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PART Ⅰ Prologue 3

1 Basic Properties of Numbers 3

2 Numbers of Various Sorts 21

PART Ⅱ Foundations 39

3 Functions 39

Appendix.Ordered Pairs 54

4 Graphs 56

Appendix 1.Vectors 75

Appendix 2.The Conic Sections 80

Appendix 3.Polar Coordinates 84

5 Limits 90

6 Continuous Functions 113

7 Three Hard Theorems 120

8 Least Upper Bounds 131

Appendix.Uniform Continuity 142

PARTⅢ Derivatives and Integrals 147

9 Derivatives 147

10 Differentiation 166

11 Significance of the Derivative 185

Appendix.Convexity and Concavity 216

12 Inverse Functions 227

Appendix.Parametric Representation of Curves 241

13 Integrals 250

Appendix.Riemann Sums 279

14 The Fundamental Theorem of Calculus 282

15 The Trigonometric Functions 300

16 π is Irrational 321

17 Planetary Motion 327

18 The Logarithm and Exponential Functions 336

19 Integration in Elementary Terms 359

Appendix.The Cosmopolitan Integral 397

PART Ⅳ Infinite Sequences and Infinite Series 405

20 Approximation by Polynomial Functions 405

21 e is Transcendental 435

22 Infinite Sequences 445

23 Infinite Series 464

24 Uniform Convergence and Power Series 491

25 Complex Numbers 517

26 Complex Functions 532

27 Complex Power Series 546

PART Ⅴ Epilogue 571

28 Fields 571

29 Construction of the Real Numbers 578

30 Uniqueness of the Real Numbers 591

Suggested Reading 599

Answers （to selected problems） 609

Glossary of Symbols 655

Index 659