A First Course in Mathematical Analysis
A First Course in Mathematical Analysis
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.
- A sequential approach to continuity, differentiability and integration to make it easier to understand the subject
- Many graded examples and exercises, with large numbers of complete solutions, to guide students through the tricky points
- Suitable for self-study or use in parallel with a standard university course; unlike other textbooks in the subject, should be intelligible to students on their own, offering considerable study help
Product details
No date availablePaperback
9780521684248
468 pages
247 × 189 × 24 mm
0.86kg
211 b/w illus. 1 table 207 exercises
Table of Contents
- 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.
