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Undergraduate Texts in Mathematics

Introduction to Calculus and Classical Analysis

Authors: Hijab, Omar

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  • Approaches calculus and introductory analysis in a nonstandard way
  • New edition extensively revised and updated
  • Completely self-contained text
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  • ISBN 978-1-4419-9488-2
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About this Textbook

This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This third 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;
  • There are 385 problems with all the solutions at the back of the text.

Reviews

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


Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-1-4419-9488-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.95
price for USA in USD
  • ISBN 978-1-4614-2842-8
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • 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
Introduction to Calculus and Classical Analysis
Authors
Series Title
Undergraduate Texts in Mathematics
Copyright
2011
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media, LLC
eBook ISBN
978-1-4419-9488-2
DOI
10.1007/978-1-4419-9488-2
Softcover ISBN
978-1-4614-2842-8
Series ISSN
0172-6056
Edition Number
3
Number of Pages
XII, 364
Topics

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