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 (pdf))
  • Commonly Used Derivatives (Slides (pdf))
  • Product and Chain Rules (Slides (pdf))
  • Multivariable Derivatives (Slides (pdf))
  • Math Trick: Combining Exponents (Slides (pdf))
  • Walkthrough: Single Variable Derivatives
  • Walkthrough: Multivariable Derivatives
• Integrals
  • Review: What is an Integral? (Slides (pdf))
  • Walkthrough: Consumer Surplus
• Practice Problems
  • Derivatives and Integrals (pdf)
  • Solutions (pdf)

Module Two: Linear Algebra

• Systems of Equations
  • Review: Systems of Equations (Slides (pdf))
  • Walkthrough: Cancellation Technique
• Matrices
  • Review: Matrix Conformity (Slides (pdf))
  • Reduced Row Echelon Form (Slides (pdf))
  • Determinants (Slides (pdf))
  • Inverting a Matrix (Slides (pdf))
  • Walkthrough: Spreadsheet Inversion
• Practice Problems
  • Matrices (pdf)
    • Solutions (pdf)

Module Three: Optimization

• Unconstrained Optimization
  • Unconstrained Optimization – Single Variable (Slides (pdf))
  • Unconstrained Optimization – Multiple Variables (Slides (pdf))
  • Math Trick: Invoking Symmetry (Slides (pdf))
  • Walkthrough: Profit Maximization – Monopoly
  • Walkthrough: Profit Maximization – Cournot Duopoly
• Constrained Optimization
  • Constraints (Slides (pdf))
  • Constrained Optimization (Slides (pdf))
  • Walkthrough: Utility Maximization
• Practice Problems
  • Optimization (pdf)
  • Solutions (pdf)