Book:C.R.J. Clapham/Introduction to Mathematical Analysis
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C.R.J. Clapham: Introduction to Mathematical Analysis
Published $\text {1973}$, Routledge & Kegan Paul
- ISBN 0 7100 7529 4
Subject Matter
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
- Answers to the Exercises
- Index
Source work progress
- 1973: C.R.J. Clapham: Introduction to Mathematical Analysis ... (previous) ... (next): Chapter $1$: Axioms for the Real Numbers: $2$. Fields: Theorem $3 \ \text {(vii)}$