Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics)

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9781461462705: Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics)
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For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs.  Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus.  Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging.

The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs.  New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.

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About the Author:

Kenneth A. Ross is currently an emeritus professor of mathematics at the University of Oregon.

Jorge M. López is currently professor of mathematics at the University of Puerto Rico.

Review:

From the reviews of the first edition:

"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis, such as continuity, convergence of sequences and series of numbers, and convergence of sequences and series of functions. There are many nontrivial examples and exercises, which illuminate and extend the material. The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and, in this reviewer’s opinion, has succeeded admirably."

―MATHEMATICAL REVIEWS

"This book occupies a niche between a calculus course and a full-blown real analysis course. ... I think the book should be viewed as a text for a bridge or transition course that happens to be about analysis ... . Lots of counterexamples. Most calculus books get the proof of the chain rule wrong, and Ross not only gives a correct proof but gives an example where the common mis-proof fails."

―Allen Stenger (The Mathematical Association of America, June, 2008)

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Other Popular Editions of the Same Title

9781493901289: Elementary Analysis: The Theory of Calculus (Undergraduate Texts in Mathematics)

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ISBN 10:  1493901281 ISBN 13:  9781493901289
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9781461462729: Elementary Analysis: The Theory of Calculus (Second Edition)

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Book Description Springer-Verlag New York Inc., United States, 2013. Hardback. Condition: New. 2nd ed. 2013. Language: English . Brand New Book. For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging.The second edition preserves the book s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton s method and the secant method, and continuous nowhere-differentiable functions. Seller Inventory # SPR9781461462705

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Book Description Springer, 2013. Condition: New. For three decades, this classic has been a must-have textbook for transitional courses from calculus to analysis, celebrated for its clear style and simple proofs. This edition adds material on the irrationality of pi, the Baire category theorem and more. Series: Undergraduate Texts in Mathematics. Num Pages: 412 pages, biography. BIC Classification: PBK; PBKB. Category: (P) Professional & Vocational. Dimension: 238 x 169 x 28. Weight in Grams: 772. . 2013. 2nd ed. 2013. Hardcover. . . . . . Seller Inventory # V9781461462705

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