Synopses & Reviews
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.and#160;
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.and#160;
Synopsis
Definitive look at modern analysis, with views ofand#160;applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis.and#160;More than 750 exercises; someand#160;hints and solutions. 1981 edition.
Synopsis
This definitive look at modern analysis includes applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. The self-contained treatment contains clear explanations and all the appropriate theorems and proofs. A selection of more than 750 exercises includes some hints and solutions. 1981 edition.
About the Author
Richard Johnsonbaugh was a professor at DePaul University.
Table of Contents
PrefacePreface to the Dover EditionI Sets and FunctionsII The Real Number SystemIII Set EquivalenceIV Sequences of Real NumbersV Infinite SeriesVI Limits of Real-Valued Functions and Continuous Functions on the Real LineVII Metric SpacesVIII Differential Calculus of the Real LineIX The Riemann-Stieltjes IntegralX Sequences and Series of FunctionsXI Transcendental FunctionsXII Inner Product Spaces and Fourier SpacesXIII Normed Linear Spaces and the Riesz Representation TheoremXIV The Lebesgue IntegralAppendix: Vector SpacesReferencesHints to Selected ExercisesIndexErrataand#160;