Calculus (Hardcover)

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.