1.1 Velocity and Distance, pp. 1-7

1.2 Calculus Without Limits, pp. 8-15

1.3 The Velocity at an Instant, pp. 16-21

1.4 Circular Motion, pp. 22-28

1.5 A Review of Trigonometry, pp. 29-33

1.6 A Thousand Points of Light, pp. 34-35

1.7 Computing in Calculus, pp. 36-43

2: Derivatives

2.1 The Derivative of a Function, pp. 44-49

2.2 Powers and Polynomials, pp. 50-57

2.3 The Slope and the Tangent Line, pp. 58-63

2.4 Derivative of the Sine and Cosine, pp. 64-70

2.5 The Product and Quotient and Power Rules, pp. 71-77

2.6 Limits, pp. 78-84

2.7 Continuous Functions, pp. 85-90

3.1 Linear Approximation, pp. 91-95

3.2 Maximum and Minimum Problems, pp. 96-104

3.3 Second Derivatives: Minimum vs. Maximum, pp. 105-111

3.4 Graphs, pp. 112-120

3.5 Ellipses, Parabolas, and Hyperbolas, pp. 121-129

3.6 Iterations x[n+1] = F(x[n]), pp. 130-136

3.7 Newton’s Method and Chaos, pp. 137-145

3.8 The Mean Value Theorem and l’Hopital’s Rule, pp. 146-153

4.1 Derivatives by the Chain Rule, pp. 154-159

4.2 Implicit Differentiation and Related Rates, pp. 160-163

4.3 Inverse Functions and Their Derivatives, pp. 164-170

4.4 Inverses of Trigonometric Functions, pp. 171-176

5.1 The Idea of an Integral, pp. 177-181

5.2 Antiderivatives, pp. 182-186

5.3 Summation vs. Integration, pp. 187-194

5.4 Indefinite Integrals and Substitutions, pp. 195-200

5.5 The Definite Integral, pp. 201-205

5.6 Properties of the Integral and the Average Value, pp. 206-212

5.7 The Fundamental Theorem and Its Consequences, pp. 213-219

5.8 Numerical Integration, pp. 220-227

6.1 An Overview, pp. 228-235

6.2 The Exponential e^x, pp. 236-241

6.3 Growth and Decay in Science and Economics, pp. 242-251

6.4 Logarithms, pp. 252-258

6.5 Separable Equations Including the Logistic Equation, pp. 259-266

6.6 Powers Instead of Exponentials, pp. 267-276

6.7 Hyperbolic Functions, pp. 277-282

7.1 Integration by Parts, pp. 283-287

7.2 Trigonometric Integrals, pp. 288-293

7.3 Trigonometric Substitutions, pp. 294-299

7.4 Partial Fractions, pp. 300-304

7.5 Improper Integrals, pp. 305-310

8.1 Areas and Volumes by Slices, pp. 311-319

8.2 Length of a Plane Curve, pp. 320-324

8.3 Area of a Surface of Revolution, pp. 325-327

8.4 Probability and Calculus, pp. 328-335

8.5 Masses and Moments, pp. 336-341

8.6 Force, Work, and Energy, pp. 342-34

9.1 Polar Coordinates, pp. 348-350

9.2 Polar Equations and Graphs, pp. 351-355

9.3 Slope, Length, and Area for Polar Curves, pp. 356-359

9.4 Complex Numbers, pp. 360-367

10.1 The Geometric Series, pp. 368-373

10.2 Convergence Tests: Positive Series, pp. 374-380

10.3 Convergence Tests: All Series, pp. 325-327

10.4 The Taylor Series for e^x, sin x, and cos x, pp. 385-390