Contents

**Chapter 1 Rates of Change and the Derivative **
1.1 Average Rates of Change

1.1.1 Exercises

1.2 Prelude to IROC's

1.2.1 Exercises

1.3 Limits and Continuity

1.3.1 Limits

1.3.2 Continuous Functions

1.3.3 Limits involving Infinity

1.3.4 Exercises

1.4 IROC's and the Derivative

1.4.1 Exercises

1.5 Extrema and the Mean Value Theorem

1.5.1 Exercises

1.6 Higher-Order Derivatives

1.6.1 Exercises

**Chapter 2 Basic Rules for Calculating Derivatives **
2.1 The Power Rule and Linearity

2.1.1 Exercises

2.2 The Product and Quotient Rules

2.2.1 Exercises

2.3 The Chain Rule and Inverse Functions

2.3.1 Exercises

2.4 The Exponential Function

2.4.1 Exercises

2.5 The Natural Logarithm

2.5.1 Exercises

2.6 General Exponential and Logarithmic Functions

2.6.1 Exercises

2.7 Trigonometric Functions: Sine and Cosine

2.7.1 Exercises

2.8 The Other Trigonometric Functions

2.8.1 Exercises

2.9 Inverse Trig Functions

2.9.1 Exercises

2.10 Implicit Functions

2.10.1 Exercises

**Chapter 3 Applications of Differentiation **
3.1 Related Rates

3.1.1 Exercises

3.2 Graphing

3.2.1 Exercises

3.3 Optimization

3.3.1 Exercises

3.4 Linear Approximation

3.4.1 Exercises

3.5 l'Hôpital's Rule

3.5.1 Exercises

**Chapter 4 Anti-differentiation & Differential Equations**
4.1 Basic Anti-Differentiation

4.1.1 Exercises

4.2 Integration by Partial Fractions

4.2.1 Exercises

4.3 What is a Differential Equation?

4.3.1 Exercises

4.4 Separable Differential Equations

4.4.1 Exercises

4.5 Approximating Solutions

4.5.1 Exercises

**Chapter 5 Continuous Sums: the Definite Integral**
5.1 Sums and Differences

5.1.1 Exercises

5.2 Prelude to the Definite Integral

5.2.1 Exercises

5.3 The Definite Integral

5.3.1 Exercises

5.4 The Fundamental Theorem of Calculus

5.4.1 Exercises

5.5 Improper Integrals

5.5.1 Exercises

5.6 Numerical Techniques

5.6.1 Exercises

**Chapter 6 Applications of Integration**
6.1 Displacement and Distance Traveled

6.1.1 Exercises

6.2 Area in the Plane

6.2.1 Exercises

6.3 Distance Traveled in Space and Arc Length

6.3.1 Exercises

6.4 Area Swept Out and Polar Coordinates

6.4.1 Exercises

6.5 Volume

6.5.1 Exercises

6.6 Surface Area

6.6.1 Exercises

6.7 Mass and Density

6.7.1 Exercises

**Chapter 7 Polynomials and Power Series **
7.1 Approximating Polynomials

7.1.1 Exercises

7.2 Approximation of Functions

7.2.1 Exercises

7.3 Error in Approximation

7.3.1 Exercises

7.4 Functions as Power Series

7.4.1 Exercises

7.5 Power Series as Functions I

7.5.1 Exercises

7.6 Power Series as Functions II

7.6.1 Exercises

**Chapter 8 Theorems on Sequences and Series**
8.1 Theorems on Sequences

8.1.1 Exercises

8.2 Basic Theorems on Series

8.2.1 Exercises

8.3 Non-negative Series

8.3.1 Exercises

8.4 Series with Positive and Negative Terms

8.4.1 Exercises

Appendix A Parameterized Curves and Motion

A.1 Parameterized Curves

A.1.1 Exercises

Appendix B Tables of Derivative Formulas

Appendix C Tables of Integration Formulas

Appendix D Answers to Odd-Numbered Problems