Hey everyone, if you would like to get a grip on differential equations and are willing to put in the work, then you should know that an instructor paced run starts on May 31st. If you know single variable calculus then you're set to jet! Please sign up here:
There are homeworks as well as lecture exercises, recitations and a final exam. As far as grading, there is an auto grader that uses sympy on the backend.
It's funny how differential equations just boil down to plain linear algebra when you restrict yourself to the discrete time domain setting. I feel like courses like this should lead with that to save time for people who will primarily handle them inside computers.
Strang has one although it kind of buried the lede on the linear algebra in my opinion. Try some of the older DE texts (Coddington) or an older Schaum’s outline
As I recall from a (very) long ago differential equations course at MIT, the intro DiffEQ course was very cookbook and, while necessary for some things like system dynamics, weren't super-interesting. (Not that I was ever very good at math.) I did always think it was cool though that you had "imaginary" i terms and they eventually disappeared and you had a real-world result.
Never took linear algebra but I gather it was embedded in other courses in various guises largely pre-computer.
I always thought that math was super well curated…right up until differential equations. Beautiful calculus and linear algebra, followed by a bag of tricks to solve DEs.
As someone who is better at coding than pen & paper math, I definitely enjoyed seeing a lot more cases where the only practical solution was numerical.
Hey, unrelated: Does anyone know why it seems MITx stopped offering new courses ~5 years ago? I'm still bummed out and check their page a few times a year.
(I can vouch for this class and the 2x2 one btw; great stuff; I'd recommend any of their math and science courses. The QM ones are especially good)
Are there any interesting modern applications of diff. equations in computer science outside physics simulators, and 3d vision? Or some adjacent areas that would benefit from skillset of working with diff. equations?
Optimization by gradient descent is used to do the learning in deep learning. For example, diff eqs are used to create optimizers that improve upon the classic 'adam' say, such as the new 'sophia' [1].
1. https://arxiv.org/abs/2305.14342
I guess it's $100 for a bunch of videos of lecturer scratching on a whiteboard something that you can learn yourself with interactive demos, sympy and a jupiter notebook.
The difference is that there are also a bunch of other people learning the same thing at the same time. Peer pressure as well as due dates helps people stay on track, and there is support on the forum in case you get stuck, or just want to talk about something cool you found related to differential equations or math.
https://mitxonline.mit.edu/courses/course-v1:MITxT+18.03.1x/
Incidentally, the prerequisite: 18.01x, also starts on May 31.
https://mitxonline.mit.edu/courses/course-v1:MITxT+18.01.1x/