Differential Equations in Action

Making Math Matter

In this course you will examine real world problems — rescue the Apollo 13 astronauts, stop the spread of epidemics, and fight forest fires…

Class Summary

In this course you will examine real world problems -- rescue the Apollo 13 astronauts, stop the spread of epidemics, and fight forest fires -- involving differential equations and figure out how to solve them using numerical methods.

What Should I Know?

You'll need a basic knowledge of programming for this course, around the level of CS 101 or equivalent. You'll also need to understand trigonometry at the high school level, as well as basic vector algebra. This class will primarily involve solving equations numerically rather than analytically, but some exposure to calculus and physics at the level of PH 100 wouldn't hurt.

What Will I Learn?

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. Along the way, you'll learn how to translate mathematical expressions into Python code, and solve some really cool problems!

Syllabus

Unit 1: Rescuing Apollo 13, Part 1

Introduction to the Forward Euler Method

Unit 2: Rescuing Apollo 13, Part 2

Comparing solvers, Heun’s Method and Symplectic Euler Method

Unit 3: Analyzing the Spread of Diseases

Implicit methods and stiffness

Unit 4: There’s Plenty of Fish in the Sea?

Stability, sensitivity, and optimization

Unit 5: Antilock Brake Systems

Friction, equilibria, and control theory

Unit 6: The Path of a Forest Fire

Partial differential equations and heat conduction

Unit 7: Advanced Applications of Numerical Methods

Chaos, software, and predictive capability

Course Instructors

Jörn Loviscach is a professor of technical mathematics and computer engineering. In a former life, he was a professor of computer graphics, animation, and simulation, worked as editor and senior editor for several computer magazines. For three years he also served as deputy editor-in-chief of c’t Magazin für Computertechnik, a renowned German biweekly. His research integrates human-computer interaction, visual computing, and audio and music computing. Both as a researcher and as a practitioner he is interested in applying digital media to education. He has published over 1800 video lectures on his YouTube channel on mathematics and computer science, and his channel is one of the most popular of its kind in Germany.

Miriam feels inspired by the inherent beauty of math and loves helping others develop confidence and excitement as they learn. Having the opportunity to do this with thousands of students all over the world through her work at Udacity is a dream come true. Outside of work, she enjoys singing, baking, teaching yoga, and tutoring high schoolers. Miriam attended Stanford University, where she earned a B.S. in Physics, a B.A. in Philosophy and Religious Studies, and an M.A. in Religious Studies.