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Foundations of Mathematical Analysis
by Richard Johnsonbaugh,W.E. Pfaffenberger
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.
Table of Contents for Foundations of Mathematical Analysis
| 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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