Calculus by Michael Spivak

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.