Calculus by Michael Spivak - 4th Edition - Full Table of Contents

PREFACE ....................................... vi

PART I: Prologue

• 1 Basic Properties of Numbers ........................... 3
• 2 Numbers of Various Sorts ............................. 21

PART II: Foundations

• 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 ................................. 115
• 7 Three Hard Theorems .................................. 122
• 8 Least Upper Bounds ................................... 133
  Appendix. Uniform Continuity .......................... 144

PART III: Derivatives and Integrals

• 9 Derivatives .......................................... 149
• 10 Differentiation ..................................... 168
• 11 Significance of the Derivative ...................... 188
  Appendix. Convexity and Concavity ..................... 219
• 12 Inverse Functions ................................... 230
  Appendix. Parametric Representation of Curves ......... 244
• 13 Integrals ............................................ 253
  Appendix. Riemann Sums ................................. 282
• 14 The Fundamental Theorem of Calculus ................. 285
• 15 The Trigonometric Functions ......................... 303
• *16 π is Irrational .................................... 324
• *17 Planetary Motion ................................... 330
• 18 The Logarithm and Exponential Functions ............. 339
• 19 Integration in Elementary Terms ..................... 363
  Appendix. The Cosmopolitan Integral ................... 402

PART IV: Infinite Sequences and Infinite Series

• 20 Approximation by Polynomial Functions ............... 411
• *21 e is Transcendental ................................ 442
• 22 Infinite Sequences .................................. 452
• 23 Infinite Series ..................................... 471
• 24 Uniform Convergence and Power Series ................ 499
• 25 Complex Numbers ..................................... 526
• 26 Complex Functions ................................... 541
• 27 Complex Power Series ................................ 555

PART V: Epilogue

• 28 Fields ............................................... 581
• 29 Construction of the Real Numbers .................... 588
• 30 Uniqueness of the Real Numbers ...................... 601

Additional Sections

• Suggested Reading ...................................... 609
• Answers (to selected problems) ......................... 619
• Glossary of Symbols .................................... 665
• Index ................................................... 669

Note: Chapters marked with * are optional or supplementary material.