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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.
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Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.
Foundations of Mathematical Analysis Richard Johnsonbaugh, W.E.
The natural audience of such a course (and hence of such notes) is given by students who have already followed a three years curriculum in mathematics, or, at least, who are supposed to be already familiar with the notions of rational numbers, real ...
(ebook) Foundations of Mathematical Analysis (9780817682927) from Dymocks online store. Mathematical analysis is fundamental to the undergraduate....
The modern foundations of mathematical analysis were established in 17th century Europe.