# 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

## 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

## Module Three: Optimization

- Unconstrained Optimization
- Constrained Optimization
- Constraints (Slides (pdf))
- Constrained Optimization (Slides (pdf))
- Walkthrough: Utility Maximization

- Practice Problems

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