Intermediate

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Course Summary

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.

Why Take This Course?

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!

Prerequisites and Requirements

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!

See the Technology Requirements for using Udacity.

What Will I Learn?

Syllabus

Lesson 1: Rescuing Apollo 13, Part 1

Introduction to the Forward Euler Method

Lesson 2: Rescuing Apollo 13, Part 2

Comparing solvers, Heun’s Method, and the Symplectic Euler Method

Lesson 3: Analyzing the Spread of Diseases

Implicit methods and stiffness

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

Stability, sensitivity, and optimization

Lesson 5: Antilock Brake Systems

Friction, equilibria, and control theory

Lesson 6: The Path of a Forest Fire

Partial differential equations and heat conduction

Lesson 7: Advanced Applications of Numerical Methods

Chaos, software, and predictive capability

Instructors & Partners

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 has had the privilege to contribute to student experience at Udacity from multiple angles. From creating new courses to working one-on-one with students to helping lead our team of Coaches, she’s loved it all and has only grown more passionate about changing education. Outside of work, she enjoys singing, baking, and teaching yoga. 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.

Frequently Asked Questions


When does the course begin?

This class is self paced. You can begin whenever you like and then follow your own pace. It’s a good idea to set goals for yourself to make sure you stick with the course.

How long will the course be available?

This class will always be available!

How do I know if this course is for me?

Take a look at the “Class Summary,” “What Should I Know,” and “What Will I Learn” sections above. If you want to know more, just enroll in the course and start exploring.

Can I skip individual videos? What about entire lessons?

Yes! The point is for you to learn what YOU need (or want) to learn. If you already know something, feel free to skip ahead. If you ever find that you’re confused, you can always go back and watch something that you skipped.

How much does this cost?

It’s completely free! If you’re feeling generous, we would love to have you contribute your thoughts, questions, and answers to the course discussion forum.

What are the rules on collaboration?

Collaboration is a great way to learn. You should do it! The key is to use collaboration as a way to enhance learning, not as a way of sharing answers without understanding them.

Why are there so many questions?

Udacity classes are a little different from traditional courses. We intersperse our video segments with interactive questions. There are many reasons for including these questions: to get you thinking, to check your understanding, for fun, etc... But really, they are there to help you learn. They are NOT there to evaluate your intelligence, so try not to let them stress you out.

What should I do while I’m watching the videos?

Learn actively! You will retain more of what you learn if you take notes, draw diagrams, make notecards, and actively try to make sense of the material.