In this course, you'll hone your problem-solving skills through learning to find numerical solutions to systems of differential equations. You'll write code in Python to fight forest fires, rescue the Apollo 13 astronauts, stop the spread of epidemics, and resolve other real-world dilemmas.
By the end of this course, you'll develop an intuition for the use of differential equations in the applied sciences. You'll also learn how to build mathematical models for systems of differential equations using a variety of techniques. Along the way, you'll learn how to translate mathematical expressions into Python code and solve some really cool problems!
You'll need a basic knowledge of programming in Python for this course, around the level of Intro to Computer Science. An understanding of Python packages, as discussed in Programming Foundations with Python, will also be helpful.
In addition, you'll need to feel comfortable with trigonometry at the high school level, as well as basic vector algebra. This class will primarily involve solving differential equations numerically rather than analytically, but some exposure to calculus and physics at the level of Intro to Physics wouldn't hurt.
Most of all, bring with you a love of learning and problem solving!
Introduction to the Forward Euler Method
Comparing solvers, Heun’s Method, and the Symplectic Euler Method
Implicit methods and stiffness
Stability, sensitivity, and optimization
Friction, equilibria, and control theory
Partial differential equations and heat conduction
Chaos, software, and predictive capability