🧵 Modern ordinary differential equations
Anonymous at Fri, 24 May 2024 01:05:57 UTC No. 16190490
I was reading an illuminating opinion piece by Giancarlo Rota on the topic of ODEs. What are your thoughts?
https://web.williams.edu/Mathematic
Are there any introductory books that follow his philosophy?
Anonymous at Fri, 24 May 2024 02:01:34 UTC No. 16190547
>>16190490
good takes. My ODEs course was still distastefully targeted towards engineers and therefore full of silly and forgettable tricks rather than interesting content.
Anonymous at Fri, 24 May 2024 03:16:24 UTC No. 16190602
>>16190490
OH NO WOE IS ME I HAVE TO TEACH DIFF EQ AT FUCKING MIT MY CAREER IS RUINED
Anonymous at Fri, 24 May 2024 03:32:48 UTC No. 16190616
>>16190490
I really don't care. His complaints are minor at best. ODE was a really easy course following Calculus, I never understood the complaints.
It's fairly straightforward too, and it teaches the most important concept of all, that the cyclic functions and the exponential rule the continuous, time series focused, world.
It's also something you quickly realize when you're working with actual data too. Anyway, his actual complaint should be: don't merge engineers with mathematicians. They look at the problems differently. The mathematicians care about the concepts and deeper ideas behind differential equations, the engineers fundamentally don't care and for very good reason, 99% of their work is equations that have to be solved computationally AND they have to learn so much in their domain across various different fields that they don't care about the intricacies. All they care about is, does it work and does it match the physical world? Then let's move forward and design the rest of the complex system.
>t. Mathematician who has has to work with engineers for years now and finally gets their grievances with math departments.
Anonymous at Fri, 24 May 2024 03:39:45 UTC No. 16190622
TLDR? I'm not reading your retard ramblings if it exceeds one 4chan post
Anonymous at Fri, 24 May 2024 03:46:29 UTC No. 16190627
>>16190616
What's funny to me is that so many parts of engineering are so heavily tied to ODEs and PDE solutions in particular. As an example, just about everything in control systems and signal processing are based on solutions to coupled constant coefficient ODE's. We have to do this balance between caring about analytical solutions for things like modeling performance predictions, but not getting lost in the weeds of the deeper mathematical properties.
Anonymous at Fri, 24 May 2024 03:47:21 UTC No. 16190628
>>16190547
why did you even waste your time in undergrad then?
Anonymous at Fri, 24 May 2024 06:06:06 UTC No. 16190714
he's completely right, and its even worse today since all the techniques you learn are completely useless in real life. Numerical methods have replaced almost all analytical methods. Only if you are doing graduate level research then you'll need this as a stepping stone to learning more advanced methods like integral transforms, and variational calculus.
Anonymous at Fri, 24 May 2024 17:00:34 UTC No. 16191293
>>16190714
I don't think this is true at all, especially for many applications of ODE's to engineering.
If you are working on a control system (for example), this is generally represented by a coupled set of potentially non-linear ODEs. Most controllers for these non-linear systems developed around linearization, and for stability you almost always need to have analytical forms as if the system is very ill-conditioned even slight errors in your approximation of the Hessian will produce a very unstable system.
Similarly, if you are doing state estimation (which is essentially just control but in the other direction) if you aren't able to produce analytical forms you won't have any meaningful performance assessments for your estimator.
That's not to say that numerical methods aren't important to know and understand, but there are still many domains where having a grasp of the analytical process is important.
Anonymous at Sat, 25 May 2024 07:20:54 UTC No. 16192248
I just use engineering math books
Anonymous at Sat, 25 May 2024 13:01:45 UTC No. 16192549
wow, these lessons look great and Prof Mattuck actually motivates the Laplace transform
https://ocw.mit.edu/courses/18-03-d
My only gripe is the accompanying book.
>Edwards, C., and D. Penney. Elementary Differential Equations with Boundary Value Problems. 6th ed.
Can I replace this by Logan or Noonburg?
Anonymous at Sat, 25 May 2024 19:32:53 UTC No. 16192982
>>16190490
I know somebody can do it, they should teach the basics of ode in 50 pages, terse like then numerical methods
Anonymous at Sun, 26 May 2024 00:23:10 UTC No. 16193372
>>16192982
I mean... let's be honest, 90% of practical ODE is
>Separation of variables
>How to transform a problem into a separable equation
>Numerical methods
Anonymous at Sun, 26 May 2024 07:49:08 UTC No. 16193726
>>16192549
Those books suck ass