Tools

Precalculus

• Operations on Functions
• Trigonometric Functions
• Slope of a Line

Single Variable Calculus

• Derivative and Tangent Line
• Constant, Linear, Quadratic and Cubic Approximations
• Newton's Method
• Numerical Integration
• Lagrange Multipliers with Two Variables

Vectors and Algebra

• Rotating Coordinates
• Operations on Vectors
• Determinant and Vector Products
• Multiplication of a Vector by a Matrix
• Linear Transformations in Three Dimensions

Application to 3D Linear Geometry

• Lines in Space
• Planes in Space

Curves

• Polar Plotter
• Curves in Two Dimensions
• Curves in Three Dimensions

Fields and Surfaces

• Directional Derivatives
• Contour Lines, Gradients and Directional Derivatives
• Curves and Surfaces
• Functions of Two Variables
• Newton's Method with Two Equations and Two Variables

Complex Numbers and Functions

• Complex Numbers
• Complex Functions

Integration on Curves

• Curves and Vector Fields
• Line Integrals

Integration on Surfaces

• Flux Integrals
• Integration Bounds

Differential Equations

• First Order ODE
• Second Order ODE
• System of First Order ODE

Applications

• Static Electric Fields in Two Dimensions
• Static Electric Fields in Three Dimensions
• Stationary Magnetic Fields in Two Dimensions
• Series RLC Circuit