Undergraduate Texts in Mathematics

Elementary Analysis

The Theory of Calculus

Authors: Ross, Kenneth A.

  • 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 
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eBook $44.99
price for USA (gross)
  • ISBN 978-1-4614-6271-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.95
price for USA
  • ISBN 978-1-4614-6270-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.95
price for USA
  • ISBN 978-1-4939-0128-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
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About this Textbook

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.

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.

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)


Table of contents (7 chapters)

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-1-4614-6271-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.95
price for USA
  • ISBN 978-1-4614-6270-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.95
price for USA
  • ISBN 978-1-4939-0128-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Elementary Analysis
Book Subtitle
The Theory of Calculus
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-1-4614-6271-2
DOI
10.1007/978-1-4614-6271-2
Hardcover ISBN
978-1-4614-6270-5
Softcover ISBN
978-1-4939-0128-9
Series ISSN
0172-6056
Edition Number
2
Number of Pages
XII, 412
Topics