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Hey sci
I'm really curious about some of the algebra behind ODE's and other seemingly-separate areas of math. For example, I always thought it was kind of arbitrary that, for an n-th order linear homogeneous ODE, the solution space is generated a linear combination of n linearly independent functions.
I'm not much of an algebraist, or whatever the proper term is, but I'd like to start looking into that side of things. I've only read the first few chapters of Artin -- would that text elaborate on some of these issues? Would Pinter suffice? I'm looking for something I could hopefully get through somewhat quickly, if possible.
Thanks in advance
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Samefag, I'd also like to know why we are able to assume
u_1'(x)*y_1(x) + u_2'(x)*y_2(x) = 0 in the parameter variation algorithm.
Anybody???
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>>9159268
>I've only read the first few chapters of Artin
emil artin or michael artin?
inb4 michael-babby-algebra-martin
also your picture makes me angry. ALL groups of order 2 are isomorphic. there is fucking only one group of order p (prime)
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>>9160633
Yeah, Michael Artin. And the pic is just for lulz.
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>>9160633
Also, did sylow or langrage first discover that all groups of order p were isomorphic? just curious, if you know off the top of your head
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>>9160731
its a direct consequence of lagrange's theorem by taking <a> for any a =/=1, so probably him
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fyi Lie came up with Lie groups to express continuous rewritings of differential equations.
https://en.wikipedia.org/wiki/Sophus_Lie
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>>9160816
Thanks senpai, I'll look into it
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>>9159268
I'd take a look at Galois Theory of Linear Differential Equations by Put and Singer. You can find it on libgen. The first chapter is pretty easy to read (barring a few things, but you should be able to understand most of it if you've gone through Artin). If you want a more focused expository paper with examples, but few proofs, you could look for "A First Look at Differential Algebra" by Hubbard and Lundell.
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>>9161138
Splendid!
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>>9161212
Actually, math is not about beating anyone. Terence Tao said in his blog that mathematics needs all the good people it can get, it is not a competition.
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>>9160598
You're not going to get a good answer if you just post one line of a derivation out of context.
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>>9161212
Ironically people who see maths that way never make it. If you don't enjoy maths for the sake of maths, find another field. It's not a dick-measuring competition.
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>>9161286
>>9161304
Yeah, I've had that image for a few years, and I thought it was funny... I'm not in it to compete, but it is really damn satisfying to understand the logic behind a major theorem and "ascend" to a higher power level -- whatever that means.
>>9161301
True. Let me post a few pics from the chapter -- bear with my crappy camera on my phone.
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>>9161361
This was my primary question. Why does the original equation offer enough "wiggle room" to let u_1'(x)*y_1(x) + u_2'(x)*y_2(x) = 0???
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>>9161363
To clarify, because it is assumed the equation is non-homogeneous, u_1(x) and u_2(x) were proven to not be constant.
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>>9161363
>Differential Equations in 24 Hours
Oh my God...
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>>9161376
lol what I'm reviewing for a modeling class. I'm just getting nitpicky about a line of algebra. great text senpai
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>>9161363
It might be that I haven't had lunch yet, but I'm not really sure what it means by "wiggle room."
That looks like a genuinely horrible textbook.
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>>9161286
professor on first day of intro to real analysis (math 350): you made a choice to take this class, its not required for any degree except mathematics, its not you vs me, its you and I vs the material.
That was the syllabus and he jumped str8 in after
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>>9161385
That's a really fun way of putting it.
Thread posts: 23
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Thread images: 7