A First Course in Mathematical Analysis

David Alexander Brannan

doi:10.1017/CBO9780511803949

Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard university course on the subject.

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A First Course in Mathematical Analysis

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-xii

1 - Numbers
pp 1-36

2 - Sequences
pp 37-82

3 - Series
pp 83-129

4 - Continuity
pp 130-166

5 - Limits and continuity
pp 167-204

6 - Differentiation
pp 205-254

7 - Integration
pp 255-312

8 - Power series
pp 313-353

Appendix 1 - Sets, functions and proofs
pp 354-358

Appendix 2 - Standard derivatives and primitives
pp 359-360

Appendix 3 - The first 1000 decimal places of √2, e and π
pp 361-362

Appendix 4 - Solutions to the problems
pp 363-456

Index
pp 457-459

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A First Course in Mathematical Analysis

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