دانلود کتاب Calculus

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Cover
Title
Copyright
Preface
Contents
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