An introduction to analysis / Gerald G. Bilodeau, Paul R. Thie, G. E. Keough.

Format:

Book

Author/Creator:

Bilodeau, Gerald G.

Contributor:

Thie, Paul R., 1938-

Keough, G. E.

Hazel M. Hussong Fund.

Series:

International series in mathematics

Language:

English

Subjects (All):

Mathematical analysis.

Physical Description:

xiii, 333 pages : illustrations ; 24 cm.

Edition:

Second edition.

Other Title:

Analysis

Place of Publication:

Sudbury, Mass. : Jones and Bartlett Publishers, [2010]

Summary:

Completely revised and updated, the second edition of An Introduction to Analysis presents a concise and sharply focused introduction to the basic concepts of analysis---from the development of real numbers through uniform convergences of a sequence of functions---and includes coverage both of the analysis of functions of more than one variable and of differential equations. This student-friendly text maintains a cautious and deliberate pace, and examples and figures are used extensively to assist the reader in understanding the concepts and then applying them. Students will become actively engaged in the learning process with a broad and comprehensive collection of problems found at the end of each section.

New and Key Features of the Second Edition:

Includes an introduction to multivariable calculus with three new sections integrated into the development of the corresponding single variable material.

Includes a new final chapter on differential equations.

A wealth of exercises, varying in style and degree of difficulty, are found in each section, and enable students to test their understanding of key material. Hints are provided for the more difficult problems, and a number of problems are broken down into more manageable parts.

An introductory note speaks to instructors who may not have time to cover all material in the text, and includes comments on the interrelationship between topics and how to modify the presentation to fit course needs.

Solutions to the text's exercises are available to qualified instructors.

Contents:

1 The Real Numbers 1

1.1 Sets 2

1.2 Functions 7

1.3 Algebraic and order properties 12

1.4 The positive integers 18

1.5 The least upper bound axiom 24

2 Sequences 33

2.1 Sequences and limits 33

2.2 Limit theorems 39

2.3 Monotonic sequences 47

2.4 Sequences defined inductively 51

2.5 Subsequences 55

2.6 Cauchy sequences 65

2.7 Infinite limits 68

3 Functions and Continuity 71

3.1 Limit of a function 71

3.2 Limit theorems 76

3.3 Other limits 81

3.4 Continuity 86

3.5 Intermediate values, extreme values 95

3.6 Uniform continuity 103

3.7 Functions of two variables 109

4 The Derivative 119

4.1 Definition of the derivative 119

4.2 Rules for differentiation 127

4.3 The Mean Value Theorem 132

4.4 Inverse functions 143

4.5 Differentiability in R2 148

5 The Integral 163

5.1 The definition of the integral 163

5.2 Properties of the integral 173

5.3 Existence theory 182

5.4 The Fundamental Theorem of Calculus 190

5.5 Improper integrals 195

5.6 Double integrals 200

6 Infinite Series 213

6.1 Basic theory 213

6.2 Absolute convergence 225

6.3 Power series 233

6.4 Taylor series 247

7 Sequences and Series of Functions 257

7.1 Uniform convergence 258

7.2 Consequences of uniform convergence 270

7.3 Two examples 281

8 Introduction to Differential Equations 289

8.1 Elementary first order differential equations 290

8.2 Existence and uniqueness 298

8.3 Power series solutions 307.

Notes:

Includes index.

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Hazel M. Hussong Fund.

ISBN:

9780763774929

0763774928

OCLC:

316327222

Publisher Number:

99937171167