Undergraduate Texts in Mathematics

Introduction to Calculus and Classical Analysis

Authors: Hijab, Omar

  • Approaches calculus and introductory analysis in a nonstandard way
  • New edition extensively revised and updated
  • Completely self-contained text
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eBook $44.99
price for USA (gross)
  • ISBN 978-3-319-28400-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
  • ISBN 978-3-319-28399-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

Involving rigorous analysis, computational dexterity, and a breadth of applications, this text is ideal for an undergraduate honors calculus course or for an introduction to analysis. This fourth 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;

• self-contained treatment of the fundamental theorems of calculus in the general case using the Sunrise Lemma

• There are 450 problems with all the solutions at the back of the text.

Reviews from previous editions:

"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

"Chapter 5 is... an astonishing tour de force"

—Steven G. Krantz, The American Mathematical Monthly

"For a treatment [of infinite products and the Bernoulli series] that is very close to Euler’s and even more elementary..." — V.S. Varadarajan, Bulletin of the American Mathematical Society 



About the authors

Omar Hijab is Professor of Mathematics and Associate Dean for Faculty Affairs, Information Technology, and Operations in the College of Science and Technology at Temple University. He received his Ph.D. in Mathematics from the University of California, Berkeley, and has served previously as Chair of the Department of Mathematics at Temple University. His research interests include systems theory and control; probability theory and stochastic processes; differential equations; mathematical physics; and optimization.

Video

Table of contents (6 chapters)

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-319-28400-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
  • ISBN 978-3-319-28399-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Calculus and Classical Analysis
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-28400-2
DOI
10.1007/978-3-319-28400-2
Hardcover ISBN
978-3-319-28399-9
Series ISSN
0172-6056
Edition Number
4
Number of Pages
XIII, 427
Number of Illustrations and Tables
68 b/w illustrations, 1 illustrations in colour
Topics