## Table of Contents

**0. Functions**

0.1 Functions and Their Graphs

0.2 Some Important Functions

0.3 The Algebra of Functions

0.4 Zeros of Functions - The Quadratic Formula and Factoring

0.5 Exponents and Power Functions

0.6 Functions and Graphs in Applications

**1. The Derivative**

1.1 The Slope of a Straight Line

1.2 The Slope of a Curve at a Point

1.3 The Derivative and Limits

1.4 Limits and the Derivative

1.5 Differentiability and Continuity

1.6 Some Rules for Differentiation

1.7 More About Derivatives

1.8 The Derivative as a Rate of Change

**2. Applications of the Derivative**

2.1 Describing Graphs of Functions

2.2 The First and Second Derivative Rules

2.3 The First and Section Derivative Tests and Curve Sketching

2.4 Curve Sketching (Conclusion)

2.5 Optimization Problems

2.6 Further Optimization Problems

2.7 Applications of Derivatives to Business and Economics

**3. Techniques of Differentiation**

3.1 The Product and Quotient Rules

3.2 The Chain Rule

3.3 Implicit Differentiation and Related Rates

**4. The Exponential and Natural Logarithm Functions**

4.1 Exponential Functions

4.2 The Exponential Function e^{x}

4.3 Differentiation of Exponential Functions

4.4 The Natural Logarithm Function

4.5 The Derivative of ln *x*

4.6 Properties of the Natural Logarithm Function

**5. Applications of the Exponential and Natural Logarithm Functions**

5.1 Exponential Growth and Decay

5.2 Compound Interest

5.3. Applications of the Natural Logarithm Function to Economics

5.4. Further Exponential Models

**6. The Definite Integral**

6.1 Antidifferentiation

6.2 The Definite Integral and Net Change of a Function

6.3 The Definite Integral and Area Under a Graph

6.4 Areas in the* xy*-Plane

6.5 Applications of the Definite Integral

**7. Functions of Several Variables**

7.1 Examples of Functions of Several Variables

7.2 Partial Derivatives

7.3 Maxima and Minima of Functions of Several Variables

7.4 Lagrange Multipliers and Constrained Optimization

7.5 The Method of Least Squares

7.6 Double Integrals

**8. The Trigonometric Functions**

8.1 Radian Measure of Angles

8.2 The Sine and the Cosine

8.3 Differentiation and Integration of sin *t* and cos *t*

8.4 The Tangent and Other Trigonometric Functions

**9. Techniques of Integration**

9.1 Integration by Substitution

9.2 Integration by Parts

9.3 Evaluation of Definite Integrals

9.4 Approximation of Definite Integrals

9.5 Some Applications of the Integral

9.6 Improper Integrals

**10. Differential Equations**

10.1 Solutions of Differential Equations

10.2 Separation of Variables

10.3 First-Order Linear Differential Equations

10.4 Applications of First-Order Linear Differential Equations

10.5 Graphing Solutions of Differential Equations

10.6 Applications of Differential Equations

10.7 Numerical Solution of Differential Equations

**11. Taylor Polynomials and Infinite Series**

11.1 Taylor Polynomials

11.2 The Newton-Raphson Algorithm

11.3 Infinite Series

11.4 Series with Positive Terms

11.5 Taylor Series

**12. Probability and Calculus**

12.1 Discrete Random Variables

12.2 Continuous Random Variables

12.3 Expected Value and Variance

12.4 Exponential and Normal Random Variables

12.5 Poisson and Geometric Random Variables