CHAPTER 1 Limits and Continuity

1.1 Limits (An Intuitive Approach)

1.2 Computing Limits

1.3 Limits at Infinity; End Behavior of a Function

1.4 Limits (Discussed More Rigorously)

1.5 Continuity

1.6 Trigonometric Functions

1.7 Inverse Trigonometric Functions

1.8 Exponential and Logarithmic Functions

CHAPTER 2 The Derivative

2.1 Tangent Lines and Rates of Change

2.2 The Derivative Function

2.3 Introduction to Techniques of Differentiation

2.4 The Product and Quotient Rules

2.5 Derivatives of Trigonometric Functions

2.6 The Chain Rule

CHAPTER 3 Differentiation

3.1 Implicit Differentiation

3.2 Derivatives of Logarithmic Functions

3.3 Derivatives of Exponential and Inverse Trigonometric Functions

3.4 Related Rates

3.5 Local Linear Approximation; Differentials

3.6 L'Hôpital's Rule; Indeterminate Forms

CHAPTER 4 The Derivative in Graphing and Applications

4.1 Analysis of Functions I: Increase, Decrease, and Concavity

4.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials

4.3 Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents

4.4 Absolute Maxima and Minima

4.5 Applied Maximum and Minimum Problems

4.6 Rectilinear Motion

4.7 Newton's Method

4.8 Rolle's Theorem; Mean-Value Theorem

CHAPTER 5 Integration

5.1 An Overview of Area and Speed-Distance Problems

5.2 The Indefinite Integral

5.3 Integration by Substitution

5.4 The Definition of Area as a Limit; Sigma Notation

5.5 The Definite Integral

5.6 The Fundamental Theorem of Calculus

5.7 Rectilinear Motion Revisited Using Integration

5.8 Average Value of a Function and its Applications

5.9 Evaluating Definite Integrals by Substitution

5.10 Logarithmic and Other Functions Defined by Integrals

CHAPTER 6 Applications of the Definite Integral

6.1 Area Between Two Curves

6.2 Volumes by Slicing; Disks and Washers

6.3 Volumes by Cylindrical Shells

6.4 Length of a Plane Curve

6.5 Area of a Surface of Revolution

6.6 Work

6.7 Moments, Centers of Gravity, and Centroids

6.8 Fluid Pressure and Force

6.9 Hyperbolic Functions and Hanging Cables

CHAPTER 7 Principles of Integral Evaluation

7.1 An Overview of Integration Methods

7.2 Integration by Parts

7.3 Integrating Trigonometric Functions

7.4 Trigonometric Substitutions

7.5 Integrating Rational Functions by Partial Fractions

7.6Using Computer Algebra Systems and Tables of Integrals

7.7 Numerical Integration; Simpson's Rule

7.8 Improper Integrals

CHAPTER 8 Mathematical Modeling with Differential Equations

8.1 Modeling with Differential Equations

8.2 Separation of Variables

8.3 Slope Fields; Euler's Method

8.4 First-Order Differential Equations and Applications

8.5 Prey-Predator Model

CHAPTER 9 Parametric and Polar Curves; Conic Sections

9.1 Parametric Equations; Tangent Lines and Arc Length for Parametric Curves

9.2 Polar Coordinates

9.3 Tangent Lines, Arc Length, and Area for Polar Curves

9.4 Conic Sections

9.5 Rotation of Axes; Second-Degree Equations

9.6 Conic Sections in Polar Coordinates

CHAPTER 10 Sequence and Infinite Series

10.1 Sequences