Über dieses Produkt
Product Identifiers
Publisher
Springer New York
ISBN-10
149394181X
ISBN-13
9781493941810
eBay Product ID (ePID)
28038374344
Product Key Features
Number of Pages
Xi, 476 Pages
Language
English
Publication Name
Real Analysis Via Sequences and Series
Subject
Functional Analysis, General, Mathematical Analysis
Publication Year
2016
Type
Textbook
Subject Area
Mathematics
Series
Undergraduate Texts in Mathematics Ser.
Format
Trade Paperback
Dimensions
Item Weight
258 Oz
Item Length
9.3 in
Item Width
6.1 in
Additional Product Features
Reviews
"The list of main topics covered is quite standard: sequences, series, limits, continuity, differentiation, Riemann integration, uniform convergence ... . This is a well-written textbook with an abundance of worked examples and exercises that is intended for a first course in analysis with modest ambitions." (Brian S. Thomson, Mathematical Reviews, March, 2016) "The authors ... introduce sequences and series at the beginning and build the fundamental concepts of analysis from them. ... it achieves the same goal of introducing students to mathematical rigor and basic concepts and results in real analysis. ... Summing Up: Recommended. Upper-division undergraduates." (D. Z. Spicer, Choice, Vol. 53 (5), January, 2016) "This textbook is based on the central idea that concepts such as continuity, differentiation and integration are approached via the concepts of sequences and series. ... Most of the sections are followed by exercises. The textbook is recommended for a first course in mathematical analysis." (Sorin Gheorghe Gal, zbMATH, Vol. 1325.26002, 2016)
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
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.
Synopsis
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 and e and a treatment of Newton's method as a special instance of finding fixed points of iterated functions., 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.
LC Classification Number
QA331.5
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