@liamwatts7105
Thank you! My professor taught it today and when asked why it works responded "it just does" so I'm grateful someone has a good explanation
@lukesacreds
it comes from hell
@henrytzuo8517
Salute to Prof Mattuck. The best explanation I have ever seen.
@grzegorzmolika4962
In common known Layons book "Understanding Digital Signal Processing" polish translator, professor engineer Jan Zarzycki from one polish university in chapter about Laplace Transform was made to modify Lyons text. So many wrongs was in it. He wrote, "mistakes are elementary." Layons mentioned Laplace Transform developed Heaviside and his method was not common approved. So question where the Laplace Transform comes from and why it works is still open.
@patrickjmt
nice explanation!
@DOR3ISH
Thank you so much. This is such a great lecture. I do recommend this to all my students. I hope everyone can see the beauty of it.
@carmelpule6954
This is how I explain how and where Laplace functions come about. Let say a teacher (T) examines a student (S). What that process is doing is trying to find out how close the knowledge of the student (S) approximates to that of the teacher (T) of perhaps we can say how much of the teacher's knowledge exists in the student. We can talk of an error function between the teacher and the student. Such an error is measured by a subtracting operation so the difference of knowledge between the teacher (T) and the student (S) can be said to be (T - S) Unfortunately, this error function (T - S) is not good enough to detect if the inequality of knowledge between the teacher and the student, as in some areas the student could be cleverer than the teacher and so if we integrate (T -- S) over the field of knowledge the integral could be ZERO. So the error ( T -- S) can be modified to operate with (error )^2= (T --- S)*( T -- S) hence ( error )^2 = ( T^2 --- 2* T*S + S^2) If we had to assign a meaning to these terms one could suggest the following, T^2 could be assigned to the energy due to the knowledge of the teacher (T) S^2 could be assigned to the energy due to the knowledge of the Student (S) (T*S ) could be a measure of how much energy due to the knowledge in the student (S) exist in the teacher ( T) Hence T*S is a recognition function of how much knowledge of (T) exists in student (S) Hence if (T) as the teacher, is taken as a reference of knowledge we can call him a KERNEL OF KNOWLEDGE and say we chose KERNEL AS BEING (e^jwt) which is a rotating vector or indeed we can go for a better KERNEL and we use e^(R+jwt) which is a rotating vector which can attenuate or increase or even reverse in rotation. The student (S) could be any unknown function to be compared to the KERNEL where the unknown function we can assume to be a rotating vector as A.e^ (--jw2.t) of a different frequency W2 than the KERNEL. To find how much (S) is contained in (T) all we have to do is to find the integral of (T*S) Hence ...................the integral of ( A.e^ (--jw2.t))*(e^(R+jwt)) will give an idea of how much of the function ( A.e^ (--jw2.t)) is contained in the KERNEL (e^(R+jwt)) The system retains stability if R is assigned a negative value which will attenuate any instability due to the function being compared with the KERNEL and this will limit the integral to a practical value of time ( in this case). So basically Laplace function is a recognition function of how much a function exists in another and the Laplace function operates on a time/frequency function to deduce what is the relation of the magnitudes of the frequency components in a time-frequency function to the frequency of the chosen KERNEL. One can select a KERNEL which not only has attenuation rate, a frequency rate, but also a phase, hence the KERNEL to compare other functions with could take the form of Kernel = e^( R+j(wt + p)) where that three-dimensional HELIX is one of the most important signals used in engineering. for stable and unstable and marginally stable systems (R) and infinite shapes containing, exponentially decaying sine, cosine, and circle functions with a positive and negative rotation( + or -- jw) including phase-shifting (p). Itis a really wonderful TEACHER KERNEL TO USE to compare other systems with.
@troponinnutrition
You will see concepts of differential equations many times and in many classes throughout your education. It tends to be after you've "learned" it through many stages of advance before you realize you know very little about differential equations.
@FF-wl1oo
Im watching this, scratching my head and while I'm doing that, (0:30) he goes: "People scratch their heads and can't figure out where it comes from..." Correct mr. Professor, I'm exposed :D
@michaelscaturro6326
I was waiting for the punch line and missed it. I am still lost.
@Eevee8858
Finally someone who explains it as a self learner who is learning laplace for simplifying my ode course i needed an explanation for why and how it came from 😅
@RubixPsyche
(4:30) can anyone explain how (x^n) in the place of (a(n)) could lead to (e^x) as mentioned? I'm a bit of a beginner, both at power series and laplace, (i know about part 2 dont worry, just sort of hung up here and my best attempt at looking it up just leads back here, guess there's a reason everyone loves this video ha)
@Pr0feBboy
I understand this professor better than our professors in my own country and even my english is not perfect OMG
@quagmire444
This isn't entirely true actually. Its certainly one way of looking at the Laplace Transform but in no way is this its actual origin. There is a more detailed description online that explains its history, relating to fourier series and Eulers study of certain integral solutions to differential equations that you can find more about. The simple answer is the answer is not really as simple as this video explains.
@gomemego3417
This video helps me in understanding alot of laplace transform
@AhmedIsam
I expected a Fourier based deviation -_-
@pefrenos
Great explanation. Nevertheless I still don´t get how S or -Ln X is also a complex number A+jB. Anybody knows another youtube video o web page where I can find that information?
@fernandowahnish5700
Thanks to this lesson, i could get my degree as a math teacher.
@yeeshubehera5687
Last two examples are pretty much cool.
@j-jcote2675