Book:Michael Spivak/Calculus

Michael Spivak: Calculus

Published $\text {1967}$, Benjamin

Subject Matter

• Calculus

Contents

Preface

Preface to the World Student Series Edition

Part I Prologue

1 Basic Properties of Numbers

2 Numbers of Various Sorts

Part II Foundations

3 Functions

Appendix. Ordered Pairs

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

Appendix. Convexity and Concavity

12 Inverse Functions

13 Integrals

14 The Fundamental Theorem of Calculus

15 The Trigonometric functions

16 $\pi$ is Irrational

17 The Logarithm and Exponential Functions

18 Integration in Elementary Terms

Part IV Infinite Sequences and Infinite Series

19 Approximation by Polynomial Functions

20 $e$ is Transcendental

21 Infinite Sequences

22 Infinite Series

23 Uniform Convergence and Power Series

24 Complex Numbers

25 Complex Functions

26 Complex Power Series

Part V Epilogue

27. Fields

28. Construction of the Real Numbers

29. Uniqueness of the Real Numbers

Suggested Reading

Answers (to selected problems)

Glossary of Symbols

Index

Next

Cited by

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces

Further Editions

• 2006: Michael Spivak: Calculus (3rd ed.)
• 2008: Michael Spivak: Calculus (4th ed.)

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $1$: Review of some real analysis: $\S 1.1$: Real Numbers

Source work progress

• 1967: Michael Spivak: Calculus ... (previous) ... (next): Part $\text I$: Prologue: Chapter $1$: Basic Properties of Numbers: $(\text P 8)$

Starting from Next:

• 1967: Michael Spivak: Calculus ... (previous) ... (next): Part $\text {III}$: Derivatives and Integrals: Chapter $18$: Integration in Elementary Terms