Authors:
- Approaches calculus and introductory analysis in a nonstandard way
- New edition extensively revised and updated
- Completely self-contained text
- Includes supplementary material: sn.pub/extras
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
About this book
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 emphasison 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
Authors and Affiliations
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Department of Mathematics, Temple University, Philadelphia, USA
Omar Hijab
Bibliographic Information
Book Title: Introduction to Calculus and Classical Analysis
Authors: Omar Hijab
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4419-9488-2
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Softcover ISBN: 978-1-4614-2842-8Published: 19 April 2013
eBook ISBN: 978-1-4419-9488-2Published: 19 March 2011
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 3
Number of Pages: XII, 364
Topics: Approximations and Expansions, Sequences, Series, Summability, Special Functions, Combinatorics