# Introduction to Calculus and Classical Analysis

Textbook

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

1. Front Matter
Pages I-X
2. Pages 1-41
3. Pages 43-62
4. Pages 63-114
5. Pages 115-171
6. Pages 173-248
7. Back Matter
Pages 249-338

### Introduction

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 second 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 366 problems.

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

### Keywords

calculus convergence differential equation integral integration real number

#### Authors and affiliations

1. 1.Department of MathematicsTemple UniversityPAUSA

### Bibliographic information

• Book Title Introduction to Calculus and Classical Analysis
• Authors Omar Hijab
• Series Title Undergraduate Texts in Mathematics
• DOI https://doi.org/10.1007/978-0-387-69316-3
• Copyright Information Springer-Verlag New York 2007
• Publisher Name Springer, New York, NY
• eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
• Hardcover ISBN 978-0-387-69315-6
• Softcover ISBN 978-1-4419-2409-4
• eBook ISBN 978-0-387-69316-3
• Series ISSN 0172-6056
• Edition Number 2
• Number of Pages X, 342
• Number of Illustrations 65 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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