1.1 Rates of Change and the Slope of a Curve

1.2 Rates of Change Using Equations

1.3 Limits

1.4 Limits and Continuity

1.5 Introduction to Derivatives

Chapter Limits Review

Rates of Change, Limits and Continuity Chapter Test

Prerequisite Skills

2.1 Derivative of Polynomial Function

2.2 The Product Rule

2.3 Velocity, Acceleration, and Second Derivatives

2.4 The Chain Rule

2.5 Derivatives of Quotients

2.6 Rate of Change Problems

Derivatives Chapter Review

Derivate Chapter Test

3.1 Increasing and Decreasing Functions

3.2 Maxima and Minima

3.3 Concavity and the Second Derivative Test

3.4 Simple Rational Functions

3.5 Putting It All Together

3.6 Optimization Problems

Chapter Review Graphing and Optimization

Chapter Test Max and Min

4.1 Instantaneous Rates of Change of Sinusodal Functions

4.2 Derivatives of the Sine and Cosine Functions

4.3 Differentiation Rules for Sinusodal Functions

4.4 Applications of Sinusoidal Functions and Their Derivatives

4.5 Chapter Review

4.6 Chapter Test

5.1 Rates of Change and the Number e

5.2 The Natural Logarithm

5.3 Derivatives of Exponential Functions

5.4 Differentiation Rules for Exponential Functions

5.5 Making Connections Exponential Models

5.6 Chapter Review

5.7 Chapter Test

6.1 Introduction to Vectors

6.2 Tutorials of Addition and Subtraction of Vectors

6.3 Tutorials of Multiplying a Vector by a Scalar

6.4 Applications of Vector Addition

6.5 Tutorials of Resolution of Vectors Into Rectangular Components

6.6 Chapter Review

Practice Test Sum of Vectors

7.1 Cartesian Vectors

7.2 Dot Product

7.3 Applications of the Dot Product

7.4 Vectors in Three-Space

7.5 Cross Product and Its Properties

7.6 Applications of the Dot Product and Cross Product

7.7 Chapter Review

7.8 Chapter Test

8.1 Equations of Lines in Two-Space

8.2 Equation of Planes

8.3 Properties of Planes

8.4 Intersections of Lines in Two-Space and Three-Space

8.5 Intersection of Lines and Planes

8.6 Intersections of Planes

8.7 Chapter Review

8.8 Chapter Test

8.10 Course Review