I wish my math teacher had been HALF as entertaining as YOU! I would be a Genius by now! Math is unusually effective: we can treat something as an operator, then treat it as 9th grade algebra, then SOLVE it! AMAZING. I was Never taught wave equation THIS way!!! Never. BTW: the entire first two semesters of circuit theory (first order PDEs particular and homogenous solutions) were also laid out in this video! Brilliant.
I was searching for wave equation and you literally posted a video about it a few minutes later. Are you a mind reader😂😂😂 At first I freaked out because of the PDE but fortunately it wasn't very hard to follow. I'll watch your videos about PDEs after my finals. They're interesting :) P.S : wtf= "want to find". I see what you did there ;)
Based on that it's easy to guess that a^2 Utt - b^2 Uxx = 0 has solution F(ax+bt) - G(ax-bt) since when expanded at the end the a^2 comes out from the double x derivatives and is added manually (from the change in the original equation) on the double time derivative so they cancel out. But that's not too useful since you could always just divide by a^2 on both sides to get a form where c^2 = b^2/a^2 and the equation becomes Utt - c^2 Uxx again
Find the distribution 𝑢(𝑥, 𝑡) by writing the wave equation and boundary conditions for a rod (one dimension) of length L=1 unit, with both ends fixed and whose initial displacement is given by 𝑓(𝑥), whose initial velocity is equal to zero. (𝑐2 = 1, 𝑘= 0.01) 𝑓(𝑥) =ksin(3𝜋x) Can you solve this question? I couldn't solve it. Can you help me
I just didn't understand how this solution is related to a wave equation ;-; I have a theory: the solution must be a sine wave function but, since any (defined) funcion can be expressed as a linear combination of infinite many sine waves and the differential equation is linear, the general solution must be the sum oftwo arbitrary functions, as shown in the video. I'd like help to answer it :)
@@drpeyam You deserve it sir!!!! I got grade A for my PDE midterm last week, incredible, like, I am crying!!! Thank you!!!! How I wish that one day I could attend your class!!!
@@madhuragrawal5685 no haha "d'Alembert" is his last name, most noble families have a "de" or "d' " in their last name, like one of our former presidents "Valery Giscard d'Estaing". It's the equivalent of "von" for the Germans
Would be surprised how poor knowledge of maths Timoshenko had when wrote Theory of Elasticity. Biharmonic equation and it's solutions for different coordinate systems. But without perceiving semantics of maths hardly can be BHE clearly solved for all those special cases.
I wish my math teacher had been HALF as entertaining as YOU! I would be a Genius by now! Math is unusually effective: we can treat something as an operator, then treat it as 9th grade algebra, then SOLVE it! AMAZING. I was Never taught wave equation THIS way!!! Never. BTW: the entire first two semesters of circuit theory (first order PDEs particular and homogenous solutions) were also laid out in this video! Brilliant.
8:30 PDE is an infinite version of Linear Algebra.
Thank you! You gave me a motivation to study linear algebra harder.
My favourite youtube maths teacher :) Your enthusiasm is so infectious
WTF = "want to find".....that's awesome!
Sehr genießbar und plausibel, bitte Mache weiter
I watch this video from Japan.Thanks for using Japanese painting on thumbnail☺️
You are an absolute legend
I was searching for wave equation and you literally posted a video about it a few minutes later. Are you a mind reader😂😂😂
At first I freaked out because of the PDE but fortunately it wasn't very hard to follow. I'll watch your videos about PDEs after my finals. They're interesting :)
P.S : wtf= "want to find". I see what you did there ;)
Yayy, d'Alembert next, too bad it doesn't hold in 3 dimensions, my life would be easier 😭😭😭😭😭
Hahaha, mine too 😭
Excellent video, and of course, C is the speed of the wave.
Based on that it's easy to guess that a^2 Utt - b^2 Uxx = 0 has solution F(ax+bt) - G(ax-bt) since when expanded at the end the a^2 comes out from the double x derivatives and is added manually (from the change in the original equation) on the double time derivative so they cancel out.
But that's not too useful since you could always just divide by a^2 on both sides to get a form where c^2 = b^2/a^2 and the equation becomes Utt - c^2 Uxx again
It seems if you edit a comment the creator's reaction dissapears :(
13:40 If you ignore 1/2c eventually, what is it good for getting a=1/2c ???
You could have ignored it without solving it.
(Thanks for your videos.)
thanks for the great job, I am a PhD student at the university of California San Diego (UCSD), where are you teaching?
UC Irvine :)
@@drpeyam amazing, hope to see you, I am going to attend the SOCAL fluid mechanics seminar which will be held in April in Caltech
Find the distribution 𝑢(𝑥, 𝑡) by writing the wave equation and boundary conditions for a rod (one dimension) of length L=1 unit, with both ends fixed and whose initial displacement is given by 𝑓(𝑥), whose initial velocity is equal to zero. (𝑐2 = 1, 𝑘= 0.01)
𝑓(𝑥) =ksin(3𝜋x)
Can you solve this question? I couldn't solve it. Can you help me
Beautiful!
Very clear. Best Regards from InterestingXPhyscis channel :D
Speaking of Adele, there's something in number theory called an Adele.
Hahahaha
en.wikipedia.org/wiki/Adele_ring
OMG, it’s true 😂😂😂 I thought you meant ideal
You will carry me through PDE
Good dr payem thnx
Another fun one :)
I tried to keep up but fell behind quickly. I need a better PDE and DiffEq refresher :(
Check out my PDE playlist in the description :)
I just didn't understand how this solution is related to a wave equation ;-; I have a theory: the solution must be a sine wave function but, since any (defined) funcion can be expressed as a linear combination of infinite many sine waves and the differential equation is linear, the general solution must be the sum oftwo arbitrary functions, as shown in the video. I'd like help to answer it :)
What you say is true, and it’ll be part of another video called separation of variables
谢谢！
For the beautiful playlist... Buy a boba tea Dr.Peyam!
Thanks so much!!!!
@@drpeyam You deserve it sir!!!! I got grade A for my PDE midterm last week, incredible, like, I am crying!!! Thank you!!!! How I wish that one day I could attend your class!!!
Omg my biggest congratulations!!!! You deserve it 😁😁
I don't know if it's the case in the US, but in France we call this equation l'équation de d'Alembert
That’ll be part of another video ;)
De d'alembert lol. Does d'alembert here mean from the place called alembert?
@@madhuragrawal5685 no haha "d'Alembert" is his last name, most noble families have a "de" or "d' " in their last name, like one of our former presidents "Valery Giscard d'Estaing". It's the equivalent of "von" for the Germans
That should make d'Alembert very happy.
CHANGE OF COORDINATE!!
0:02 you're welcome
I have to admit that the T-shirt made me lose my attention.
*Chen Lu!*
❤👆👆👏🏻👏🏻👏🏻
Wow physics❤👍👍👍👍
I hope to understand this...
But seems a lot of thing in math.
Who would dislike this? 🤔
Would be surprised how poor knowledge of maths Timoshenko had when wrote Theory of Elasticity. Biharmonic equation and it's solutions for different coordinate systems. But without perceiving semantics of maths hardly can be BHE clearly solved for all those special cases.
WTF -> want to find
your notation confuses me -- i prefer the standard notation with the partial ∂t/∂x for example
theyre both pretty standard
Thing that's waving
th-cam.com/video/A3SSf-PoBg4/w-d-xo.html