Calculus
Calculus
£46.99
GBPSpivak's celebrated textbook is widely held as one of the finest introductions to mathematical analysis. His aim is to present calculus as the first real encounter with mathematics: it is the place to learn how logical reasoning combined with fundamental concepts can be developed into a rigorous mathematical theory rather than a bunch of tools and techniques learned by rote. Since analysis is a subject students traditionally find difficult to grasp, Spivak provides leisurely explanations, a profusion of examples, a wide range of exercises and plenty of illustrations in an easy-going approach that enlightens difficult concepts and rewards effort. Calculus will continue to be regarded as a modern classic, ideal for honours students and mathematics majors, who seek an alternative to doorstop textbooks on calculus, and the more formidable introductions to real analysis.
- One of the most celebrated texts of its type now readily available outside of the US: combines the rigor of more formidable books with the leisurely explanations, profusion of examples, exercises and illustrations associated with 'doorstops'
- Ideal for students; clear, crisp explanations of what analysis and mathematics are really about
- Full range of exercises, from the straightforward to the challenging that deepen understanding; solutions available in book form via http://www.mathpop.com/bookhtms/cal.htm
Product details
June 2006Hardback
9780521867443
681 pages
259 × 231 × 41 mm
1.78kg
700 b/w illus.
Available
Table of Contents
- Preface
- Part I. Prologue:
- 1. Basic properties of mumbers
- 2. Numbers of various sorts
- Part II. Foundations:
- 3. Functions
- 4. Graphs
- 5. Limits
- 6. Continuous functions
- 7. Three hard theorems
- 8. Least upper bounds
- Part III. Derivatives and Integrals:
- 9. Derivatives
- 10. Differentiation
- 11. Significance of the derivative
- 12. Inverse functions
- 13. Integrals
- 14. The fundamental theorem of calculus
- 15. The trigonometric functions
- 16. Pi is irrational
- 17. Planetary motion
- 18. The logarithm and exponential functions
- 19. Integration in elementary terms
- Part IV. Infinite Sequences and Infinite Series:
- 20. Approximation by polynomial functions
- 21. e is transcendental
- 22. Infinite sequences
- 23. Infinite series
- 24. Uniform convergence and power series
- 25. Complex numbers
- 26. Complex functions
- 27. Complex power series
- Part V. Epilogue:
- 28. Fields
- 29. Construction of the real numbers
- 30. Uniqueness of the real numbers
- Suggested reading
- Answers (to selected problems)
- Glossary of symbols
- Index.
