Math Refresher

This website helps you prepare for our MAE and MSE programs by reviewing commonly used mathematical techniques. The material below is organized into three modules: Calculus, Linear Algebra, and Optimization. At the end of each set of videos there are several practice problems. While optional, it is strongly encouraged to complete these problems as a practice before you start the Master program.

• Module One: Calculus
  • Derivatives
    • Review: What is a Derivative? (Slides)
    • Commonly Used Derivatives (Slides)
    • Product and Chain Rules (Slides)
    • Multivariable Derivatives (Slides)
    • Math Trick: Combining Exponents (Slides)
    • Walkthrough: Single Variable Derivatives
    • Walkthrough: Multivariable Derivatives
  • Integrals
    • Review: What is an Integral? (Slides)
    • Walkthrough: Consumer Surplus
  • Practice Problems
    • Derivatives and Integrals
      • Solutions
• Module Two: Linear Algebra
  • Systems of Equations
    • Review: Systems of Equations (Slides)
    • Walkthrough: Cancellation Technique
  • Matrices
    • Review: Matrix Conformity (Slides)
    • Reduced Row Echelon Form (Slides)
    • Determinants (Slides)
    • Inverting a Matrix (Slides)
    • Walkthrough: Spreadsheet Inversion
  • Practice Problems
    • Matrices
      • Solutions
• Module Three: Optimization
  • Unconstrained Optimization
    • Unconstrained Optimization – Single Variable (Slides)
    • Unconstrained Optimization – Multiple Variables (Slides)
    • Math Trick: Invoking Symmetry (Slides)
    • Walkthrough: Profit Maximization – Monopoly
    • Walkthrough: Profit Maximization – Cournot Duopoly
  • Constrained Optimization
    • Constraints (Slides)
    • Constrained Optimization (Slides)
    • Walkthrough: Utility Maximization
  • Practice Problems
    • Optimization
      • Solutions