Book:William K. Smith/Limits and Continuity

William K. Smith: Limits and Continuity

Published $\text {1964}$, MacMillan

Subject Matter

• Real Analysis

Contents

Preface

Chapter 1. Introduction

Chapter 2. Notation and Prerequisites

2.1 Sets

2.2 Functions

2.3 Inequalities

2.4 Absolute Value

Chapter 3. The Basic Definition

3.1 The First Version

3.2 Second and Third Versions

3.3 The Fourth Version

3.4 Final Version, or Success at Last

Chapter 4. Variations on the Basic Definition

4.1 Statements Involving $\infty$

4.2 One-sided Limits

4.3 Limits of Sequences

Chapter 5. Continuity

5.1 Preliminary Discussion and Definition

5.2 Further Remarks

Chapter 6. Some $\delta - \epsilon$ Techniques

6.1 Introduction

6.2 Illustrative Examples

6.3 Relation Between $\epsilon$ and Maximum $\delta$

Chapter 7. Theorems on Limits and Continuity

7.1 The Limit Theorems

7.2 Illustrations and Application of the Theorems

7.3 Theorems on Sequences

7.4 Uniform Continuity

7.5 Additional Theorems about a Function Continuous on a Closed Interval

Answers

Index

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