### 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 Rules and Rates of Change | Exercises | p.115 |

2.3 | Produce 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

Applications 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 | Riemann Sums and Definite Integrals | Exercises | p.278 |

4.4 | The Fundamental Theorem of Calculus | Exercises | p.291 |

4.5 | Integration by Substitution | Exercises | p.304 |

4.6 | Numerical Integration | Exercises | p.314 |

Review Exercises | p.316 | ||

Problem Solving | p.319 |

### Chapter 5

Logarithmic, Exponential, And Other Transcendental Functions

5.1 | The Natural Logarithmic Function: Differentiation | Exercises | p.329 |

5.2 | The Natural Logarithmic Function: Integration | Exercises | p.338 |

5.3 | Inverse Functions | Exercises | p.347 |

5.4 | Exponential Functions: Differentiation and Integration | Exercises | p.356 |

5.5 | Bases Other Than e and Applications | Exercises | p.366 |

5.6 | Inverse Trigonometric Functions: Differentiation | Exercises | p.377 |

5.7 | Inverse Trigonometric Functions: Integration | Exercises | p.385 |

5.8 | Hyperbolic Functions | Exercises | p.396 |

Review Exercises | p.399 | ||

Problem Solving | p.401 |

### Chapter 6

Differential Equations

6.1 | Slope Fields and Euler's Method | Exercises | p.409 |

6.2 | Differential Equations: Growth and Decay | Exercises | p.418 |

6.3 | Separation of Variables and the Logistic Equation | Exercises | p.429 |

6.4 | First-Order Linear Differential Equations | Exercises | p.438 |

Review Exercises | p.441 | ||

Problem Solving | p.443 |

### Chapter 7

Applications Of Integration

7.1 | Area of a Region Between Two Curves | Exercises | p.452 |

7.2 | Volume: The Disk Method | Exercises | p.463 |

7.3 | Volume: The Shell Method | Exercises | p.472 |

7.4 | Arc Length and Surfaces of Revolution | Exercises | p.483 |

7.5 | Work | Exercises | p.493 |

7.6 | Moments, Centers of Mass, and Centoids | Exercises | p.504 |

7.7 | Fluid Pressure and Fluid Force | Exercises | p.511 |

Review Exercises | p.513 | ||

Problem Solving | p.515 |

### Chapter 8

Integration Techniques, L'Hopital's Rule, And Improper Integrals

8.1 | Basic Integration Rules | Exercises | p.522 |

8.2 | Integration by Parts | Exercises | p.531 |

8.3 | Trigonometric Integrals | Exercises | p.540 |

8.4 | Trigonometric Substitution | Exercises | p.549 |

8.5 | Partial Fractions | Exercises | p.559 |

8.6 | Integration by Tables and Other Integration Techniques | Exercises | p.565 |

