### 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 | Fitting Models to Data | Exercises | p.34 |

Review Exercises | p.37 | ||

Problem Solving | p.39 |

### Chapter 1

Limits And Their Properties

1.1 | A Preview of Calculus | Exercises | p.47 |

1.2 | Finding Limits Graphically and Numerically | Exercises | p.54 |

1.3 | Evaluating Limits Analytically | Exercises | p.67 |

1.4 | Continuity and One-Sided Limits | Exercises | p.78 |

1.5 | Infinite Limits | Exercises | p.88 |

Review Exercises | p.91 | ||

Problem Solving | p.93 |

### Chapter 2

Differentiation

2.1 | The Derivative and the Tangent Line Problem | Exercises | p.103 |

2.2 | Basic Differentiation | Exercises | p.115 |

2.3 | Product and Quotient Rules and Higher-Order Derivatives | Exercises | p.126 |

2.4 | The Chain Rule | Exercises | p.137 |

2.5 | Implicit Differentiation | Exercises | p.146 |

2.6 | Related Rates | Exercises | p.154 |

Review Exercises | p.158 | ||

Problem Solving | p.161 |

### Chapter 3

Application Of Differentiation

3.1 | Extrema on an Interval | Exercises | p.169 |

3.2 | Rolle's Theorem and the Mean Value Theorem | Exercises | p.176 |

3.3 | Increasing and Decreasing Functions and the First Derivative Test | Exercises | p.186 |

3.4 | Concavity and the Second Derivative Test | Exercises | p.195 |

3.5 | Limits at Infinity | Exercises | p.205 |

3.6 | A Summary of Curve Sketching | Exercises | p.215 |

3.7 | Optimization Problems | Exercises | p.223 |

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 | Reimann Sums and Definite Integrals | Exercises | p.278 |

4.4 | The Fundamental Theorem of Calculus | Exercises | p.293 |

4.5 | Integration by Substitution | Exercises | p.306 |

4.6 | Numerical Integration | Exercises | p.316 |

Review Exercises | p.318 | ||

Problem Solving | p.321 |

### Chapter 5

Logarithmic, Exponential, And Other Transcendental Functions

5.1 | The Natural Logarithmic Function: Differentiation | Exercises | p.331 |

5.2 | The Natural Logarithmic Function: Integration | Exercises | p.340 |

5.3 | Inverse Functions | Exercises | p.349 |

5.4 | Exponential Functions: Differentiation and Integration | Exercises | p.358 |

5.5 | Bases Other Than e and Applications | Exercises | p.368 |

5.6 | Inverse Trigonometric Functions: Differentiation | Exercises | p.379 |

5.7 | Inverse Trigonometric Functions: Integration | Exercises | p.387 |

5.8 | Hyperbolic Functions | Exercises | p.398 |

Review Exercises | p.401 | ||

Problem Solving | p.403 |

### Chapter 6

Differential Equations

6.1 | Slope Fields and Euler's Method | Exercises | p.411 |

6.2 | Differential Equations: Growth and Decay | Exercises | p.420 |

6.3 | Separation of Variables and the Logistic Equation | Exercises | p.431 |

6.4 | First-Order Linear Differential Equations | Exercises | p.440 |

Review Exercises | p.443 | ||

Problem Solving | p.445 |

### Chapter 7

Application Of Integrals

7.1 | Area of a Region Between Two Curves | Exercises | p.454 |

7.2 | Volume: The Disk Method | Exercises | p.465 |

7.3 | Volume: The Shell Method | Exercises | p.474 |

7.4 | Arc Length and Surfaces of Revolution | Exercises | p.485 |

7.5 | Work | Exercises | p.495 |

7.6 | Moments, Centers of Mass, and Centeroids | Exercises | p.506 |

7.7 | Fluid Pressure and Fluid Force | Exercises | p.513 |

Review Exercises | p.515 | ||

Problem Solving | p.517 |

### Chapter 8

Integration Techniques, L'Hôpital's Rules, And Improper Integrals

8.1 | Basic Integration Rules | Exercises | p.524 |

8.2 | Integration by Parts | Exercises | p.533 |

8.3 | Trigonometric Integrals | Exercises | p.542 |

8.4 | Trigonometric Substitution | Exercises | p.551 |

8.5 | Partial Fractions | Exercises | p.561 |

8.6 | Integration by Tables and Other Integration Techniques | Exercises | p.567 |

