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＜電子ブック＞
Introduction to Calculus and Classical Analysis / by Omar Hijab
(Undergraduate Texts in Mathematics. ISSN:21975604)

版	2nd ed. 2007.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2007
本文言語	英語
大きさ	X, 342 p. 65 illus : online resource
著者標目	*Hijab, Omar author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Functions of real variables FREE:Analysis FREE:Real Functions
一般注記	The Set of Real Numbers -- Continuity -- Differentiation -- Integration -- Applications This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This second edition includes corrections as well as some additional material. Some features of the text: * The text is completely self-contained and starts with the real number axioms; * the integral is defined as the area under the graph, while the area is defined for every subset of the plane; * there is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; * there are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; * traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; * there are 366 problems. About the first edition: This is a very intriguing, decidedly unusual, and very satisfying treatment of calculus and introductory analysis. It's full of quirky little approaches to standard topics that make one wonder over and over again, "Why is it never done like this?" John Allen Paulos, author of Innumeracy and A Mathematician Reads the Newspaper HTTP:URL=https://doi.org/10.1007/978-0-387-69316-3

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