/sci/ - Science & Math

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Anonymous Sat Jun 20 22:56:01 2015 No.7343268 [Reply] [Original]

How does Partial Differential Equations compare to Ordinary Differential Equations?

I'm taking an introductory ODE class right now and it's honestly the most tedious and boring math class I've taken.

Mind you that I have about a 97% average in the class. It's all just about mechanics and solving silly ideal equations that youd likely never encounter in the real world. In addition it seems like a class completely tailored to the physicists and engineers, with nothing interesting in it for the math majors.

Also, after taking Calculus 1-3 and now ODEs, I'm getting a bit bored of the calculus series.

What areas should I explore next? I was thinking of taking courses in Abstract Algebra, Modern Geometry, or Combinatorics.

Anonymous Sat Jun 20 23:00:32 2015 No.7343273

PDE undergrad uses some of the stuff in your ODE class and adds the use of Fourier series. It's still the same boring thing of applying some problem solving techniques and then going through some long calculation.

Modern PDEs are only teached in grad school because they require advanced analytical techniques. Most people never get that far with their math studies.

Anonymous Sat Jun 20 23:03:37 2015 No.7343282

I took PDE's, the math was boring to me, but the physics connection was cool. We basically only studied the big three heat, wave, and laplace, and then did some Fourier shit.

Try abstract algebra, cause it's totally different and the objects under study (at least at first) are surprisingly simple, pretty, and easy to play around with on your own. If you like that kind of thing, try it.

>>	Anonymous Sat Jun 20 23:04:37 2015 No.7343284 Maybe you're just on a shitty class with a shitty tutor doing some entry level shit. ODEs are by no means boring, especially when applied to physics. Let's see you try to solve some non-linear ODEs and deal with Chaos Theory.

>>	Anonymous Sat Jun 20 23:04:49 2015 No.7343285 >>7343268 Try Complex analysis if you're bored of Calc. It's still calc but far more analytical. Have you done a real analysis course either? Both are worth doing to grasp a better understanding of what calculus is actually about.

>>	Anonymous Sat Jun 20 23:07:34 2015 No.7343290 ODEs are easy and PDEs are hard.

Anonymous Sat Jun 20 23:10:22 2015 No.7343295

>>7343282
I'm taking Linear Algebra right now and the more abstract aspects of it seem interesting so Abstract Algebra sounds like it'd be a fun class.

>>7343285
I'd need to take real analysis first.

>>7343284
My professor is pretty good, actually. Also, I did in fact say it was an introductory class. My issue with it is mostly due to the textbook we use: A First Course in DEs by Zill. This is quite possibly the worst book ever written in any STEM field.

http://www.amazon.com/gp/product/1111827052/ref=ox_sfl_cart_mbc_s1?ie=UTF8&psc=1&serverToken=Obidos

Anonymous Sat Jun 20 23:51:19 2015 No.7343363

>>7343295
Im glad I'm not the only one having trouble with that textbook.Unfortunately its also my main source of information for ODEs since I'm taking it online.

My Calc 2 professor does research in applied PDEs so he taught 1/4th of ODE in my Calc 2 class.

>>	Anonymous Sun Jun 21 06:38:19 2015 No.7343814 >>7343273 What are examples of those modern PDEs? I got stuck with the three classics, wave, heat and transport only. I have engineer tier math only, so I guess it's normal.

>>	Anonymous Sun Jun 21 07:05:52 2015 No.7343828 >>7343295 You don't need real analysis to take complex, if that's what you mean in your 2nd reply.

Anonymous Sun Jun 21 07:24:22 2015 No.7343841

Well because you're working in several-dimensional domains, PDE has more prerequisites because it requires at least some functional analysis and differential geometry to even start doing anything rigorous.
The notion of solution in PDE is not well-defined, you have the classical solutions (that have the same degree of regularity as the equation) but these usually don't exist everywhere or diverge very fast so you need to define a less rigid notion of solution, usually by looking for solutions in the space of distributions which is much bigger, that allow you to prove existence (then you examine these solutions to see if they are classical). However you don't want too many solutions (ideally you want a unique solution) so you have to restrict the space in which you're looking. Thus the notion of weak solution depends on the equation you're looking at and is by itself quite subtle (hence the need for functional analysis).
Besides, obviously the consideration of boundaries becomes much more complicated in a 2D domain than on an interval, hence (among other things) the need for differential geometry.

Anonymous Sun Jun 21 07:28:37 2015 No.7343844

>>7343814
https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations

If you do CFD etc. you will be exposed to modern PDEs in your senior year, in my chemeng reaction eng we also worked with a lot of nonlinear PDE systems, but we generally have justification to reduce them to ODEs in test conditions rather than simulation so not everyone bothers to learn how to solve the full PDEs.

>>	Anonymous Sun Jun 21 09:31:00 2015 No.7343927 I would like to contribute in a thread about PDE's, but this thread seems to be about nothing. OP doesn't like it much. Okay. So?

>>	Anonymous Sun Jun 21 09:35:15 2015 No.7343930 >>7343927 give your opinion?

>>	Anonymous Sun Jun 21 09:36:08 2015 No.7343932 File: 130 KB, 400x256, 1292357404292.png [View same] [iqdb] [saucenao] [google] >>7343927 Create a PDE appreciation thread ? Could be interesting, we never have specialized discussions here

>>	Anonymous Sun Jun 21 09:51:14 2015 No.7343942 >>7343932 >we never have specialized discussions here For a reason

>>	Anonymous Sun Jun 21 11:19:29 2015 No.7344055 >>7343268 same shit except you don't have Cauchy-Lipshitz theorem, so it's fucking hard to tell anything about a PDE

>>	Anonymous Sun Jun 21 11:24:19 2015 No.7344064 >>7343268 You should take Differential Geometry. Interesting stuff, especially if you get to the Riemannian level.

Anonymous Sun Jun 21 12:04:01 2015 No.7344117

>>7343927
>I would like to contribute in a thread about PDE's, but this thread seems to be about nothing.
>OP doesn't like it much. Okay. So?

False. I don't much like ODEs but I'm currently signed up to take PDEs next semester. I simply wanted to know if this was a good idea.

I'm a chemistry major by the way.

>>	Anonymous Sun Jun 21 12:09:53 2015 No.7344128 >>7344117 OP you might find this PDE interesting, it's used a lot in ChemE, but it many amazing applications in many science fields: https://en.wikipedia.org/wiki/Reaction%E2%80%93diffusion_system

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