8.7 | Indeterminate Forms and L'Hopital's Rule | Exercises | p.574 |

8.8 | Improper Integrals | Exercises | p.585 |

Review Exercises | p.589 | ||

Problem Solving | p.591 |

### Chapter 9

Infinite Series

9.1 | Sequences | Exercises | p.602 |

9.2 | Series and Convergence | Exercises | p.612 |

9.3 | The Integral Test and p-Series | Exercises | p.620 |

9.4 | Comparisons of Series | Exercises | p.628 |

9.5 | Alternating Series | Exercises | p.636 |

9.6 | The Ratio and Root Tests | Exercises | p.645 |

9.7 | Taylor Polynomials and Approximations | Exercises | p.656 |

9.8 | Power Series | Exercises | p.666 |

9.9 | Representation of Functions by Power Series | Exercises | p.674 |

9.10 | Taylor and Maclaurin Series | Exercises | p.685 |

Review Exercises | p.688 | ||

Problem Solving | p.691 |

### Chapter 10

Conics, Parametric Equations, And Polar Coordinates

10.1 | Conics and Calculus | Exercises | p.704 |

10.2 | Plane Curves and Parametric Equations | Exercises | p.716 |

10.3 | Parametric Equations and Calculus | Exercises | p.725 |

10.4 | Polar Coordinates and Polar Graphs | Exercises | p.736 |

10.5 | Area and Arc Length in Polar Coordinates | Exercises | p.745 |

10.6 | Polar Equations of Conics and Kepler's Laws | Exercises | p.753 |

Review Exercises | p.756 | ||

Problem Solving | p.759 |

### Chapter 11

Vectors And The Geometry Of Space

11.1 | Vectors in the Plane | Exercises | p.769 |

11.2 | Space Coordinates and Vectors in Space | Exercises | p.778 |

11.3 | The Dot Product of Two Vectors | Exercises | p.787 |

11.4 | The Cross Product of Two Vectors in Space | Exercises | p.796 |

11.5 | Lines and Planes in Space | Exercises | p.805 |

11.6 | Surfaces in Space | Exercises | p.818 |

11.7 | Cylindrical and Spherical Coordinates | Exercises | p.825 |

Review Exercises | p.827 | ||

Problem Solving | p.829 |

### Chapter 12

Vector-Valued Functions

12.1 | Vector-Valued Funcions | Exercises | p.837 |

12.2 | Differentiation and Integration of Vector-Valued Functions | Exercises | p.846 |

12.3 | Velocity and Acceleration | Exercises | p.854 |

12.4 | Tangent Vectors and Normal Vectors | Exercises | p.863 |

12.5 | Arc Length and Curvature | Exercises | p.875 |

Review Exercises | p.879 | ||

Problem Solving | p.881 |

### Chapter 13

Functions Of Several Variables

13.1 | Introduction to Functions of Several Variables | Exercises | p.892 |

13.2 | Limits and Continuity | Exercises | p.902 |

13.3 | Partial Derivatives | Exercises | p.912 |

13.4 | Differentials | Exercises | p.921 |

13.5 | Chain Rules for Functions of Several Variables | Exercises | p.929 |

13.6 | Directional Derivatives and Gradients | Exercises | p.940 |

13.7 | Tangent Planes and Normal Lines | Exercises | p.949 |

13.8 | Extrema of Functions of Two Variables | Exercises | p.958 |

13.9 | Applications of Extrema of Functions of Two Variables | Exercises | p.964 |

13.10 | Lagrange Multipliers | Exercises | p.974 |

Review Exercises | p.976 | ||

Problem Solving | p.979 |

### Chapter 14

Multiple Integration

14.1 | Iterated Integrals and Area in the Plane | Exercises | p.988 |

14.2 | Double Integrals and Volume | Exercises | p.997 |

14.3 | Change of Variables: Polar Coordinates | Exercises | p.1006 |

14.4 | Center of Mass and Moments of Inertia | Exercises | p.1015 |

14.5 | Surface Area | Exercises | p.1022 |

14.6 | Triple Integrals and Applications | Exercises | p.1032 |

14.7 | Triple Integrals in Cylindrical and Spherical Coordinates | Exercises | p.1040 |

14.8 | Change of Variables: Jacobians | Exercises | p.1047 |

Review Exercises | p.1048 | ||

Problem Solving | p.1051 |

### Chapter 15

Vector Analysis

15.1 | Vector Fields | Exercises | p.1063 |

15.2 | Line Integrals | Exercises | p.1075 |

15.3 | Conservative Vector Fields and Independence of Path | Exercises | p.1086 |

15.4 | Green's Theorem | Exercises | p.1095 |

15.5 | Parametric Surfaces | Exercises | p.1105 |

15.6 | Surface Integrals | Exercises | p.1118 |

15.7 | Divergence THeorem | Exercises | p.1126 |

15.8 | Stoke's Theorem | Exercises | p.1133 |

Review Exercises | p.1134 | ||

Problem Solving | p.1137 |