Normal Derivative
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- เผยแพร่เมื่อ 25 ก.ค. 2024
- Normal Derivative
In this video, I define a really cool and useful concept called the normal derivative, which allows us to talk about the behavior of a function on the boundary of a region. This is very useful especially for PDEs, and the next couple of videos illustrate the power of that. Enjoy!
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No “thanks for watching”?
True feelings are indescribable!💖
Actually I love your videos!
Hahaha
@@drpeyam Keep uploading such videos for someone who wants to explore the depth of mathematics. Thanks, Dr.Peyam ☺️
Love from an Indian Math enthusiast.♥️
Thank you so much! This video was really helpful!
Dr Peyam, Thank you for explaining very clearly (and enthusiastically as always) the normal derivative. Ideas like this one are often either assumed to be too easy to be discussed in detail or just mentioned during some elaborate calculation. I do not know if you have a video on Lipschitz domain which is also about the boundary of a domain.
I really appreciate the notation using nu for the normal
I like your enthusiasm, I also like the math
Does the good Doc. have a video on multi-dim. IBP yet? If not I await in earnest!
Thank you a lot. I follow your channel for a long time.
What software & hardware did you use for this video?
Microsoft Whiteboard
Thanks a lot! And what hardware if I may ask?
Hi Dr. Peyam!!! I haven't stopped in for quite some time but wanted to for this video. In Calc3; partials, gradient, and the TNB space was one of the biggest "Ah HA!!!!" moments in my maths career. It was also one of the most exciting because of all the immense power you now wielded. TNB was very hard for me to understand initially but once I realized it was another Cartesian coordinate plane "flying" around in the primary coordinate plane, anchored to the curve in question. I envisioned it as a roller coaster track and I am in the coaster car riding along, and me sitting in the car is one frame of reference, the TNB frame. Riding through the primary space of x,y,z. Once I realized that, it was like an avalanche of realizations all happening in short order. It was amazing TBH. So yeah, these topics are really awesome.
I am in diffeq now and due to being "taught" remotely, I am failing horribly. Its not even failing, its like I understand absolutely zero. I will be retaking it in the spring, assuming we are back to REAL school and not this remote learning "socio-political experiment" or whatever you want to call it.
What is TNB? Tangent, Normal, and Binormal vectors, I am guessing? Just never heard it referred to like that before. Makes sense though, their being orthogonal and all!
If u is a function of |x|, the normal derivative of u on a surface of constant |x| is obviously going to be u' of |x|, according to the explanation of the normal derivative. The example is really checking that the definition gives the right result for a case where we know what the answer should be, so it's good that we aren't surprised.
That’s interesting and makes total sense, thank you!
What a cliffhanger :( I'm really looking forward to see that video.
What kind of function is v in the integral you showed at the end?
Any function
what does W has to satisfy to have the normal defined at least almost everywhere?
Smooth boundary
Is their any difference between the divergence and the normal derivative they seem to measure the same thing
Two different things, the divergence measures how something expands and the normal derivative measures how much something flows out of a surface.
Dr Peyam I don’t really understand the difference is there an equation that relates the two functions using the gradient or does curl have anything to do with it?
There’s no equation relating them since they’re two different things. The only relationship maybe is that if you integrate the divergence of the gradient, by the divergence theorem you get the gradient dotted with the normal vector which is the normal derivative
@@drpeyam so the derivative of the normal derivative is the divergence of the gradient or the laplacian
Is the normal derivative tied to flux? If so, how exactly are they related?
By the divergence theorem
@@drpeyam Thank you :)
Hi Blackpenredpen!
Why you take (1,f') as a tangent vector? shouldn't be (x,f'(x))?
No, (1,f’) is correct. If you go 1 unit to the right, you go up f’(x) units
@@drpeyam The curve have the representation (x,f(x)) at each points in it, so can we think about (1,f'(x)) as the gradient w.r.t x of the u where u= (x,f(x))?
thnks for watching, hey i just watch ur video until 10 second 🤣🤣