Ladies and gentlemen, Dr. Peyam!! Yayyyyyyyyyyyyyyyy!!!!!!!!
@mohan153doshi
7 жыл бұрын
You two are awesome - the best calculus teachers in the world - yaaaaaaaaaaaaaaaaaaaaaaaaaaaaay !!!!!!!!!!!
@SlingerDomb
4 жыл бұрын
This is a very very amazing video. I was so curious about what the relationship between ODE’s and Linear algebra. Dr.Peyam always has the answer for me!
@1willFALL
5 жыл бұрын
4:18 - 4:21 should be a meme.
@michaelempeigne3519
7 жыл бұрын
shortcut for compound interest problems find the amount of compound interest on a principal of 660 dollars if the interest rate is 44.44% per year for 2 years 44.44% = 4 / 9 so on 9 dollars you will have 13 dollars after one year. 9 ------ > 13 so another 9 --------- > 13 multiply vertically yields 81 ---- > 169 so on 81 you have an increase of 88 so for 660 you will have : (660 / 81 ) * 88 = 717.04 in compound interest also, we can use this to find the amount after a length of time : for this question it would be : (660 / 81 ) * 169 = 1377.04
@HDQuote
4 жыл бұрын
I LOVE YOUR VIDEO! Finally I got to do some Analysis II stuff again
@adamhernandez7847
5 жыл бұрын
Thanks for the help Professor!! Your videos are still very helpful.
@drpeyam
5 жыл бұрын
OMG, hi Adam! Hope things are well :)
@Nutshell_Mathematica
Жыл бұрын
This is super super interesting
@subhasispanda5039
Жыл бұрын
@drpeyam Why did you choose the particular solution in that form? Any motivation behind that? Thank you.
@cedricp.4941
7 жыл бұрын
Amazing !!
@MrRyanroberson1
7 жыл бұрын
Lol. 4:32 ive seen that sooo many times, it's the rotation matrix! Ive been doing a rotation formula in 3d to do tons of stuff, and the inverse happens to just have the negative theta as input.
@danielhaselbauer2549
7 жыл бұрын
I understood Trainstation
@f3ynman44
3 жыл бұрын
5:23 Where does this Variation of Parameter Formula come from? I don't understand how it suddenly appeared from the last step. Is there another video where you derive it?
@ericlizalde5362
7 жыл бұрын
Loved this videeeo!!!
@arafet3198
7 жыл бұрын
Can u show us how to derive the formula in 6:21 and keep u the good work love u أنا احبك
@KeyMan137
7 жыл бұрын
en.wikipedia.org/wiki/Invertible_matrix#Inversion_of_2_.C3.97_2_matrices It would be fun to see how they would derive the result. There are many resources if you want to know more.
@f3ynman44
4 жыл бұрын
I like to solve 2nd order differential equations with the exponential function. What's if I said the homogeneous solution was exp ( i * x), without rewriting it as cos and sin. Could one solve this problem only using exp?
@drpeyam
4 жыл бұрын
Yes
@kalamasin
6 жыл бұрын
ありがとう ;)
@chandankar5032
5 жыл бұрын
Hey peyam , does variation of parameters works for the d.e. of degree more than 2 if it is linear ?
@drpeyam
5 жыл бұрын
Yeah, definitely! It’s pretty much the same process
@chandankar5032
5 жыл бұрын
@@drpeyam 14:10 how to find inverse? I think we can use Cramer's rule to solve for v'1 and v'2 but for finding inverse the adj(A)/det(A) will be too lengthy. Do you have any better option ?
@drpeyam
5 жыл бұрын
That’s the best we can do, sadly! It’s not very hard though because there are lots of zeros
@mihaly1027
7 жыл бұрын
In the first element of the column vector 0, tanx, why is it 0 I'm curious
@drpeyam
7 жыл бұрын
It's basically to simplify your work a bit. The gist is that you plug in v1(x) cos(x) + v2(x) sin(x) into your equation, and you get a bunch of equations involving v1' and v2', and at some point you get a really complicated equation, and to simplify this you just say "Assume cos(x) v1'(x) + sin(x) v2'(x) = 0", and you deal with the rest, which involves tan(x). That's why the first element is 0.
@mihaly1027
7 жыл бұрын
Dr. Peyam's Show ohhh right the assumption, that makes sense now, thank you !
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