**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