Never stop making these videos, please! I love to see all these topics explained in a better way than they were taught (are being taught) to me at the university :)
Dunno if you guys gives a damn but if you guys are stoned like me during the covid times you can watch all of the latest movies on Instaflixxer. Have been binge watching with my brother recently =)
Even though shortly into this video I realised I didnt have close to the prerequisite knowledge to understand this topic, I came away having learnt a lot. I thought youe explanation at 640 was fantastic, thanka
Dude, These videos are unbelievably good. I'm currently trying to learn/relearn a number of different Mathematics techniques that I haven't looked at in yours or even seen in some cases and your videos are so incredibly helpful. Keep it up!
I was reading Stanley Farlow's PDE book that covers Green's function very briefly. At some point it shows one equation without proof(p296, notes 1), so I was looking for more info to understand it...and this is it. Thanks! (As a side note, this is an ingenious method to solve this type of PDE.)
Have been struggling with Green’s method for a few weeks now ever since it was introduced in my electromagnetism class. I’ve watched various videos and read the textbooks but really with very little gain in understanding. Thanks a million for this video, I finally feel like I crossed the hump from ignorance into intuition. Especially nice was how simply you derived Green’s identities and then subsequently showed their use in the PDE. Again, I cannot thank you enough. I will go reread my textbooks armed with the lessons I learned from this video. Do you have any plans on covering the Neumann boundary condition? It’s not strictly necessary since the fundamental concept was phenomenally explained in this video, but more content from you is always welcome.
Hey Mr khan, I really appreciate these,. You have provided me with good understanding of such topics. I do have a request for you though, can you make a video on solving PDEs (wave equation specifically) using greens function in spherical coordinates ? Like I'm basically trying to solve the main pdes in spherical using greens function. Thanks alot.
(9:43) Not sure I agree with [or understand] your "so it stands to reason" statement; integrate the delta function over either set of variables, and dependence on those variables vanishes. Most of the time I'm left wishing you would give more insights into the meaning behind the steps in your derivations, and tie the derivations into more fundamental concepts (e.g. how the Green's function relates to convolution); but what you offer is so much better than other options, that I shouldn't be complaining. Great videos!
Hello! I spent a lot of time on your videos, and they are very helpful! And I want to ask that do you have any plan to make more videos about this series?
This video was super helpful, everything is very well explained in a concise way. The only thing that I'm uncertain about now is how can we apply the boundary condition when the G*du/dn is within an integral?
Thank you for the kind words! I'm not sure how to explain this differently from how the video does it, but I'll try: The integral is over the surface S, which happens to be the boundary of the region where we're solving our PDE. Therefore, the functions u and G in the surface integral only take on the values they take on at the boundary S; this is why it makes sense to use the boundary conditions (boundary conditions = the values of u and G on the boundary S, the region our surface integral is also integrating over). Hope that helps, and if you still need clarification, let me know!
Here is an honest question: at time 2:46 , I am not sure you did the right thing with that divergence operation. You said before that v was a scalar right? How can you apply chain rule to F? the divergence of a scalar doesn't make sense. Also, you use the notation for a gradient vector as a result, while even if v was a vector, the divergence of v should be a scalar, not a vector at all. Please answer me, I would like to know if I am wrong.
Hi your way of teaching is very good and the usage of black board. Can you tell me which app are you using and how you use different color pens. I want to follow your method.
I'm reviewing for my applied PDE course, and this is honestly a lifesaver. But does anyone have the same experience as having to play the same clips of the video 3-5 times before it starts making sense? I've been feeling pretty stupid in my grad program (being surrounded by geniuses), and was wondering if anyone else ever had the same feeling...
Hello , I have a request. I want to solve poisson equation to find out electric potential in a device. and I want to use Green's Function's approach. IWill it give a unique solution? I listened to your lectures on PDE's. They are amazing but Green's functions are really tough. Can you please provide more tutorials/ lecture notes on the topic. It would be a great help. Thank you
G must also satisfy the same type of homogeneous boundary conditions that the solution u does in the original problem. The reason for this is straightforward. Take, for example, the case of a homogeneous Dirichlet boundary condition u = 0 for x ∈ ∂Ω. For any point x on the boundary, it must be the case that the integral over Ω of G(x, x0)f(x0) dx0 vanishes. Since this must be true for any choice of f, it follows that G(x, x0) = 0 for boundary points x (note that x0 is treated as a constant in this respect, and can be any point in the domain). I have this from www.math.arizona.edu/~kglasner/math456/greens.pdf at page 5.
At 8:30 G() is equal to zero at the boundry. This should, however, also imply that the directional derivative of G() should be zero at the boundry, after all, a zero function can not have a non-zero partial derivative. However, you retain this derivative at the border, and, moreover, replace u() at the border with h(). Please explain this mw, as I get confused.
The fact that a function is zero at one point does not imply that its derivative at that point is also zero, think of the function f(x) = x. At x=0 the function has zero value, but its derivative is f'(0) = 1, same for partial/directional derivatives.
At the 4 minute mark when the equation (G1*) is introduced, how are you allowed to subtract these equations because u,v in (G1) are different functions than u and v in (G1*)?
@@naeemakhtar4239 Now that I look back on it, my problem was actually related to the decomposition of the vector field. I'd say only some vector fields can be decomposed into u grad(v) and also in v grad(u) but I don't have any proof, just a gut feeling. And finding these scalar functions u,v seems like a rather difficult task. What would you say? EDIT: Nevermind misconception on my part, it's cleared up now.
@@liamoneillll123 The functions u and v can be chosen arbitrarily. We can then make two vector fields one u grad(v) and the other v grad(u) and apply green's identity to both vector fields. I initially thought we had to find a vector field which you could decompose into v grad(u) and u grad(v). Luckily this is not the case. I hope this clears it up.
