# Elementary Analysis

## The Theory of Calculus

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

Textbook

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

For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging.

The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.

Review from the first edition:

"This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably."

—MATHEMATICAL REVIEWS

Bolzano-Weierstrass theorem L'Hospital's rule Riemann integral Riemann-Stieltjes integral Taylor's theorem continuous functions differentiation elementary analysis fundamental theorem of calculus integration limits of sequences mean value theorem monotone subsequences nowhere-differentiable functions power series rational zeros theorem

- DOI https://doi.org/10.1007/978-1-4614-6271-2
- Copyright Information Springer Science+Business Media New York 2013
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-1-4614-6270-5
- Online ISBN 978-1-4614-6271-2
- Series Print ISSN 0172-6056
- Buy this book on publisher's site