Spivak'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.
Author(s): Michael Spivak
Edition: 3
Publisher: Cambridge University Press
Year: 2006
Language: English
Commentary: Fourth printing 2009
Pages: 681
City: Cambridge
Tags: Calculus; Functions; Limits; Derivatives; Integrals; Sequences; Series
Preface
Part I. Prologue:
1. Basic properties of numbers
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.
