HN Academy

Differential Equations in Action https://www.udacity.com/course/differential-equations-in-act...

It's not an intense differential equations course, and I don't think you even need calculus to understand or complete the exercises. It has a lot of really great, well, explained, fun exercises like computing a gravitational slingshot, computing the spread of an epidemic, then N-body problem, and others. The exercises are solved programmatically, not with math equations.

America's Unwritten Constitution https://www.coursera.org/learn/unwritten-constitution America's Written Constitution https://www.coursera.org/learn/written-constitution

If you're American, you'll likely find both of these courses extremely interesting. What they (probably) taught you in grade/high school was very overly simplified, or just wrong. This is geared toward people who have no background in law. I don't remember there being amazing exercises to do, but there were a lot of mind blowing facts I learned about things the constitution does and doesn't cover.

While the linked course seems a lot more thorough, I took the Udacity "Differential Equations in Action" [1] course, which I found very well done. For the homework you write Python programs to compute things like gravitational slingshots, modeling epidemics, wildfires, and the n-body problem.

[1] https://www.udacity.com/course/differential-equations-in-act...

⬐ nraynaud

Can we get to the text and videos without all the school-ish crud? (starting a course, timelines etc.)

⬐ gmiller123456

Yes [1]. I haven't taken a Udacity course in quite a while, but at the time all of their videos were hosted on Youtube, so you should be able to find a lot of their courses just on Youtube. For the homework, I remember there was an include file that they didn't provide the source code for, but a Google search turned up a version someone wrote for using it locally. Usually it's pretty obvious when you've solved the problem and have the correct code, but to make absolutely sure, you have to upload your code to their server for verification. But you can take the whole class without ever visiting Udacity.

[1] https://www.youtube.com/watch?v=8cLXVG2Q6D4&list=PLAwxTw4SYa...

⬐ nraynaud

thanks!

⬐ madengr

I took the first part of that course, enough to write an n-body game:

https://github.com/madengr/nbody

While it was a good course, I wish it covered the analytic portion, rather than dive straight into numerical solutions.

⬐ salty_biscuits

That is pretty neat. Improvements on the analytic side (if you are interested in the opinion of a random person on the internet) would be to scale your coordinate system (e.g. scale the distance and time to make average velocity and radius equal 1) and look into using a symplectic integrator. Better for these types of systems.

⬐ madengr

Thanks. I remember in the course, keeping the energy constant is the big issue. They used the symplectic integrator to improve it. In the game, if you let it run long enough, the error visibly shows up.

⬐ sampo

While the linked course notes (I looked at the pdf, definitely good textbook quality and not just course notes, really) are absolutely more thorough in the classical undergrad diff.eq. topics, the Udacity course touches some further topics (stiffness, implicit methods, control theory) that the course notes don't.

https://www.udacity.com/course/differential-equations-in-act...

I'm sure there are others, but this is a pretty good introduction. It focuses quite a bit on numerical solutions (using python programs that are automatically graded.)

The Udacity course on numerical diffy-Q covers some of this.

https://www.udacity.com/course/cs222

I wrote a simple N-body simulator game after viewing the course, although I'm still having issues with the energy conservation.

https://github.com/madengr/nbody