Real Analysis via Sequences and Series / by Charles H.C. Little, Kee L. Teo, Bruce van Brunt.

Format:

Book

Author/Creator:

Little, Charles H.C., Author.

Teo, Kee L., Author.

Van Brunt, B. (Bruce), Author.

Series:

Undergraduate Texts in Mathematics, 0172-6056

Language:

English

Subjects (All):

Functions of real variables.

Sequences (Mathematics).

Real Functions.

Sequences, Series, Summability.

Local Subjects:

Real Functions.

Sequences, Series, Summability.

Physical Description:

1 online resource (XI, 476 p. 27 illus.)

Edition:

1st ed. 2015.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 2015.

Language Note:

English

Summary:

This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results, and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e, and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.

Contents:

Preface

1. Introduction

2. Sequences

3. Series

4. Limits of Functions

5. Continuity

6. Differentiability

7. The Riemann Integral

8. Taylor Polynomials and Taylor Series

9. The Fixed Point Problem

10. Sequences of Functions

Bibliography

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Description based on publisher supplied metadata and other sources.

ISBN:

1-4939-2651-9

OCLC:

910877573