Differential equations

>>8092703
That's exactly why I enjoyed it, just plug and chug!

File: 63044243.png (220KB, 858x725px) Image search: [Google]

220KB, 858x725px

>>8092707

"I obviously have no idea what I am talking about" - The Thread

>>8092703
it's a tragedy that most ODE are taught from the "plug and chug" perspective. some students enjoy this since it's fairly easy and gives them a sense of understanding. however, it hides the centuries of theory that was put into it. it hides a fair amount of intuition in favour of ease of computation

this is the price we pay in order to pump out the number of engineers that we do

File: 1457446357809.jpg (24KB, 317x432px) Image search: [Google]

24KB, 317x432px

>>8092709
Well i'm asking a question, wether it's worth knowing the rest of the solution methods. You obviously don't know shit because if you knew something, being the cuntface that you are, you wouldn't have passed the opportunity to shame me big time.

>>8092703
fucks sake mate, at least learn state space analysis

>>8092713
You're question is retarded because you are assuming two retarded things:

>One method will always be able to solve every application

>The subject of Differential Equations is only about memorizing solution methods and applying them

File: 1454962803603.png (10KB, 362x358px) Image search: [Google]

10KB, 362x358px

>>8092730
>You're question

I'm making an assumption and asking if it's wrong, i'm not stating it as a fact at all, your posts are two literal shitposts since you just said i was wrong and not why.
Sure i agree with the fact that one method will not always works, but from the looks of what i knew it did, for the applications an engineer could have,a proper reply would've been something like this >>8092718 which explicitly shames on the use of Laplace transforms on control theory.

>>8092736
>on control theory.
correction, on **this case** of control theory.

>>8092703
What you're talking about is applied math and introductory. Real ODE's is a subsection of analysis.

>>8092736
Not him but yes, you are wrong. Calc 1, your first linear algebra, and ODE's are all plug n' chug. I'm actually considering doing Dynamical Systems for grad school (departments usually shove DE's in that field) next year. Pure math is my thing but I want to be employed and having looked around, I don't even think I'll be disappointed with the field.

>>8092895
Looking at my answer, I might not have driven the point home enough. There's still a lot of interesting and hard problems still present in the theory of ODE's, at least from an applied perspective.

>>8092712
not being a dick or anything but can you point me somewhere to read the theory or tell me about it?

ihavent taken ode

>>8092979
>not being a dick or anything but can you point me somewhere to read the theory or tell me about it?

I have never taken an ODE theory course, but for PDE theory the book by Evans is good.

(you don't need to study ODE theory before PDE theory btw)

Also, you need to be very comfortable with Analysis before attempting ODE or PDE theory.

>>8092703
Yes. Try to model something properly where it isn't plug and chug aka real shit. Learn about where they actually use it. Also learn why it gives you a fucking solution. Become a real engineer. Oh one more step, the first step of becoming a real engineer is instead of asking stupid questions realize that there are hundreds of books written on the subject so read a few of them.

>>8092703
Even my undergrad engineering DE course had no plugging involved. Do universities in the US seriously have such a big focus on calculations? No wonder there is so little interest in higher math.

>>8093409
I took DE in the US while studying abroad and it wasn't plug and chug

Also why do you think they're American? nothing in his post necessarily points to that, their English isn't very good either

>>8092703
I think that the Laplace transform is one of those beautiful things in mathematics. I was a math major, so I was never taught it (though the engineers were), but when I learned it I was surprised how elegant it is. The thing is that you can't use the Laplace transform for systems of ODEs, you need to calculate the Jacobian and find the eigenvalues/eigenvectors.

>>8093426
> their

Neither is yours. That's the plural third person, you want the gender neutral (in the case of unknown gender) which is he.

>>8093437
my bad, I am not American so my English isn't too good

but yeah I studied abroad at UC Berkeley and my DE class was nothing like what this person describes.

>>8093438
I'm screwing with you, haha, that grammar naziism is trivial. Which DE class was that? I had one freshman year that was pretty plug and chug. They taught separation of variables and variation of parameters, but it was very procedure focused. We briefly did systems of ODEs and linearization, but I only really focused on that when I took a dynamical systems and nonlinear ODEs class later on. I had a PDEs class that was also pretty procedure heavy, but because it was a 4xxx class it also focused on the theory a fair amount.

Your an engineering major, clearly something went wrong for you favor laplace transform over fourier transform.

That being said. Many ODE and PDE are too complex to solve or find good closed form solutions for. Especially in the real world when you need too compute real world problems. It's good to understand how to solve them but better to understand how to use them in practical situations. Sure you can plug and chug to get a solution but in a real world problem it may not be computationally efficient to use your solution.

While laplace is absolutely a great tool, know when to use it vs fourier. Also, numerical analysis(FDM and FEA) and state space equations are super important when real life happens. Obviously linear algebra should be second nature(GS,SVT)...

>(GS,SVT)
what

Is that supposed to be gaussian elimination and spectral value decomposition?

>>8093433
>The thing is that you can't use the Laplace transform for systems of ODEs

Not necessarily true.

>>8092703
What, I liked Diff Eq. I thought it was deefeekewl. I don't know what your problem is.

>>8093564
GS = Gram-Schmidt, a process through which a person can find an additional (n - 1) orthogonal vectors given a starting vector (total of n orthogonal vectors) for an n dimensional space. I honestly, didn't know that engineers learned this.

SVD = singular value decomposition, this is also upper level linear algebra that I didn't know engineers learned (see wikipedia - https://en.wikipedia.org/wiki/Singular_value_decomposition it explains better than I could).

>>8093573
I didn't think you could. I'm sure if you can it would be easier for some real pain in the ass systems, but it seems like the Jacobian is just an easier, more direct way to go about it.

>>8093644
I think that only electrical engineers learn it in most cases