Table of Contents

Chapter 1: Prerequisites for Calculus

1.1 Linear Functions

1.2 Functions and Graphs

1.3 Exponential Functions

1.4 Parametric Equations

1.5 Inverse Functions and Logarithms

1.6 Trigonometric Functions

Chapter 2: Limits and Continuity

2.1 Rates of Change and Limits

2.2 Limits Involving Infinity

2.3 Continuity

2.4 Rates of Change, Tangent Lines, and Sensitivity

Chapter 3: Derivatives

3.1 Derivative of a Function

3.2 Differentiability

3.3 Rules for Differentiation

3.4 Velocity and Other Rates of Change

3.5 Derivatives of Trigonometric Functions

Chapter 4: More Derivatives

4.1 Chain Rule

4.2 Implicit Differentiation

4.3 Derivatives of Inverse Trigonometric Functions

4.4 Derivatives of Exponential and Logarithmic Functions

Chapter 5: Applications of Derivatives

5.1 Extreme Values of Functions

5.2 Mean Value Theorem

5.3 Connecting ƒ_ and ƒ _ with the Graph of ƒ

5.4 Modeling and Optimization

5.5 Linearization, Sensitivity, and Differentials

5.6 Related Rates

Chapter 6: The Definite Integral

6.1 Estimating with Finite Sums

6.2 Definite Integrals

6.3 Definite Integrals and Antiderivatives

6.4 Fundamental Theorem of Calculus

6.5 Trapezoidal Rule

Chapter 7: Differential Equations and Mathematical Modeling

7.1 Slope Fields and Euler’s Method

7.2 Antidifferentiation by Substitution

7.3 Antidifferentiation by Parts

7.4 Exponential Growth and Decay

7.5 Logistic Growth

Chapter 8: Applications of Definite Integrals

8.1 Accumulation and Net Change

8.2 Areas in the Plane

8.3 Volumes

8.4 Lengths of Curves

8.5 Applications from Science and Statistics

Chapter 9: Sequences, L’Hospital’s Rule, and Improper Integrals

9.1 Sequences

9.2 L ’Hospital’s Rule

9.3 Relative Rates of Growth

9.4 Improper Integrals

Chapter 10: Infinite Series

10.1 Power Series

10.2 Taylor Series

10.3 Taylor’s Theorem

10.4 Radius of Convergence

10.5 Testing Convergence at Endpoints

Chapter 11: Parametric, Vector, and Polar Functions

11.1 Parametric Functions

11.2 Vectors in the Plane

11.3 Polar Functions


A1 Formulas from Precalculus Mathematics

A2 A Formal Definition of Limit

A3 A Proof of the Chain Rule

A4 Hyperbolic Functions

A5 A Very Brief Table of Integrals


Selected Answers

Applications Index

Subject Index