### Chapter 1

Functions And Models

1.1 | Four Ways to Represent a Function | Exercises | p.19 |

1.2 | Mathematical Models: A Catalog of Essential Functions | Exercises | p.33 |

1.3 | New Functions from Old Functions | Exercises | p.42 |

1.4 | Graphing Calculators and Computers | Exercises | p.50 |

1.5 | Exponential Functions | Exercises | p.57 |

1.6 | Inverse Functions and Logarithms | Exercises | p.69 |

Review: Concept Check | p.72 | ||

Review: True-False Quiz | p.72 | ||

Review: Exercises | p.73 |

### Chapter 2

Limits And Derivatives

2.1 | The Tangent and Velocity Problems | Exercises | p.86 |

2.2 | The Limit of a Function | Exercises | p.96 |

2.3 | Calculating Limits Using the Limit Laws | Exercises | p.106 |

2.4 | The Precise Definition of a Limit | Exercises | p.116 |

2.5 | Continuity | Exercises | p.127 |

2.6 | Limits at Infinity; Horizontal Asymptotes | Exercises | p.140 |

2.7 | Derivatives and Rates of Change | Exercises | p.150 |

2.8 | The Derivative as a Function | Exercises | p.162 |

Review: Concept Check | p.165 | ||

Review: True-False Quiz | p.166 | ||

Review: Exercises | p.167 |

### Chapter 3

Differentiation Rules

3.1 | Derivatives of Polynomials and Exponential Functions | Exercises | p.181 |

3.2 | The Product and Quotient Rules | Exercises | p.189 |

3.3 | Derivatives of Trigonometric Functions | Exercises | p.197 |

3.4 | The Chain Rule | Exercises | p.205 |

3.5 | Implicit Differentiation | Exercises | p.215 |

3.6 | Derivatives of Logarithmic Functions | Exercises | p.223 |

3.7 | Rates of Change in the Natural and Social Sciences | Exercises | p.233 |

3.8 | Exponential Growth and Decay | Exercises | p.242 |

3.9 | Related Rates | Exercises | p.248 |

3.10 | Linear Approximations and Differentials | Exercises | p.255 |

3.11 | Hyperbolic Functions | Exercises | p.262 |

Review: True-False Quiz | p.264 | ||

Review: Concept Check | p.264 | ||

Review: Exercises | p.265 |

### Chapter 4

Applications Of Differentiation

4.1 | Maximum and Minimum Values | Exercises | p.280 |

4.2 | The Mean Value Theorem | Exercises | p.288 |

4.3 | How Derivatives Affect the Shape of a Graph | Exercises | p.297 |

4.4 | Indeterminate Forms and l'Hospitals Rule | Exercises | p.307 |

4.5 | Summary of Curve Sketching | Exercises | p.317 |

4.6 | Graphing with Calculus and Calculators | Exercises | p.324 |

4.7 | Optimization Problems | Exercises | p.331 |

4.8 | Newton's Method | Exercises | p.342 |

4.9 | Antiderivatives | Exercises | p.348 |

Review: Concept Check | p.351 | ||

Review: True-False Quiz | p.351 | ||

Review: Exercises | p.352 |

### Chapter 5

Integrals

5.1 | Areas and Distances | Exercises | p.369 |

5.2 | The Definite Integral | Exercises | p.382 |

5.3 | The Fundamental Theorem of Calculus | Exercises | p.394 |

5.4 | Indefinite Integrals and the Net Change Theorem | Exercises | p.403 |

5.5 | The Substitution Rule | Exercises | p.413 |

Review: Concept Check | p.415 | ||

True-False Quiz | p.416 | ||

Review: Exercises | p.416 | ||

5.5 | The Substitution Rule | Problems | p.420 |

### Chapter 6

Applications Of Integration

6.1 | Areas Between Curves | Exercises | p.427 |

6.2 | Volumes | Exercises | p.438 |

6.3 | Volumes by Cylindrical Shells | Exercises | p.444 |

6.4 | Work | Exercises | p.449 |

6.5 | Average Value of a Function | Exercises | p.453 |

Review: Concept Check | p.457 | ||

Review Exercises | p.457 |

### Chapter 7

Techniques Of Integration

7.1 | Integration by Parts | Exercises | p.468 |

7.2 | Trigonometric Integrals | Exercises | p.476 |

7.3 | Trigonometric Substitution | Exercises | p.483 |

7.4 | Integration of Rational Functions by Partial Fractions | Exercises | p.492 |

7.5 | Strategy for Integration | Exercises | p.499 |

7.6 | Integration Using Tables and Computer Algebra Systems | Exercises | p.504 |

