Foundations of Mathematical Analysis (eBook)

Richard Johnsonbaugh, W.E. Pfaffenberger (Autoren)

eBook Download: EPUB

2012
448 Seiten
Dover Publications (Verlag)
978-0-486-13477-2 (ISBN)

Infos

Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

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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.

Autor

Richard Johnsonbaugh was a professor at DePaul University.

Inhalt

Preface Preface 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 ExercisesIndexErrata

Produkt-Details

• Erscheint lt. Verlag: 11.9.2012
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 140 x 140 mm
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: Applied Statistics • college calculus • college level math • Differential Calculus • Differential Equations • foundational math • Fourier series • Functional Analysis • graduate level math • Inner product spaces • Lebesgue integral • limit concept • Mathematical Analysis • modern analysis • Numerical analysis • Riemann Stieltjes integral • Riesz representation theorem • Sequences and Series of functions • transcendental functions
• ISBN-10: 0-486-13477-6 / 0486134776
• ISBN-13: 978-0-486-13477-2 / 9780486134772