### Chapter P

Preparation For Calculus

P-1 | Graphs and Models | Exercises | p.8 |

P-2 | Linear Models and Rates of Change | Exercises | p.16 |

P-3 | Functions and Their Graphs | Exercises | p.27 |

P-4 | Review of Trigonometric Functions | Exercises | p.38 |

Review Exercises | p.41 | ||

Problem Solving | p.43 |

### Chapter 1

Limits And Their Properties

1-1 | A Preview of Calculus | Exercises | p.51 |

1-2 | Finding Limits Graphically and Numerically | Exercises | p.59 |

1-3 | Evaluating Limits Analytically | Exercises | p.71 |

1-4 | Continuity and One-Sided Limits | Exercises | p.83 |

1-5 | Infinite Limits | Exercises | p.92 |

Review Exercises | p.95 | ||

Problem Solving | p.97 |

### Chapter 2

Differentiation

2-1 | The Derivative and the Tangent Line Problem | Exercises | p.107 |

2-2 | Basic Differentiation Rules and Rates of Change | Exercises | p.118 |

2-3 | Product and Quotient Rules and Higher-Order Derivatives | Exercises | p.129 |

2-4 | The Chain Rule | Exercises | p.140 |

2-5 | Implicit Differentiation | Exercises | p.149 |

2-6 | Related Rates | Exercises | p.157 |

Review Exercises | p.161 | ||

Problem Solving | p.163 |

### Chapter 3

Applications Of Differentiation

3-1 | Extrema on an Interval | Exercises | p.171 |

3-2 | Rolle's Theorem and the Mean Value Theorem | Exercises | p.178 |

3-3 | Increasing and Decreasing Functions and the First Derivative Test | Exercises | p.187 |

3-4 | Concavity and the Second Derivative Test | Exercises | p.196 |

3-5 | Limits and Infinity | Exercises | p.206 |

3-6 | A Summary of Curve Sketching | Exercises | p.215 |

3-7 | Optimization Problems | Exercises | p.224 |

3-8 | Newton's Method | Exercises | p.233 |

3-9 | Differentials | Exercises | p.240 |

Review Exercises | p.242 | ||

Problem Solving | p.245 |

### Chapter 4

Integration

4-1 | Antiderivatives and Indefinite Integration | Exercises | p.255 |

4-2 | Area | Exercises | p.267 |

4-3 | Riemann Sums and Definite Integrals | Exercises | p.277 |

4-4 | The Fundamental Theorem of Calculus | Exercises | p.292 |

4-5 | Integration by Substitution | Exercises | p.305 |

Review Exercises | p.309 | ||

Problem Solving | p.311 |

### Chapter 5

Logarithmic, Exponential, And Other Transcendental Functions

5-1 | The Natural Logarithmic Function: Differentiation | Exercises | p.321 |

5-2 | The natural Logarithmic Function: Integration | Exercises | p.330 |

5-3 | Inverse Functions | Exercises | p.339 |

5-4 | Exponential Functions: Differentiation and Integration | Exercises | p.348 |

5-5 | Bases Other than e and Applications | Exercises | p.358 |

5-6 | Indeterminate Forms and L'Hopital's Rule | Exercises | p.369 |

5-7 | Inverse Trigonometric Functions: Differentiation | Exercises | p.379 |

5-8 | Inverse Trigonometric Functions: Integration | Exercises | p.387 |

5-9 | Hyperbolic Functions | Exercises | p.397 |

Review Exercises | p.400 | ||

Problem Solving | p.403 |

### Chapter 6

Differential Equations

6-1 | Slope Fields and Euler's Method | Exercises | p.411 |

6-2 | Growth and Decay | Exercises | p.420 |

6-3 | Separation of Variables and the Logistic Equation | Exercises | p.429 |

6-4 | First-Order Linear Differential Equations | Exercises | p.436 |

Review Exercises | p.439 | ||

Problem Solving | p.441 |

### Chapter 7

Applications Of Integration

7-1 | Area of a Region Between Two Curves | Exercises | p.450 |

7-2 | Volume: The Disk Method | Exercises | p.461 |

7-3 | Volume: The Shell Method | Exercises | p.470 |

7-4 | Arc Length and Surfaces of Revolution | Exercises | p.481 |

7-5 | Work | Exercises | p.491 |

7-6 | Moments, Centers of Mass, and Centroids | Exercises | p.502 |

7-7 | Fluid Pressure and Fluid Force | Exercises | p.509 |

Review Exercises | p.511 | ||

Problem Solving | p.513 |

### Chapter 8

Integration Techniques And Improper Integrals

8-1 | Basic Integration Rules | Exercises | p.520 |

8-2 | Integration by Parts | Exercises | p.529 |

8-3 | Trigonometric Integrals | Exercises | p.538 |

8-4 | Trigonometric Substitution | Exercises | p.547 |

8-5 | Partial Fractions | Exercises | p.557 |

8-6 | Numerical Integration | Exercises | p.564 |

8-7 | Integration by Tables and Other Integration Techniques | Exercises | p.570 |