7.7 | Approximate Integration | Exercises | p.516 |

7.8 | Improper Integrals | Exercises | p.527 |

Review: Concept Check | p.529 | ||

Review: True-False Quiz | p.530 | ||

Review Exercises | p.530 |

### Chapter 8

Further Applications Of Integration

8.1 | Arc Length | Exercises | p.543 |

8.2 | Area of a Surface of Revolution | Exercises | p.550 |

8.3 | Applications to Physics and Engineering | Exercises | p.560 |

8.4 | Applications to Economics and Biology | Exercises | p.566 |

8.5 | Probability | Exercises | p.573 |

Concept Check | p.575 | ||

Review Exercises | p.575 |

### Chapter 9

Differential Equations

9.1 | Modeling with Differential Equations | Exercises | p.584 |

9.2 | Direction Fields and Euler's Method | Exercises | p.592 |

9.3 | Separable Equations | Exercises | p.600 |

9.4 | Models for Population Growth | Exercises | p.613 |

9.5 | Linear Equations | Exercises | p.620 |

9.6 | Predator-Prey Systems | Exercises | p.627 |

Review | p.629 | ||

True-False Quiz | p.629 | ||

Review Exercises | p.630 |

### Chapter 10

Parametric Equations And Polar Coordinates

10.1 | Curves Defined by Parametric Equations | Exercises | p.641 |

10.2 | Calculus with Parametric Curves | Exercises | p.651 |

10.3 | Polar Coordinates | Exercises | p.662 |

10.4 | Areas and Lengths in Polar Coordinates | Exercises | p.668 |

10.5 | Conic Sections | Exercises | p.676 |

10.6 | Conic Sections in Polar Coordinates | Exercises | p.684 |

Concept Check | p.685 | ||

True-False Quiz | p.685 | ||

Review Exercises | p.686 |

### Chapter 11

Infinite Sequences And Series

11.1 | Sequences | Exercises | p.700 |

11.2 | Series | Exercises | p.711 |

11.3 | The Integral Test and Estimates of Sums | Exercises | p.720 |

11.4 | The Comparison Tests | Exercises | p.726 |

11.5 | Alternating Series | Exercises | p.731 |

11.6 | Absolute Convergence and the Ratio and Root Tests | Exercises | p.737 |

11.7 | Strategy for Testing Series | Exercises | p.740 |

11.8 | Power Series | Exercises | p.745 |

11.9 | Representations of Functions as Power Series | Exercises | p.751 |

11.10 | Taylor and Maclaurin Series | Exercises | p.765 |

11.11 | Applications of Taylor Polynomials | Exercises | p.774 |

True-False Quiz | p.778 | ||

Concept Check | p.778 | ||

Review Exercises | p.779 |

### Chapter 12

Vectors And The Geometry Of Space

12.1 | Three-Dimensional Coordinate Systems | Exercises | p.790 |

12.2 | Vectors | Exercises | p.798 |

12.3 | The Dot Product | Exercises | p.806 |

12.4 | The Cross Product | Exercises | p.814 |

12.5 | Equations of Lines and Planes | Exercises | p.824 |

12.6 | Cylinders and Quadric Surfaces | Exercises | p.832 |

Concept Check | p.834 | ||

True-False Quiz | p.834 | ||

Review Exercises | p.835 |

### Chapter 13

Vector Problems

13.1 | Vector Functions and Space Curves | Exercises | p.845 |

13.2 | Derivatives and Integrals of Vector Functions | Exercises | p.852 |

13.3 | Arc Length and Curvature | Exercises | p.860 |

13.4 | Motion in Space: Velocity and Acceleration | Exercises | p.870 |

True-False Quiz | p.873 | ||

Concept Check | p.873 | ||

Review Exercises | p.874 |

### Chapter 14

Partial Derivatives

14.1 | Functions of Several Variables | Exercises | p.888 |

14.2 | Limits and Continuity | Exercises | p.899 |

14.3 | Partial Derivatives | Exercises | p.911 |

14.4 | Tangent Planes and Linear Approximations | Exercises | p.922 |

14.5 | The Chain Rule | Exercises | p.930 |

14.6 | Directional Derivatives and the Gradient Vector | Exercises | p.943 |

14.7 | Maximum and Minimum Values | Exercises | p.953 |

14.8 | Lagrange Multipliers | Exercises | p.963 |

True-False Quiz | p.967 | ||

Concept Check | p.967 | ||

Review Exercises | p.968 |

### Chapter 15

Multiple Integrals

15.1 | Double Integrals over Rectangles | Exercises | p.981 |

15.2 | Iterated Integrals | Exercises | p.987 |

15.3 | Double Integrals over General Regions | Exercises | p.995 |

15.4 | Double Integrals in Polar Coordinates | Exercises | p.1002 |

15.5 | Applications of Double Integrals | Exercises | p.1012 |

15.6 | Surface Area | Exercises | p.1016 |

15.7 | Triple Integrals | Exercises | p.1025 |

15.8 | Triple Integrals in Cylindrical Coordinates | Exercises | p.1031 |

15.9 | Triple Integrals in Spherical Coordinates | Exercises | p.1037 |

15.10 | Change in Variables in Multiple Integrals | Exercises | p.1047 |

Concept Check | p.1049 | ||

True-False Quiz | p.1049 | ||

Review Exercises | p.1050 |

### Chapter 16

Vector Calculus

16.1 | Vector Fields | Exercises | p.1061 |

16.2 | Line Integrals | Exercises | p.1072 |

16.3 | The Fundamental Theorem for Line Integrals | Exercises | p.1082 |

16.4 | Green's Theorem | Exercises | p.1089 |

16.5 | Curl and Divergence | Exercises | p.1097 |

16.6 | Parametric Surfaces and Their Areas | Exercises | p.1108 |

16.7 | Surface Integrals | Exercises | p.1120 |

16.8 | Stoke's Theorem | Exercises | p.1127 |

16.9 | The Divergence Theorem | Exercises | p.1133 |

True-False Quiz | p.1136 | ||

Concept Check | p.1136 | ||

Review Exercises | p.1137 |

### Chapter 17

Second-Order Differential Equations

17.1 | Second-Order Linear Equations | Exercises | p.1148 |

17.2 | Nonhomogeneous Linear Equations | Exercises | p.1155 |

17.3 | Applications of Second-Order Differential Equations | Exercises | p.1163 |

17.4 | Series Solutions | Exercises | p.1168 |

Review Exercises | p.1169 | ||

Concept Check | p.1169 | ||

True-False Quiz | p.1169 |