Introduction to calculus and classical analysis [electronic resource] / Omar Hijab.

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Introduction to calculus and classical analysis [electronic resource] / Omar Hijab.

Fourth edition.

9783319284002 (electronic book)
3319284002 (electronic book)
9783319283999 print

Cham : Springer, 2016.

English

1 online resource (xiii, 427 pages) : illustrations.

10.1007/978-3-319-28400-2 doi

QA303.2

515

This completely self-contained text is intended either for a course in honors calculus or for an introduction to analysis. Beginning with the real number axioms, and involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate math majors. This fourth edition includes an additional chapter on the fundamental theorems in their full Lebesgue generality, based on the Sunrise Lemma. Key features of this text include: ℓ́Ø Applications from several 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; ℓ́Ø A heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; ℓ́Ø Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; ℓ́Ø A self-contained treatment of the fundamental theorems of calculus in the general case using the Sunrise Lemma; ℓ́Ø The integral is defined as the area under the graph, while the area is defined for every subset of the plane; ℓ́Ø 450 problems with all the solutions presented at the back of the text. Reviews: "Chapter 5 isℓ́Œan astonishing tour de forceℓ́Œ" ℓ́ℓSteven G. Krantz, American Math. Monthly "For a treatmentℓ́Œ[of infinite products and Bernoulli series] that is very close to Eulerℓ́ℓs and even more elementaryℓ́Œ" ℓ́ℓV. S. Varadarajan, Bulletin AMS "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?'" ℓ́ℓJohn Allen Paulos, Author of Innumeracy and A Mathematician Reads the Newspaper.

Includes bibliographical references and index.

Access limited to authorized users.

Online resource; title from PDF title page (SpringerLink, viewed February 19, 2016).

Undergraduate texts in mathematics.

Print version: 9783319283999

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