Laplace transform: sin(at) and cos(at)

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Let's, once again, kill two birds with one stone! We are taking a look at the laplace transformation of a time dependent complex valued exponential function to find out the transforms of the sine and cosine. Enjoy! =)
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[@estuardodiaz2720]

really cool derivation of the sin and cosine Laplace transforms :D

[@yahyatamur1385]

Since s is a complex number, and a is a real number, a/(s²+a²) may also be a complex number. so even if ℒcos x + i ℒsin x = s/(s²+a²) + i a/(s²+a²) , since all of those arguments may be complex, i don't think this is enough proof for the laplace transforms of cos(at) and sin(at) to equal to s/(s²+a²) and a/(s²+a²) respectively. this also applies to the hyperbolic sine/cosine video.

[@BengaliEastwood]

Cool🥶

[@SchrondingersCat]

Why did you only consider the real part of s? Did I miss something?

[@ditsogiftmogotsi1234]

helpful................... Thank u

[@MrRyanroberson1]

don't ALL derivations related to sine and cosine automatically interchange? just offset the boundary. for some f(x)=sin(x); u=x+pi/2; f(u)=cos(x); du=dx; the only difference is the range where a

[@SteamPunkLV]

dogs, math, memes
is this Heaven?

[@sergpodolnii3962]

When you describe Laplace transform you constantly emphasize its convergence criteria. It would be interesting to see when this transformation is actually not convergent.

[@sergpodolnii3962]

Yeap. It would be an interesting case. In reality all physical process are Laplace convergent. However, for instance, try to transform infinity ;)

[@DendrocnideMoroides]

easy make a function that goes to ∞ faster than e^st for example t^t

[@prasansharma29]

Pls explain complete laplace transform in short it is request

[@rikthecuber]

Me: wasting hours doing integration by parts to compute laplace transform of sines and cosine
Meanwhile this guy: Bow down to the euler's

[@MohitKumar-qn6pg]

Great only you gave ROC for the transform, none of the other videos does it.

[@deeptochatterjee532]

Are there really no comments yet?

[@dppid083wk7]

same

[@SOBIESKI_freedom]

You need to do something about your autofocus.

[@SOBIESKI_freedom]

I hope you get one soon. 😄
And keep up the good work! 😜

[@1997charlos]

Ya dame la maldita formula >:v

[@muhannad_9960]

Hello
I had some questions in laplace and i need solution very important please any one answer me

[@pascal3458]

وه عربي

[@pascal3458]

وه عربي