Overview


This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm grounding in modern analysis.
A self-contained text, it presents the necessary background on the limit ...
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Foundations of Mathematical Analysis

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Overview


This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm grounding in modern analysis.
A self-contained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a one-semester introduction to limits. Subsequent chapters discuss differential calculus of the real line, the Riemann-Stieltjes integral, sequences and series of functions, transcendental functions, inner product spaces and Fourier series, normed linear spaces and the Riesz representation theorem, and the Lebesgue integral. Supplementary materials include an appendix on vector spaces and more than 750 exercises of varying degrees of difficulty. Hints and solutions to selected exercises, indicated by an asterisk, appear at the back of the book.
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Editorial Reviews

From The Critics
This advanced calculus textbook reviews the concept of limits, then introduces the theory of Riemann-Stieltjes integration, sequences and series of functions, Fourier series, the Riesz representation theorem, and the Lebesque integral. A slightly corrected reprint of the 1981 edition published by Marcel Dekker. Annotation c. Book News, Inc., Portland, OR
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Product Details

  • ISBN-13: 9780486134772
  • Publisher: Dover Publications
  • Publication date: 8/14/2012
  • Series: Dover Books on Mathematics
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 448
  • Sales rank: 1,347,587
  • File size: 34 MB
  • Note: This product may take a few minutes to download.

Table of Contents


Preface
Preface to the Dover Edition
I Sets and Functions
II The Real Number System
III Set Equivalence
IV Sequences of Real Numbers
V Infinite Series
VI Limits of Real-Valued Functions and Continuous Functions on the Real Line
VII Metric Spaces
VIII Differential Calculus of the Real Line
IX The Riemann-Stieltjes Integral
X Sequences and Series of Functions
XI Transcendental Functions
XII Inner Product Spaces and Fourier Spaces
XIII Normed Linear Spaces and the Riesz Representation Theorem
XIV The Lebesgue Integral
Appendix: Vector Spaces
References
Hints to Selected Exercises
Index
Errata
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