Table of 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 𝜋 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

20 Approximation by Polynomial Functions

Part V Epilogue
 28 Fields
 29 Construction of the Real Numbers
 30 Uniqueness of the Real Numbers