Table of Contents for AP Calculus: The "C" Topics
Table of Contents for AP Calculus: The "C" Topics


Chapter One - Infinite Series

   Section      Title                                                     Page 
    1.0     Essay                                                           1	
    1.1     Infinite Sequences                                              6
    1.2     Partial Sums and the Definition of Infinite Series             10
    1.3     Geometric Series                                               14
    1.4     Tests for Convergence of Positive Term Series - Part I         18
    1.5     Tests for Convergence of Positive Term Series - Part II        28
    1.6     Series With Both Positive and Negative Terms                   35
    1.7     Cauchy's Ratio Test and the Root Test                          40
    1.8     Power Series                                                   45
    1.9     Taylor Series                                                  52
    1.10    Error Bounds for Taylor Polynomial Approximations              60
    1.11    Error Bounds for Alternating Series. Radius of Convergence     69
    1.12    Hyperbolic Functions and Euler's Amazing Formula               73


Chapter Two - Antiderivatives and Integrals

   Section     Title                                                         Page 
    2.0     Essay                                                             79
    2.1     Riemann Sums                                                      85
    2.2     Proving the Fundamental Theorem of Calculus                       92
    2.3     Areas and Volumes by Riemann Sums                                 96
    2.4     Arc Length                                                       105
    2.5     Work                                                             109
    2.6     Antiderivatives by Parts                                         114
    2.7     Antiderivatives by Substitution                                  119
    2.8     Antiderivatives by Partial Fractions                             123
    2.9     Improper Integrals                                               127
    2.10    Antiderivatives and Integrals - A Summary of Facts and Formulas  131

Chapter Three - The Calculus of Parametric, Vector, and Polar Functions

   Section      Title                                            Page 
    3.0     Essay                                                 137
    3.1     The Calculus of Parametric Equations                  143
    3.2     Vector Valued Functions in the Plane                  150
    3.3     Polar Graphing Via Distance Modulator Functions       156
    3.4     Arc Length and Area in Polar Form                     162
    3.5     Areas of Overlapping Polar Regions                    166
    3.6     Modeling the Motion of a Projectile                   169


Chapter Four - Differential Equations

   Section      Title                                            Page 
    4.0     Essay                                                 171
    4.1     The Logistic Differential Equation                    178
    4.2     Slope Fields                                          185
    4.3     Euler's Method                                        190
    4.4     Final Thoughts                                        195							

Answers to Selected Problems                                      201


Index                                                             215