Book:Michael Spivak/Calculus/Fourth Edition

Michael Spivak: Calculus (4th Edition)

Published $\text {2008}$, Publish or Perish

ISBN 0-914-09891-8

Subject Matter

• Calculus

Contents

Preface

Part I. Prologue

1. Basic Properties of Numbers

2. Numbers of Various Sorts

Part II. Foundations

3. Functions

Appendix. Ordered Pairs

4. Graphs

Appendix 1. Vectors

Appendix 2. The Conic Sections

Appendix 3. Polar Coordinates

5. Limits

6. Continuous Functions

7. Three Hard Theorems

8. Least Upper Bounds

Appendix. Uniform Continuity

Part III. Derivatives and Integrals

9. Derivatives

10. Differentiation

11. Significance of the Derivative

Appendix. Convexity and Concavity

12. Inverse Functions

Appendix. Parametric Representation of Curves

13. Integrals

Appendix. Riemann Sums

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

Appendix. The Cosmopolitan Integral

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

Further Editions

• 1967: Michael Spivak: Calculus
• 2006: Michael Spivak: Calculus (3rd ed.)