Book:Michael Spivak/Calculus

From ProofWiki
Jump to navigation Jump to search

Michael Spivak: Calculus

Published $\text {1967}$, Benjamin.

Subject Matter


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


Cited by

Further Editions


Source work progress