The Weak Derivative
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- Опубликовано: 28 янв 2018
- Have you ever wondered how to differentiate a function that is not differentiable? In this video, I will show you how! It all relies on a simple integration by parts and a tiny bit of linear algebra. I will start by calculating the derivative of x^2, then I will calculate the derivative of |x|, and, more surprisingly, the second derivative of |x|. Be prepared to be amazed! :D
When you use integrals to calculate derivatives you have achieved true transcendence.
Any day that Dr. Peyam uploads a video is a great day.
When you said Heaviside function in example 2, I think you meant sgn() function. A Heaviside function is basically a unit step. That said - phenomenal lecture! Just like this, now I understand the big idea of generalized derivatives of distributions. Thanks, Dr. Peyam! 🙏🏽😊🎊
Destroy an undesttroyable shield with a sword wich can not destroy anything.
General derivative = gender
Please differentiate something like the Weierstrass function: continuous but non-differentiable everywhere :D
I remember you as a graduate student at Berkeley, and I was also jealous when people would walk out of your section with cake before my class.
Me: it's |x|/x. Everyone: the true intellectual
You could define (|x|)' as |x|/x.
In all honesty, I'm finding it hard to see the crayon writing against the dirty blackboard...
one of the coolest dudes on youtube! i've become addicted to your videos
Woah... does this bring back a ton of memories... Having to deal with the derivative of |x| (the absolute value) tormented me daily... Generalized derivatives.. a great topic (although I didn't end up using them). Heaviside functions is one of my favourite math inventions - I just find this theory very elegant.
"how to get an integer quotient in n/m for integers 0
sees video title
If one studies generalized functions and integral transforms (Laplace's or Fourier's) and convolutions, then the similar thing is done with Heaviside and Dirac functions. Does the `distribution theory' claim that we can choose any compact support infinitely differentiable kernel with zero boundaries we can have the similar effect, moreover, it has relation to intergral transforms?
I'm not sure I completely understood the technique. I'll watch it again later when I have time, but I'd like to see the technique applied to some more interesting non-differentiable (or even, merely "hard-to-differentiate") function. Nothing too wild and crazy, but something more interesting. Also, it would be interesting if there was some discussion of graphical interpretations of this technique (if there exists some sensible way to visualize it).
Thank you for keeping inspiring me! Do you have any recomended book for learning distribution theory on a graduate level? I have some books, but im always looking for more ways to learn this :)
Your presentation is pretty cool :)
Nice video! Does anyone know what the 'motivation' means at around the one minute mark? Thanks.
Special but interesting. Thanks.