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Foundations Of Mathematical Analysis (Dover Books On Mathematics)
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This classroomtested 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. Upperlevel 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 selfcontained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a onesemester introduction to limits. Subsequent chapters discuss differential calculus of the real line, the RiemannStieltjes 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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