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Calculus

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 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
                 

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