Energy Method

[@redhotminipepper1]

great pronounciation on the 'integraal' Dr Peyam! Groeten uit NL

[@drpeyam]

Hahahaha

[@quietstorm1519]

I was wondering about the potential energy at 11:31, because from the limited physics I was taught, PE = mgh. However, since we are working with periodical functions, PE = 1/2k(∆x)^2 (k ≥ 0), which lines up perfectly what with is shown (1/2c^2*(U_x)^2). Anyways, great video as always!

[@piyushchandra4758]

Feynman in his famous "Feynman Lectures" called Parseval's identity for Fourier series as "Energy Theorem". Energy of a wave is average square of its amplitude. This implies average of square of a function is sum total of squares of coefficients of the Fourier series of the given function. This video is like a very elementary introduction.

[@drpeyam]

Wow, I never made the connection, thank you!!!

[@shambosaha9727]

YEAH!!

[@adityaujjwalmain5943]

Great as always!

[@hidalgohernandezmauricio5728]

OMG love his energy!!

[@souvikbhunia3669]

He never disappoint to anyone.

[@hocineslamene9135]

Simplified and very useful for physics students. Your pronunciation " Integraal " in Dutch is very funny, try to pronunciate it in french " L'intégrale ". greetings from Algeria

[@nournote]

Dutch, not German

[@hocineslamene9135]

@@nournote OOOOPS, it's my fault. Thank you Sir.

[@michaelzumpano7318]

Beautifully explained!

[@samuelmedlock849]

At 8:07, how are you able to do this operation on the heat equation when it has u_{tx} and not u_{xt}?

[@drpeyam]

utx = uxt by clairaut

[@RYO-wd2cp]

We appreciate the energy method!

[@murielfang755]

Energy method is so elegant.

[@drpeyam]

My favorite method!!

[@drpeyam]

Thanks for watching my playlist btw, I love your comments!!

[@hitchedtothestitch]

Thank you so much! Your explanations are fantastic, 10/10!!!!

[@Л.С.Мото]

Hello Dr. Peyam I'm no mathematician, nor do I work in a field where math is needed. I'm just an ethusiast. Nothing more, nothing less. But please tell me, why do mathematicians tend to be hostile towards physicists or engineers? I mean, they just use math to explain things, or make things happen.

[@drpeyam]

I don’t think they’re really hostile, just some friendly banter

[@dramwertz4833]

Right here Right now so im not old enough to br sure but i believe its mostly because of strange matgs they use. E.g. with the engineers ofc it makes sense to approximate and add random constant because then you can get away with a quite right solution but as someone who likes math it just hurts sometimes

[@RalphDratman]

You didn't ask me, of course, but I have never been aware of mathematicians being hostile toward physicists or engineers! Maybe mathematicians are upset because physicists and engineers use mathematics informally. I am not a mathematician, but to some extent I agree with that. Physicists, particularly, are not usually too concerned with all the details of a particular mathematical manipulation. They quite often do not take time to get definitions straight and so forth. But that would not make me "hostile" to physicists!

[@Л.С.Мото]

@@RalphDratman and Dr. Peyam Maybe hostile was a wrong word to use on my part. However, I have been watching flammable maths, and he tends to make a lot of remarks and jokes about other fields. As a mathematician, he does really seem to attack engineers, and that to a point, where I don't even know if those are still jokes, or his real opinion. In the comments of various math videos, I see a lot of accusations towards engineers, most popular being them round pi and e to 3. I watched many engineers lectures, and they have never done that. Yes, they rather just apply math, and throw in some extra numbers or constants usually to make sure its safe what they are making - but I find it hard to discredit their use of math.

[@RalphDratman]

@@Л.С.Мото Thanks for your reply. I have not seen flammable maths yet. Is there a particular video I could watch to get an example of his digs at engineers?

[@nirorit]

Awesome. As always

[@sandorszabo2470]

You 2 tee 😊 Nice derivation.

[@اميمةخروبي]

Please sir, what is the interperitation of E(t), and how to use E(t) to prove the unicité of the solution of pde

[@nimbaneedison4904]

How can we apply the energy method for a damped wave equation

[@aryammlg6833]

Hello Dr.Peyam Thank u very much for your videos. I've been watching your PDE playlist and so far it's been soo helpful and crystal clear. in your last video, u demonstrated D'alembert formula and derived it and since u solved it generally the answer in the formula is unique. I was wondering if we could use the same D'alambert formula in the last video and replace phi and psi functions with 0, as they are the conditions of this problem and show that the answer u=0 is unique. is that a correct method of showing that? or is there sth missing? I'd really appreciate it if u could answer

[@drpeyam]

Thank you! And sadly no, D’Alembert is for the whole real line, but here we’re focusing on [0,l]

[@yashvindersingh832]

Thanks for the video. Can you please also do a video on Green's Function and provide some intuition ( like how it is related to electric potentials)?

[@drpeyam]

Unfortunately I don’t know much about Green’s functions

[@shambosaha9727]

@@drpeyam Come on, Dr Peyam, whom are you trying to fool?

[@AlexandreGurchumelia]

Both are kinetic together, it's a free field so it has no potential. If you add V(u) in the Hamiltonian that would be a potential energy.

[@aunglwin3458]

Thanks u very much sir. I want to learn strong maximum principal for harmonic function.

[@drpeyam]

Maximum Principle kzbin.info/www/bejne/hn7Nq3p7hdCEqpo

[@정대영-l1e]

Neat and beautiful!

[@nomoremathhere]

I want an energy drink

[@dgrandlapinblanc]

Thank you very much. Come back for me.

[@manfredwitzany2233]

In Physics we directly use energy and moventum conservation to solve PDE easily. It is intersting that it is possible to use these techniques from the back side.

[@rodrigo_p2821]

Hello!!!

[@drpeyam]

Hi!!!

[@RalphDratman]

Haven't taken physics in 30 years???? That cannot be true! You last took physics when you were 3 years old?

[@drpeyam]

13 :)

[@RalphDratman]

​@@drpeyam 13 years makes a lot more sense! Sorry, I heard you wrong. For my part, I have not taken a physics course in 50 years (Berkeley 1970). Yet I like to suppose I still remember most of what I learned up at Birge Hall, next to the Campanile. Except to be honest, I spent most of my time learning how to program the old IBM 1620 computer in the 2nd sub-basement underneath Birge. That opened up a career in computers for me, and so my practical education, if not my credentialing, was accomplished. Regardless, I think you got the potential and kinetic energies right. Assuming U(x,t) represents the displacement (say in the z direction) away from the equilibrium (unplucked) position of a point x between 0 and L on a tensioned string at time t, then Uxx(x,t) represents the force at the point x of the string due to the curviness of the string at x, given by the 2nd space derivative at that point. The stretched string experiences a force that is trying to get it back to a straight line at each point, trying to make the 2nd space derivative zero. Then Utt(x,t) represents the acceleration (2nd time derivative) of a point x on the string at time t. Since force = mass times acceleration, and assuming m=1, you get your original PDE. (I think.)

[@drpeyam]

OMG, Cal!!! I did my undergrad and grad there 😍

[@RalphDratman]

@@drpeyam I know you did, and now you are at Irvine, is that right?

[@drpeyam]

Correct 🙂