8-8 | Improper Integrals | Exercises | p.579 |

Review Exercises | p.583 | ||

Problem Solving | p.585 |

### Chapter 9

Infinite Series

9-1 | Sequences | Exercises | p.596 |

9-2 | Series and Convergence | Exercises | p.605 |

9-3 | The Integral Tests and p-Series | Exercises | p.613 |

9-4 | Comparisons of Series | Exercises | p.620 |

9-5 | Alternating Series | Exercises | p.629 |

9-6 | The Ratio and Root Tests | Exercises | p.637 |

9-7 | Taylor Polynomials and Approximations | Exercises | p.648 |

9-8 | Power Series | Exercises | p.658 |

9-9 | Representation of Functions by Power Series | Exercises | p.666 |

9-10 | Taylor and Maclaurin Series | Exercises | p.677 |

Review Exercises | p.680 | ||

Problem Solving | p.683 |

### Chapter 10

Conics, Parametric Equations, And Polar Coordinates

10-1 | Conics and Calculus | Exercises | p.696 |

10-2 | Plane Curves and Parametric Equations | Exercises | p.707 |

10-3 | Parametric Equations and Calculus | Exercises | p.715 |

10-4 | Polar Coordinates and Polar Graphs | Exercises | p.726 |

10-5 | Area and Arc Length in Polar Coordinates | Exercises | p.735 |

10-6 | Polar Equations of Conics and Kepler's Laws | Exercises | p.743 |

Review Exercises | p.746 | ||

Problem Solving | p.749 |

### Chapter 11

Vectors And The Geometry Of Space

11-1 | Vectors in the Plane | Exercises | p.759 |

11-2 | Space Coordinates and Vectors in Space | Exercises | p.767 |

11-3 | The Dot Product of Two Vectors | Exercises | p.777 |

11-4 | The Cross Product of Two Vectors in Space | Exercises | p.785 |

11-5 | Lines and Planes in Space | Exercises | p.794 |

11-6 | Surfaces in Space | Exercises | p.806 |

11-7 | Cylindrical and Spherical Coordinates | Exercises | p.813 |

Review Exercises | p.815 | ||

Problem Solving | p.817 |

### Chapter 12

Vector-Valued Functions

12-1 | Vector-Valued Functions | Exercises | p.825 |

12-2 | Differentiation and Integration of Vector-Valued Functions | Exercises | p.834 |

12-3 | Velocity and Acceleration | Exercises | p.842 |

12-4 | Tangent Vectors and Normal Vectors | Exercises | p.852 |

12-5 | Arc Length and Curvature | Exercises | p.864 |

Review Exercises | p.867 | ||

Problem Solving | p.869 |

### Chapter 13

Functions Of Several Variables

13-1 | Introduction to Functions of Several Variables | Exercises | p.880 |

13-2 | Limits and Continuity | Exercises | p.891 |

13-3 | Partial Derivatives | Exercises | p.900 |

13-4 | Differentials | Exercises | p.909 |

13-5 | Chain Rule for Functions of Several Variables | Exercises | p.917 |

13-6 | Directional Derivatives and Gradients | Exercises | p.928 |

13-7 | Tangent Planes and Normal Lines | Exercises | p.937 |

13-8 | Extrema of Functions of Two Variables | Exercises | p.946 |

13-9 | Applications of Extrema | Exercises | p.953 |

13-10 | Lagrange Multipliers | Exercises | p.962 |

Review Exercises | p.964 | ||

Problem Solving | p.967 |

### Chapter 14

Multiple Integration

14-1 | Iterated Integrals and Area In the Planes | Exercises | p.976 |

14-2 | Double Integrals and Volume | Exercises | p.987 |

14-3 | Change of Variables: Polar Coordinates | Exercises | p.995 |

14-4 | Center of Mass and Moments of Inertia | Exercises | p.1004 |

14-5 | Surface Area | Exercises | p.1011 |

14-6 | Triple Integrals and Applications | Exercises | p.1021 |

14-7 | Triple Integrals in Other Coordinates | Exercises | p.1029 |

14-8 | Change of Variables: Jacobians | Exercises | p.1036 |

Review Exercises | p.1038 | ||

Problem Solving | p.1041 |

### Chapter 15

Vector Analysis

15-1 | Vector Fields | Exercises | p.1053 |

15-2 | Line Integrals | Exercises | p.1065 |

15-3 | Conservative Vector Fields and Independence of Path | Exercises | p.1076 |

15-4 | Green's Theorem | Exercises | p.1085 |

15-5 | Parametric Surfaces | Exercises | p.1095 |

15-6 | Surface Integrals | Exercises | p.1108 |

15-7 | Divergence Theorem | Exercises | p.1116 |

15-8 | Stokes's Theorem | Exercises | p.1123 |

Review Exercises | p.1124 | ||

Problem Solving | p.1127 |