Everything you need to know about Laplace transforms

This is the ultimate engineer's introduction to Laplace transforms!
0:00 - Preamble
1:02 - Where does the Laplace transform come from?
1:47 - Why is the Laplace transform defined this way?
4:03 - How do we use Laplace transforms?
6:01 - What's the difference between Laplace and Fourier transforms?
6:42 - Final thoughts

[@danielflood1309]

Explained better than any college professor I've had, well done!

[@farwamumtaz176]

Why i didn't find you before.Amazing ❤

[@aalperenpolat]

I wish you could be my Signals and Systems teacher

[@chaotic_spirits]

this is the most beautiful explanation I have ever heard, thank you for the contribution to the community.

[@alvaroaberastainmarzorati7029]

Hey, I saw your post on reddit and i´m surprised by the quality of your videos. Keep it up!

[@cyadid]

Best explanation I have seen ! I wish I could get this when I first learned about Laplace Transform Well done !

[@amanagnihotri6871]

This channel is life saver. Thank you sir, please keep uploading such informative content

[@nielscarpentier4616]

Thank you so much!

[@adambrekibirgisson1670]

Very well explained, the quality of your videos is on par with the best education channels

[@Adhithya2003]

Thank you so much , That analogy of PDF -> Word -> PDF was so awesome.

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Am happy I found ur channel

[@patrice9480]

incredible quality, really !

[@mrmatias2618]

Thanks man, the PDF example made my day. subscribed.

[@bunkydunk7500]

Great explanation! Much appreciated!

[@kennethkyalo3821]

Excellent

[@jacobseal]

Nice video. That backing beat made me want to grab a mic and lay down some soulful 90's raps.

[@danielsadeko8499]

Thank you for this explanation

[@danielsharkoff4013]

Wow what an amazing video.. immediately subscribed after watching.

[@theawantikamishra]

This is amazing. Subscribed

[@sharadwade987]

Loved it

[@irfansyahril8511]

Amazing!!

[@Kobs.A]

Your analogies are insane

[@abdelrahmankhalil8878]

best video on laplace transform ground up deserves better

[@The_double_side]

such a confident man .....

[@ashwiniked]

You are a great teacher. Put more informative videos.

[@MisterBinx]

I remember doing these in differential equations years ago. Now I have to figure them out again in mechanical vibrations.

[@aravinthdravid9183]

Buddy which book did you referred to give this easy understanding of Laplace Transform. Kindly share if you have any.

[@stevematson4808]

What model of scope is that behind you?

[@elaymisgav1879]

Hi thank you very much love your videos! I am now taking linear systems course , it feel that I don't understand well the difference between Laplace transform and Fourier, and in addition in which sort of problems I will use which of them. If their is anyway to make it clearer that will be great! thanks again!

[@carultch]

Good question. The Fourier transform is a special case of the Laplace transform, once the system achieves steady state and initial transient behavior settles. Corresponding to the steady state, the real part of the Laplace domain variable s, will approach zero. The s-domain variable will become a purely imaginary number for the Fourier frequency domain, which is j*omega. The Fourier transform is a spectrum of sine and cosine waves that model the signal. The Laplace transform is a spectrum of exponentially decaying sine and cosine waves, and some with no decay, that models the behavior of the signal, inclusive of both the initial transient, and the steady state condition.

[@chrisoca958]

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[@Nahash5150]

So I want to make a dual band filter that attenuates a signal by 1dB at 250 hz and at 2.5 khz. The Q should be about 0.5

[@utkarshtrehan9128]

MVP

[@to_YouTube]

pls upload practical applications of duality , autocorrelation , sample theorem .... this will help us a lots ...

[@amanravan9795]

👍👍

[@Kobs.A]

I didn't get the Fourier analogy

[@vaibhavpatil9956]

please explain why it works!!!!!

[@anirbanmukherjee5073]

Pls make for Fourier also

[@aspirohk3558]

Sample of solving the 'convution' solving in the time domain Why do they use s for frequency domain like f could work easy like f(t) t=time but f(f) f=frequency

[@carultch]

I believe s is supposed to stand for state. Either that, or it's just a completely arbitrary letter, when other letters were spoken-for when the concept was coined. It's more than just frequency, so they don't just use f. It is called complex frequency, because it is a complex number where its real part represents exponential decay, and its imaginary part represents angular frequency. It's common to use the trio p/q/r, as the equivalents of s, when using position domain instead of time domain. The Laplace domain variable for x is p, for y is q, and for z is r. The next letter in this group is s, which is the Laplace domain variable that corresponds to t for time. Fourier transform could use omega or f, for frequency, or omega for radian frequency, depending on which variant of the transform you use. In the f-world, Fourier transform and inverse Fourier transform, are both identical processes, so it makes it easy to match the pairs. In the omega-world, you accumulate a constant. Some tables will normalize this constant, by including a factor of 1/sqrt(2*pi), so an omega-world Fourier transform is bidirectional with the time domain.

[@kratomleaf8937]

bro where have you gone

[@DhanushKumark]

i wish he would have been my teacher

[@el_witcher]

+1 Sub 😉

[@mahmoudshata1105]

i just wonder why s equals this ?

[@carultch]

The Laplace domain variable s, represents complex frequency. The real part is exponential decays, and the imaginary part is oscillation. The Laplace transform converts a time-domain function into an s-domain function, and that s-domain function is a spectrum of various amplitudes, frequencies, and decay rates, of sine and cosine waves enveloped by exponential decay functions.