The Chain Rule

[@ChristopherLum]

In case it is helpful, here are all my calculus videos in a single playlist kzbin.info/aero/PLxdnSsBqCrrGHwNWnP5XVhytcGL9ExuPE. You can support this channel via Patreon at www.patreon.com/christopherwlum or by clicking on the 'Thanks' button underneath the video. Please let me know what you think in the comments. Thanks for watching!

[@dsizov]

The Jacobian part is absolutely brilliant! Thanks Chris

[@ChristopherLum]

I'm glad it was helpful, thanks for watching!

[@ebrewste]

I’ve never seen the decomposition approach. It makes deeper sense than memorizing the chain rule!

[@Tamanaaaa1]

AE 501: Great video. Thank you!

[@jacobgivens2000]

AE 501, Thank you for the refresher!

[@keyshawnb4845]

AE 501: This video broke down the chain rule in a way that was easy to comprehend. I feel comfortable that I can tackle chain rule scenarios now.

[@bosanova1643]

Merci ! From France

[@bosanova1643]

A playlist on sensor fusion? KF, EKF, UKF, etc.?

[@ChristopherLum]

Hi, First let me say thank you for your generous support of the channel, it is very much appreciated! Thanks for the suggestions on KF, EKF, etc. I'm working on some estimation and observer videos and hope to have the up soon. In any event, I want to again say thank you for your contribution and for supporting the channel. I hope to hear from you at a future KZbin video! -Chris

[@SomeTechGuy666]

The Julia language is excellent at doing work like this. You should incorporate it into your teachings.

[@LilanieAlfredaAbdur-Rahman]

AE501: That was a whirlwind! A specific application would help a lot

[@FatherGapon-gw6yo]

I am a simple cat-I see Lum and I click play.

[@fionaryan3708]

AE501: Thank you for the helpful video on the chain rule! Just a quick question: why is dw/dy = -8y and not dw/dy = 2x^2 - 8y?

[@Mandollr]

Can you make a lesson about Kalman Filter ?

[@dsizov]

But why should we multiply the two rates, and not, say, add them together? IMO this part is the hardest to explain

[@bosanova1643]

I think it should be seen as leverage effects in a chain. If I have two levers connected and equal, a small amplitude variation on the first lever will be reproduced with the same amplitude at the end of the second lever. Depending on the length of the levers, the amplitude of the variation can be multiplied or reduced (demultiplied), allowing for adjustments in the range of movements

[@bosanova1643]

Of course, the different lever arm ratios represent the rates of variation. For example, a 1:2 ratio linked to another 1:2 will give an amplitude of 1:4. A 1:1 ratio linked to another 1:1 will give an amplitude of 1.A 3:1 ratio linked to a 2:1 will give an amplitude of 6:1.

[@rfo3225]

Thank you for your many helpful videos. Just one minor point. In the first portion, shouldn't the cubic function f be negative for negative x instead of positive as drawn in the rough graph. I only point it out because it may confuse and distract some. Thanks.

[@ChristopherLum]

Thanks for catching this, you are absolutely correct and this picture is inaccurate for negative x values. I made a note of this in the video. The lecture notes that are associated with this video are correct. Thanks again for bringing this up and nice job noticing these inconsistencies. If you see anything else in this or other videos please let me know. Thanks for watching!

[@malachimorris1649]

AE501 - Malachi Morris

[@rfo3225]

Perhaps you meant to indicate a graph of h(u) instead of the label f(x).

[@CodySmith]

AE501