Real Analysis via Sequences and Series

Real Analysis via Sequences and Series
Author: Charles H.C. Little
Publisher: Springer
Total Pages: 483
Release: 2015-05-28
Genre: Mathematics
ISBN: 1493926519


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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.


Real Analysis via Sequences and Series
Language: en
Pages: 483
Authors: Charles H.C. Little
Categories: Mathematics
Type: BOOK - Published: 2015-05-28 - Publisher: Springer

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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
Real Analysis (Classic Version)
Language: en
Pages: 0
Authors: Halsey Royden
Categories: Functional analysis
Type: BOOK - Published: 2017-02-13 - Publisher: Pearson Modern Classics for Advanced Mathematics Series

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This text is designed for graduate-level courses in real analysis. Real Analysis, 4th Edition, covers the basic material that every graduate student should know
A Sequential Introduction To Real Analysis
Language: en
Pages: 274
Authors: J Martin Speight
Categories: Mathematics
Type: BOOK - Published: 2015-10-29 - Publisher: World Scientific Publishing Company

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Real analysis provides the fundamental underpinnings for calculus, arguably the most useful and influential mathematical idea ever invented. It is a core subjec
Basic Real Analysis
Language: en
Pages: 671
Authors: Anthony W. Knapp
Categories: Mathematics
Type: BOOK - Published: 2007-10-04 - Publisher: Springer Science & Business Media

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Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment
Real Analysis
Language: en
Pages: 170
Authors: Frank Morgan
Categories: Mathematics
Type: BOOK - Published: 2005 - Publisher: American Mathematical Soc.

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Real Analysis builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in $\mathbb{R}^n$. It gives t