Overview

You’ve heard math can solve real-world problems, but how? You model real-world systems as equations, which are typically nonlinear. However, you and your computer can only solve linear equations precisely. Moreover, your partner, a computer, operates in a discrete world, while your equations are defined in continuous space and their analytic solutions exist only in very limited cases. So, to answer real-world questions, how do you solve these equations with your computer?

This course bridges this gap by covering how to solve those equations computationally while understanding the mathematical foundations behind these methods. Through classical lectures, homework, exams, and hands-on projects, this course develops holistic skills for computational problem-solving and deepens your mathematical understanding through real-world applications.

Lectures

This course introduces graduate and advanced undergraduate students to the fundamentals needed to study computational methods. This class is intended for a broad spectrum of students in Engineering, Sciences and Mathematics. Topics include:

• Fundamental theorems used in numerical analysis

• Error analysis

• Root-finding methods for nonlinear equations

• Interpolation

• Approximation

• Numerical integration and differential equations

Group Project

Beyond classroom topics, students will tackle real-world problems with their group members by implementing the computational methods or extend their theoretical knowledge. Groups are expected to present their results in the final "minisymposium."