It's been awhile since I've had a Diff EQ class, but isn't the harmonic motion one an ODE?
PDEs you should know
11–20 of 102 posts
Re: PDEs you should know
#12PDEs are really useful if you are in the rare domains where they are useful. But most PDEs don't have even have closed form solutions for non-trivial boundary conditions. So unless you are a physicist or something adjacent, no, no you really don't need to know these. Hard to say what's the intended audience for the page though. Could be a message aimed at physics undergrads or something. If so, then indeed, you shoul…
Most useful equations don't have a closed form solution. This is why things like machine learning exist. More specifically PDEs are a hot topic in DNNs at the moment. See physics informed neural networks: https://en.m.wikipedia.org/wiki/Physics-informed_neural_netw...
Re: PDEs you should know
#13Boltzmann equation?
Re: PDEs you should know
#14PDEs are really useful if you are in the rare domains where they are useful. But most PDEs don't have even have closed form solutions for non-trivial boundary conditions. So unless you are a physicist or something adjacent, no, no you really don't need to know these. Hard to say what's the intended audience for the page though. Could be a message aimed at physics undergrads or something. If so, then indeed, you shoul…
Why does a PDE need an analytical solution?
Are you arguing that e.g. Navier-Stokes isn't useful?
edit: Just noticed that Navier-Stokes isn't even on here. This is frankly a weird list.
Re: PDEs you should know
#15The Black–Scholes equation is basically identical to the heat equation. Divide through by σ^2 and let n = σ^2 * (T - t) if you want to derive it.
Re: PDEs you should know
#16PDEs are really useful if you are in the rare domains where they are useful. But most PDEs don't have even have closed form solutions for non-trivial boundary conditions. So unless you are a physicist or something adjacent, no, no you really don't need to know these. Hard to say what's the intended audience for the page though. Could be a message aimed at physics undergrads or something. If so, then indeed, you shoul…
Most useful equations don't have a closed form solution. This is why things like machine learning exist. More specifically PDEs are a hot topic in DNNs at the moment. See physics informed neural networks: https://en.m.wikipedia.org/wiki/Physics-informed_neural_netw...
The point is that equations without closed form solutions are pretty useless if you aren't into pretty hairy maths, Green's functions and the like.
An equation everyone should know is Hooke's law. That's useful at a high school level.
Re: PDEs you should know
#17PDEs are really useful if you are in the rare domains where they are useful. But most PDEs don't have even have closed form solutions for non-trivial boundary conditions. So unless you are a physicist or something adjacent, no, no you really don't need to know these. Hard to say what's the intended audience for the page though. Could be a message aimed at physics undergrads or something. If so, then indeed, you shoul…
Why does a PDE need an analytical solution? Are you arguing that e.g. Navier-Stokes isn't useful? edit: Just noticed that Navier-Stokes isn't even on here. This is frankly a weird list.
Well, to be useful, wouldn't you need to be able to use it? Most people outside of physicists and physics-adjacent fields are very far away from the mathematical tools to deal with these equations.
Re: PDEs you should know
#18Earlier quoted context omitted.
Most useful equations don't have a closed form solution. This is why things like machine learning exist. More specifically PDEs are a hot topic in DNNs at the moment. See physics informed neural networks: https://en.m.wikipedia.org/wiki/Physics-informed_neural_netw...
The point is that equations without closed form solutions are pretty useless if you aren't into pretty hairy maths, Green's functions and the like. An equation everyone should know is Hooke's law. That's useful at a high school level.
i disagree. equations are useful only if you have use for them. this is by definition of the term. on the other hand, high schoolers rarely feel like Hooke's law is useful!
Re: PDEs you should know
#19Earlier quoted context omitted.
Why does a PDE need an analytical solution? Are you arguing that e.g. Navier-Stokes isn't useful? edit: Just noticed that Navier-Stokes isn't even on here. This is frankly a weird list.
Well, to be useful, wouldn't you need to be able to use it? Most people outside of physicists and physics-adjacent fields are very far away from the mathematical tools to deal with these equations.
cs is a dominant topic on hn. cs is definitely physics and math adjacent
Re: PDEs you should know
#20Earlier quoted context omitted.
Most useful equations don't have a closed form solution. This is why things like machine learning exist. More specifically PDEs are a hot topic in DNNs at the moment. See physics informed neural networks: https://en.m.wikipedia.org/wiki/Physics-informed_neural_netw...
The point is that equations without closed form solutions are pretty useless if you aren't into pretty hairy maths, Green's functions and the like. An equation everyone should know is Hooke's law. That's useful at a high school level.
Isn't Hooke's law a solution to the harmonic motion PDE in that page?