# Book:C.R.J. Clapham/Introduction to Mathematical Analysis

## C.R.J. Clapham: Introduction to Mathematical Analysis

Published $1973$, Routledge & Kegan Paul

ISBN 0 7100 7529 4.

### Contents

Preface
1. Axioms for the Real Numbers
1 Introduction
2 Fields
3 Order
4 Completeness
5 Upper bound
6 The Archimedean property
Exercises
2. Sequences
7 Limit of a sequence
8 Sequences without limits
9 Monotone sequences
Exercises
3. Series
10 Infinite series
11 Convergence
12 Tests
13 Absolute convergence
14 Power series
Exercises
4. Continuous Functions
15 Limit of a function
16 Continuity
17 The intermediate value property
18 Bounds of a continuous function
Exercises
5. Differentiable Functions
19 Derivatives
20 Rolle's theorem
21 The mean value theorem
Exercises
6. The Riemann Integral
22 Introduction
23 Upper and lower sums
24 Riemann-integral functions
25 Examples
26 A necessary and sufficient condition
27 Monotone functions
28 Uniform continuity
29 Integrability of continuous functions
30 Properties of the Riemann integral
31 The mean value theorem
32 Integration and differentiation
Exercises