Book:William K. Smith/Limits and Continuity

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William K. Smith: Limits and Continuity

Published $1964$, MacMillan.


Subject Matter


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