Introduction to Mathematical Analysis

1. Front Matter

   Pages ii-vii

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2. Axioms for the Real Numbers

   • C. R. J. Clapham

   Pages 1-17

3. Sequences

   • C. R. J. Clapham

   Pages 18-26

4. Series

   • C. R. J. Clapham

   Pages 27-35

5. Continuous Functions

   • C. R. J. Clapham

   Pages 36-44

6. Differentiable Functions

   • C. R. J. Clapham

   Pages 45-53

7. The Riemann Integral

   • C. R. J. Clapham

   Pages 54-77

8. Answers to the Exercises

   • C. R. J. Clapham

   Pages 78-79

9. Back Matter

   Pages 81-83

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I have tried to provide an introduction, at an elementary level, to some of the important topics in real analysis, without avoiding reference to the central role which the completeness of the real numbers plays throughout. Many elementary textbooks are written on the assumption that an appeal to the complete­ ness axiom is beyond their scope; my aim here has been to give an account of the development from axiomatic beginnings, without gaps, while keeping the treatment reasonably simple. Little previous knowledge is assumed, though it is likely that any reader will have had some experience of calculus. I hope that the book will give the non-specialist, who may have considerable facility in techniques, an appreciation of the foundations and rigorous framework of the mathematics that he uses in its applications; while, for the intending mathe­ matician, it will be more of a beginner's book in preparation for more advanced study of analysis. I should finally like to record my thanks to Professor Ledermann for the suggestions and comments that he made after reading the first draft of the text.

• Riemann integral
• calculus
• continuous function
• derivative
• differential equation
• limit of a function
• mathematical analysis
• mean value theorem

• Department of Mathematics, University of Aberdeen, UK

  C. R. J. Clapham

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