Book:William K. Smith/Limits and Continuity

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