Convolution

Convolution
In this video, I introduce the notion of convolution and give an example and some applications. It is a very way of multiplying two functions that is useful analysis and PDEs.
Here is the demo I showed: phiresky.githu...
Convolution Intuition: • Convolution Intuition
Check out my PDE playlist: • Laplace equation
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[@benburdick9834]

I just got out of my PDE's lecture 15 minutes ago. This was exactly what we were talking about. Thank you so much for this; you are a great teacher.

[@ryaneakins7269]

Thank-you for this. I'd only ever seen the convolution in terms of ℒ(f 🌟 g) = ℒ(f)ℒ(g), and it's nice to see some actual examples.

[@adityaekbote8498]

Understood everything let's gooo you are the best Dr Peyam

[@elyepes19]

Thanks Dr Peyman. In the last few days, I've been precisely reviewing the intuition behind convolution. Your timing is perfect

[@toaj868]

The quick sketch of e^x was amazing!

[@MrCigarro50]

Finalmente soy de los primeros 10 en ver sus videos. Gracias, este video también es muy importante para nosotros los estadísticos. La convolución nosotros la usamos para encontrar la distribución de la suma de variables aleatorias.

[@leickrobinson5186]

Aargh! How come the KZbin app won’t let me translate this? Come ON, Google! Disappointed!!

[@md2perpe]

When I first saw the convolution in math formula books, I thought that it was a strange construction. But nowadays I love it, both since it can be used for solving differential equations, and for how usable it is for creating smooth functions that approximate any given function (what Dr Peyam was talking about at the end).

[@prateekmourya9567]

Channel is underrated

[@Himarim]

Dr. Peyam, Microsoft Whiteboard provides it's own ruler, it's under the erasor icon, so you don't need to use an actual ruler for drawing straight lines. c:

[@drpeyam]

Yeah I know but it doesn’t seem to work with the Wacom tablet, I can’t get it to rotate the ruler for some reason

[@ObsidianParis]

This thumbnail reminds me of the Heineken logo. I think I'll have one…

[@adityaekbote8498]

Just a doubt tho so the convolution is a line integral right? I don't know much about those but like for the integral over R² you parameterize stuff and then integrate from the inside out right? So what would happen for a infinite dimensional case say R^n where n is not finite

[@iabervon]

One day, one of my TAs said "The convolution is like a dot product in an uncountably infinite number of dimensions", which isn't really true, but it's an oddly useful way of thinking about it. It's a "how well do these functions line up times the product of their sizes" sort of thing, but it's as a function of how you shift them relative to each other.

[@ikocheratcr]

Great video, and I like a lot better the "digital board" you are now using. BUT one suggestion, can you do black background, Khan academy style? In my opinion it way easier on the eyes.

[@drpeyam]

I’ll try! I’m not 100% sure how visible it will be though

[@TheTKPizza]

@@drpeyam I would prefer that as well, ty for the great video. Liebe Grüße aus Deutschland. :)

[@pranavsawantcoder]

1*1 = t Very interesting

[@Jim-be8sj]

Some of the hardest proofs I ever had to do were proving basic properties of convolutions. I don't remember all the details, but I think many of the powerful convergence theorems from measure theory were required to show even simple properties like continuity of convolutions.

[@realcirno1750]

Amazing

[@Santi._.403]

I love convolutions!

[@nicholasroberts2933]

Dr Peyam, great video. Can you please tell me what software you use to take your notes on like in this video?

[@drpeyam]

Microsoft whiteboard + Zoom

[@md2perpe]

The fundamental solution is rather a solution to △U = -δ, where δ is the Dirac distribution. Outside of origin, one is solving △U = 0, though.

[@Kdd160]

Analysis is beautiful

[@patryk_49]

Wikipedia says that the star symbol you used for thumbnail represents something called "cross corelation" and is very simmilar to a convolution.

[@drpeyam]

Yep same thing, sum of P(y) P(x-y)

[@1willFALL]

Convolution in time domain is multiplication in Laplace domain 💙

[@ElijahAmirianfar]

Love love love love thissssss

[@drpeyam]

Mersiii

[@clydeherbert8188]

I’m only in calc 3, not sure why this was recommended but I guess I followed along

[@AnjaniGupta1]

Board and chalk/marker are better than digital pen, plzzz 🙂

[@drpeyam]

No, then people tell me “Sir, you’re covering your board” 😠

[@AnjaniGupta1]

Oh it seems generation gap! Anyways, happy with the content 👍

[@NovaWarrior77]

Cool!

[@Денис-с6р1г]

Can you show convolution solves with Laplace transform and with Z transform for discrete-time systems, please? :)

[@drpeyam]

LOL, no

[@1willFALL]

That's more of EE, I don't think that is in the realm of Dr. Peyam's specialty

[@Денис-с6р1г]

@@1willFALL maybe, but basics is from math

[@HeyKevinYT]

wowowoowowowowow