(2:2) Where the Laplace Transform comes from (Arthur Mattuck, MIT)

[tsyedtayyabshah]

for me! this is not a correct explanation.How is he relating S with -Logx

S is intact a complex number S=A+jB

[TheBeardedThinker]

this guy is badass.

[longerob]

Wiadomo skąd to "s" się bierze, przynajmniej nie z dupy...

[ozzyv]

most teachers just copy whats written in textbooks to the board. but teachers like these do the actual teaching. this is how it's done.

[UnAlesharl576]

soso is ja cool

[TashaM0901]

such a great explanation! love this!

[asddgfzg]

amazing explanation!

[jads92]

came here out of curiosity about Laplace transforms thinking they were ingenious constructs, and looking for an explanation about where they come from. I got exactly what I wanted. Thanks!

[9906197439]

O, Is that all???



[BisratGabriel]

Thank you so much it's very helpful!!!



[hamsterpoop]

@MatrixOfDynamism

read the video description

[asyd03]

excellent explanation

[ryanmonte]

@alquiora He mentions that the function ln(x) can only be a function of negative values of x. When you input a negative value into a natural log function you get a complex number. So the variable IS complex, no trickery here

[angryparrot]

My prof never explained where this thing came from when I took 2nd year ODE. This explains a lot :)

[MrFrankco1]

Good explanation

[YellowCakeKid]

i see what you did there

[kyle3420]

I wanna go to MIT sooo bad :(

[grahamwebb2000]

good handwriting

[alquiora]

Most of the texts define s as a complex variable but in this lecture he defines s as ln(x) .... which one is right? Is he just tricking the students?

[ryanmonte]

@alquiora He mentions that the function ln(x) can only be a function of negative values of x. When you input a negative value into a natural log function you get a complex number. So the variable IS complex, no trickery here.

[alquiora]

@ryanmonte I must have missed it

[weezilla]

Well put and good to know (a lot simpler than I thought). I still need to find the proof as to why Laplace and inverse Laplace transforms work the way they do (yielding solutions to deqs). Wish he would've covered that here.

[adriancho07070707]

Excelente, tomé esta misma clase en la universidad, una linda manera de explciar el origen de la transformada de Laplace............Excelent I took this same lesson at university, it's a wonderful way of describing the origin of Laplace's transform ........Yes, mexicans as myself know math of this level.

[azmathmoosa]

nice. had to replay like a million times to understand. but gr8!! i know laplace transform's origin now!!

[k9triz]

An excellent explanation. However, he fails to explain why 's' must be a complex number in order for L(s) to qualify as a laplace transform.

[weezilla]

@k9triz I thought s was just a dummy real variable to be used for transforms. I've never worked with it complex, what do you mean?

[axedrecista]

MIT?? holly crap better put attention

[Chubigans]

my mind has been blown by this great description.

[lbocvarov89]

Much better than the explanation i got in my college. Like X 10000

[IanFarias00]

Oh, is that all?

=DD

[yanmich]

really nice! once more the discrete plays along with the continuous!

[tarmizi2005]

very interesting, i didn't know the way they derived the laplace transform. As an Engineering Student, i just apply the transform without knowing the origin.

[MsIzadi]

Not only the lecturing is great but the idea of the introducing the concept of Laplace transform from its origin is the greatest which, on the one hand, makes the theory far more interesting in terms of the relationship between mathematical analysis and differential equations, on the other hand, it explains the deep connection between a discrete phenomenon and its continuous counterpart. In conclusion, it is just amazing.

F. A. I

[anandparalkar]

Phenomenal! Most interesting. Most insightfull explanation of how Laplace (and other) transform(s) works.

It helped me appreciate Fourier transform like never before.

[znhait]

That's why MIT is MIT.

[lagolfa123]

wow, when do they learn it at MIT???

[troponinnutrition]

It will depend on your level of education before college. If you took multivariable calculus at a university level in high school, you may have this class in your first semester at university.

I don't know if MIT has a mathematical "sequence" for majors involving mathematics that is "mandatory" though.

Differential equations is what made physics "come alive" for me.

[djwilliamt]

nice video i was also wondering the other day where it came from and now i know

[luliyo94]

gracias a la persona que publico este gran video me ayudo mucho ya que no habia podido encontrar una demostracion tan formal.

z

[dzalf]

La persona que publico esto se llama MIT y es la mejor escuela del mundo

jeje saludos