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© 2013

Elementary Analysis

The Theory of Calculus

Benefits

  • Revised and updated second edition with new material

  • Text for a transition course between calculus and more advanced analysis courses

  • Contains new material on topics such as irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions

  • Includes new examples and improved proofs

Textbook

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Kenneth A. Ross
    Pages 1-32
  3. Kenneth A. Ross
    Pages 33-121
  4. Kenneth A. Ross
    Pages 123-185
  5. Kenneth A. Ross
    Pages 187-221
  6. Kenneth A. Ross
    Pages 223-268
  7. Kenneth A. Ross
    Pages 269-338
  8. Kenneth A. Ross
    Pages 339-364
  9. Back Matter
    Pages 365-409

About this book

Introduction

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.

Review from 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.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably."

—MATHEMATICAL REVIEWS

Keywords

Bolzano-Weierstrass theorem L'Hospital's rule Riemann integral Riemann-Stieltjes integral Taylor's theorem continuous functions differentiation elementary analysis fundamental theorem of calculus integration limits of sequences mean value theorem monotone subsequences nowhere-differentiable functions power series rational zeros theorem

Authors and affiliations

  1. 1.EugeneUSA

About the authors

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.

Bibliographic information

  • Book Title Elementary Analysis
  • Book Subtitle The Theory of Calculus
  • Authors Kenneth A. Ross
  • Series Title Undergraduate Texts in Mathematics
  • Series Abbreviated Title Undergraduate Texts Mathematics
  • DOI https://doi.org/10.1007/978-1-4614-6271-2
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-1-4614-6270-5
  • Softcover ISBN 978-1-4939-0128-9
  • eBook ISBN 978-1-4614-6271-2
  • Series ISSN 0172-6056
  • Edition Number 2
  • Number of Pages XII, 412
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
    Real Functions
  • Buy this book on publisher's site
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Reviews

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)