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