Book:Michael Spivak/Calculus

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Michael Spivak: Calculus

Published $\text {1967}$, Benjamin.


Subject Matter


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


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