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.
目錄:
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.