Laplace Transforms and Convolution

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
Instructor: Gilbert Strang

When the input force is an impulse, the output is the impulse response. For all inputs the response is a "convolution" with the impulse response.

License: Creative Commons BY-NC-SA

[ervivekchoubey]

I wish someone had taught us so well in the University. Hats off this is gem.

[lokmanehamdani]

No words can describe the beauty of this teaching, I wish I had the possibility in the past to study like this

[williamkwiatkowski]

"because I don't plan to check" had me laughing out loud in the library, great video. thanks.

[ozzyfromspace]

Me: Education is a scam
The internet: hold my beer *plays this wonderful video :)*
Thank you!

[georgesadler]

This is a solid introduction to convolution.

[burayaltun]

What a nice explanation, thank you so much professor :)

[crazyoldhippieguy]

30-01-2023.A good exaple of a deformation of a object in time, were the eleaments are noted in a 3-D Matrix, just saying.

[ervivekchoubey]

Laplace transform is one of the best things calculus has in itself

[lindsaysmall]

Is there a link to the video he references talking about the input and growth function over the remaining time?

[tripp]

6:38 is wrong isn't it? Transform of y' should be sY(s) - y(0)

[ranam]

Ok genius iam also approaching the problem same way like you I don't use matheMatical way my question is so simple because LTI depends on convulution here's my question below
Convulution is nothing but stacks and scales the input that's why the input to an amplifier is stacked and scaled or amplified but in filter design it attenuate frequency so I don't know how it regret certain frequency by stacking and scaling the input if possible some one explain to me


Also application

Brother I know mechanical engineers could find resonance but when I had a deep thought on this resonance Is an slow accumulation of energy which is accumulated very high in small installments when the frequencies match if you strike a turning fork of 50 hz you get the same frequency of vibration on another tuning fork so they both vibrate if you strike it harder the amplitude changes hence loudness is a human factor the frequency is the same the languages that human speak through out the world the sound only resonate your ear drum for few seconds my question is that the harmonics is the fundamental frequency and overtones are the frequency that follow it take a word in any language you spell it according to convolution the thing scales and ques and stack the signal so convolution can be used to model resonance so when your ear drum vibrates it vibrates so the electrical signals are carried to brain like tuning fork ear drums vibrate within the audible spectrum 20 hz to 20000 hz hence resonance is caused by the word we speak and within the audible range the ear drums vibrate and we make sense of words I have seen in one videos on YouTube that due to harmonics in any sound causes resonance which could be modelled by convolution recalling the resonance its destructive because slow and steady accumulation of sound on the mass causes high stress and high energy to build inside and stress increase and the system fractures or collapses but our ear drum hearing the sound from human languages try to vibrate but why our ear drum when subjected to continuous exposure of sound does not fracture or rupture like a wine glass iam not telling about high loud sound higher than 80 db but a audible range sound within the frequency of 20 hz to 20000 hz under continuous exposure why it's not damaging it again not failure by high energy but low one in synchronisation on air . But I tried it in my students when I told them to be quite in class they did not listen to me so I took my phone and set an frequency 14000 hz and they told it was irritating the idea of resonance is "small effort but large destruction " just like Tacoma bridge where the wind just slowly accumulated energy on the bridge and it collapsed it so my conclusion is if an audible frequency at continuous exposure to an human ear can it cause bleeding again "small effort but great destruction" sorry for the long story I you are able to reach hear you must be as curious as me so still not finished the ear drum is shook by harmonics in the sound we make by the words( or )overtones in the sound we make by the words I know harmonics is the fundamental frequency and overtones are following it which under slow and steady accumulation of sound energy resonates and could damge the ear drums again "small effort but big destruction" not to mention we assume the person is in coma or brain dead hence when the sound irritates him he or she could not make a move so my question is so simple normally human ear responds to harmonics or overtones according to convolution which could be a disaster but with minimal effort 🙏🙏🙏🙏 at here I could be wrong because harmonics can also be used to construct sound so can it be destructive or the overtones which are the trouble makers and which one according to this gives a response curve when two signals convolved by harmonics or overtones which is destructive but with minimal effort and convolution happens when ear drums oscillate is by harmonics or the overtones or also the trouble makers there

[johnmajok]

This is an amazing lecture, thanks 🙏 so much sir

[hathuytu]

now I know where the operator convolution comes from.

[jaedonheartright]

i wish herbert gross had one on transforms

[austinfritzke]

It's Dr. Frankenstein!
I kid, I kid--he's cool.

[Mufti]

Why am I wasting thousands of dollars in uni when I can learn all this for

[IamGX]

ahhh fuck...the word convolution triggered my PTSD.