Along with the announcement that Udacity's Logic & Discrete Math offering would be cancelled, a new course on applied differential equations was announced. The course will be starting up on September 3, 2012, and taught by Jörn Loviscach with Miriam Swords Kalk, who I assume will be TA'ing and moderating the discussions.
Personally, I'm not sure how much time I will have to focus on this course. With a full 17-credit semester coming up, I may have to leave this course for around the end of the year when I will have more free time. I'm definitely looking forward to it, but more important courses must be focused on first.
The prerequisites (more recommendations than requirements) list knowledge of basic computer programming, calculus, and physics. You could tackle the programming and physics requirements via Udacity's CS101 and PH101 classes, while Khan Academy will help you shore up the Calculus. More information from Udacity's course page below:
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
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