Laplace transform of a piecewise function, sect7.2#11

Laplace transform of a piecewise function,

[dhanashreeingale]

Thats just the most unique mic i have ever seen in my life

[huehue]

Awesome, most videos on youtube don't explain a solid method to solve those functions and they never solve examples of this complexity. Good work my friend.

[hrshpegu]

Loved your DI method it made my life so easy, thank you so much

[guadalupeabigailhernandezs]

It's 12:48 am and i'm preparing my exam for today, thank u very much! A big hold from Mexico City

[Zonnymaka]

That was an helluva of algebra :)
I think it's much easier by using the unit step function u(t-a) (aka the Heaviside function).
Since f(t) is defined like that, we must "flip" the Heaviside function and use (1-u(t-pi)).
Hence, we are looking for:
L{sin(t)*(1-u(t-pi))} = L{sin(t)}-L{sin(t)*u(t-pi)} =
= L{sin(t)}-e^(pi*s)*L{-sin(t)} = L{sin(t)}+e^(pi*s)*L{sin(t)} = L{sin(t)}*(e^(pi*s)+1)
= (e^(pi*s)+1)/(1+s^2)
That's it!

[kkenny]

Have been watching so many of your vids and I swear you have had about 3-4 different hairstyles

[Dana__black]

Do you have a video on that DI method? I have never seen it before and it looks super helpful!

[BadThetan]

I love your integration by parts. I was taught the u du v Dv method.

[najmulhisammudin]

Thank you! very helpful and i like the way you explained everything!

[olivioarmandocordeirojunio]

Thank you very much. Your DI method is wonderful.

[leakhoury]

I have a task where I have the Laplace transforms given and I have to find the original function... How can I do that? Any ideas?

[PalinDynamics]

What should we do when the intervals are not just, greater than or less than, but instead greater than or equal to, less than or equal to?

[JOHNCUDJOEKUMAKO]

If it was less than or equal to, what happens?

[miracyan]

is the e power of -st part of the formula for the piecewise questions?

[maelenaomi]

Whats the name of the book you use to get these exercises?

[letahmhlongo]

can you please do Transforms of Piecewise Continuous Functions

[tentonk]

Do you have any videos on laplace transformation of piecewise functions that include unit step functions.

[nazlicankaplankiran]

Hes teaching Grogu by holding his metal ball to make him listen

[kodistamana]

We was not supposed to integrate the e^t and differentiate sin(t)???

[tag_of_frank]

Oh snap, what is that integration by parts method called? I only know the long annoying way.