# Introduction to Calculus and Classical Analysis

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

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Textbook

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

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.

About the first edition:

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

calculus convergence differential equation integral integration real number

- 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
- Print ISBN 978-0-387-69315-6
- Online ISBN 978-0-387-69316-3
- Series Print ISSN 0172-6056
- Buy this book on publisher's site