Calculus and Vectors

Unit 1

1.1 - Rates of Change and Slope of a Curve

1.2 - Rates of Change Using Equations

1.4 - Limits and Continuity

1.5 - Introduction to Derivatives

Unit 3

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

Unit 5

5.1 - Exponential and Logarithmic Functions

5.2 - Derivatives of Exponential Functions

5.3 - Exponential Models

Unit 7

7.1 - Cartesian Vectors

7.2 - Dot Product

7.3 - Applications of Dot Product

7.4 - Vectors in Three-Space

7.5 - The Cross Product and Its Properties

7.6 - Applications of the Dot and Cross Products

Unit 2

2.1 - Derivatives of a Polynomial Function

2.2 - Product Rule

2.3 - Velocity, Acceleration and Second Derivatives

2.4 - The Chain Rule

2.5 - The Quotient Rule

2.6 - Rate of Change Problems

Unit 4

4.1 - Derivatives of Sinusoidal Functions

4.2 - Differentiation Rules for Sinusoidal Functions

4.3 - Applications of Sinusoidal Functions

Unit 6

6.1 - Introduction to Vectors

6.2 - Addition and Subtraction of Vectors

6.3 - Multiplying a Vector by a Scalar

6.4 - Applications of Vector addition

6.5 - Resolution of Vectors Into Components

Unit 8

8.1 - Equations of lines in Two-Space and Three-Space

8.2 - Equations of Planes

8.3 - Properties of Planes

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

8.5 - Intersections of Lines and Planes

8.6 - Intersections of Planes