8.7 | Indeterminate Forms and L'Hôpital's Rules | Exercises | p.576 |

8.8 | Improper Integrals | Exercises | p.587 |

Review Exercises | p.591 | ||

Problem Solving | p.593 |

### Chapter 9

Infinite Series

9.1 | Sequences | Exercises | p.604 |

9.2 | Series and Convergence | Exercises | p.614 |

9.3 | The Integral Test and p-Series | Exercises | p.622 |

9.4 | Comparisons of Series | Exercises | p.630 |

9.5 | Alternating Series | Exercises | p.638 |

9.6 | The Ratio and Root Tests | Exercises | p.647 |

9.7 | Taylor Polynomials and Approximations | Exercises | p.658 |

9.8 | Power Series | Exercises | p.668 |

9.9 | Representation of Functions by Power Series | Exercises | p.676 |

9.10 | Taylor and Maclaurian Series | Exercises | p.687 |

Review Exercises | p.690 | ||

Problem Solving | p.693 |

### Chapter 10

Conics, Parametric Equations, And Polar Coordinates

10.1 | Conics and Calculus | Exercises | p.706 |

10.2 | Plane Curves and Parametric Equations | Exercises | p.718 |

10.3 | Parametric Equations and Calculus | Exercises | p.727 |

10.4 | Polar Coordinates and Polar Graphs | Exercises | p.738 |

10.5 | Area and Arc Length in Polar Coordinates | Exercises | p.747 |

10.6 | Polar Equations of Conics and Kepler's Laws | Exercises | p.755 |

Review Exercises | p.758 | ||

Problem Solving | p.761 |

### Chapter 11

Vectors And The Geometry Of Space

11.1 | Vectors in the Plane | Exercises | p.771 |

11.2 | Space Coordinates and Vectors in Space | Exercises | p.780 |

11.3 | The Dot Product of Two Vectors | Exercises | p.789 |

11.4 | The Cross Product of Two Vectors in Space | Exercises | p.798 |

11.5 | Lines and Planes in Space | Exercises | p.807 |

11.6 | Surfaces in Space | Exercises | p.820 |

11.7 | Cylindrical and Spherical Coordinates | Exercises | p.827 |

Review Exercises | p.829 | ||

Problem Solving | p.831 |

### Chapter 12

Vector-Valued Functions

12.1 | Vector-Valued Functions | Exercises | p.839 |

12.2 | Differentiation and Integration of Vector-Valued Functions | Exercises | p.848 |

12.3 | Velocity and Acceleration | Exercises | p.856 |

12.4 | Tangent Vectors and Normal Vectors | Exercises | p.865 |

12.5 | Arc Length and Curvature | Exercises | p.877 |

Review Exercises | p.881 | ||

Problem Solving | p.883 |

### Chapter 13

Functions Of Several Variables

13.1 | Introduction to Functions of Several Variables | Exercises | p.894 |

13.2 | Limits and Continuity | Exercises | p.904 |

13.3 | Partial Derivatives | Exercises | p.914 |

13.4 | Differentials | Exercises | p.923 |

13.5 | Chain Rules for Functions of Several Variables | Exercises | p.931 |

13.6 | Directional Derivatives and Gradients | Exercises | p.942 |

13.7 | Tangent Planes and Normal Lines | Exercises | p.951 |

13.8 | Extrema of Functions of Two Variables | Exercises | p.960 |

13.9 | Applications of Extrema of Functions of Two Variables | Exercises | p.966 |

13.10 | Lagrange Multipliers | Exercises | p.976 |

Review Exercises | p.978 | ||

Problem Solving | p.981 |

### Chapter 14

Multiple Integration

14.1 | Iterated Integrals and Area in the Plane | Exercises | p.990 |

14.2 | Double Integrals and Volume | Exercises | p.1000 |

14.3 | Change of Variables: Polar Coordinates | Exercises | p.1009 |

14.4 | Center of Mass and Moments of Inertia | Exercises | p.1018 |

14.5 | Surface Area | Exercises | p.1025 |

14.6 | Triple Integrals and Applications | Exercises | p.1035 |

14.7 | Triple Integrals in Cylindrical and Spherical Coordinates | Exercises | p.1043 |

14.8 | Change of Variables: Jacobians | Exercises | p.1050 |

Review Exercises | p.1052 | ||

Problem Solving | p.1055 |

### Chapter 15

Vector Analysis

15.1 | Vector Fields | Exercises | p.1067 |

15.2 | Line Integrals | Exercises | p.1079 |

15.3 | Conservative Vector Fields and Independence of Path | Exercises | p.1090 |

15.4 | Green's Theorem | Exercises | p.1099 |

15.5 | Parametric Surfaces | Exercises | p.1109 |

15.6 | Surface Integrals | Exercises | p.1122 |

15.7 | Divergence Theorem | Exercises | p.1130 |

15.8 | Stoke's Theorem | Exercises | p.1137 |

Review Exercises | p.1138 | ||

Problem Solving | p.1141 |