A first course in mathematical analysis
著者
書誌事項
A first course in mathematical analysis
Cambridge University Press : Open University, 2006
- : hbk
- : pbk.
- タイトル別名
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Mathematical analysis
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注記
Includes index
内容説明・目次
内容説明
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.
目次
- Preface
- Introduction: calculus and analysis
- 1. Numbers
- 2. Sequences
- 3. Series
- 4. Continuity
- 5. Limits and continuity
- 6. Differentiation
- 7. Integration
- 8. Power series
- Appendix 1. Sets, functions and proofs
- Appendix 2. Standard derivatives and primitives
- Appendix 3. The first 1,000 decimal places of the square root of 2, e and pi
- Appendix 4. Solutions to the problems
- Index.
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