Laplace Transform 3 (L{sin(at)})

[youngspen]

is this right?: i let u = e^-st and dv = sin at

then differentiate u for du = -1/s e^-st

then integrate dv for v = -a cos at

i dont get how you got (a cos at) as positive.

[ahmoodloova]

@sadga03

haha hate it too but look to this simple method=

we all know--> cos t=1/2[e^jt+e^-jt] ,we can use that to solve

so it will be F(s)= (integration of cos t .e^-st)=

integration of (1/2[e^jt+e^-jt].e^-st)=

i/2[(1/s-j)=(1/s+j)]...=s/s^2+­1^2

its much easier than all of that ^_^

[sadga03]

that's y i hate integration by parts... it make me confius... huh... =.="

[SeanRVCA]

I FREAKIN hate integration by parts!!

[Bisharpual]

9:25 "...cos at, now i wanna make sure i dont make any careless mistakes *checks intently* ... ok so now there's a minus sign *scratches out t thinking its a + sign*" lol

[9588alamALI]

wow ! great videos ! pure concept building

[curiosityuniversal]

Whoa infinite loop!!!... going to watch the next video to see how you get out of this one xD

[jailisfornobody]

mindrape...

[frazali007]

HEllo,, i did this question by his method in my test , but my teacher is not getting the idea of why are we taking u(dash)= e^(-st) ...khan hasnt explained in detail.. can anyone please help me with this asap...thanks..:)

[fakeplayer]

@frazali007 you just right exp-st=(1/-s * exp^-st)' and the inside of the ( ) u name it as U

[scottishlad1987]

did you make a mistake on by parts? i do it differently.

[sxtaco]

this is like devil magic haha.

[bluenmoon]

super hairy equations

[yeng0823]

some mistake during factorise out -exp power -st

[akd4ivt]

shave the hair and use Eulers formula

[TheMaku]

lol @ scribbling out the t in the cos.

[ClaraRose99]

What the hell is a "hairy" problem?

[dalcde]

@ClaraRose99 A hairy problem is a problem which you don't want to encounter.

[PrinceFX]

lol! light at the end of the tunnel

[annie14411]

Eulers formula is a much easier way to get the identity for sin and cos

[chevy112112]

who gives a fuck??? save it.. i got a test tmrw on this shit!!!! hahaa

[liquidstl]

@chevy112112 my test is on the 19t... for some reason I feel comfterble computing laplace transforms by indefinate integrals, but using gamma functions and tables i feel marginally confused about

[gematt7]

thank you!

[sikory]

I saw an interesting and much faster way to derive this by using the backwards Euler Formula: sin(at)=(exp(iat)-exp(-iat))/2­i

or by taking the imaginary part of the Laplace transform of exp(iat)

[Hinpaki]

Only integration by parts was difficult to understand.. Thanks!!

Also in our class and textbooks they use a formula of integral of e(pow)at sin(dt) dt = (e(pow)at/(a2+b2)) X (asinbt-bcosbt)...

We will change f(t) to sin(at) in the standard formula..

[Ganjin88]

Hey Guys, I heard of an ILATE Method to determine U and V by integration by parts. Sometimes, the Method is LIATE but its mostly ILATE. For anyone curious of what it means. Just google it.

[lopokillo]

he use the wrong U. He put U' after the minus integer of uv '

[Greafgriet]

Actually, you can do it both ways.

1. uv = ∫uv' + ∫vu'

Your textbook subtracts ∫vu' so you get

2. ∫uv' = uv - ∫vu'

But you can subtract ∫uv' from 1. too.

3. ∫vu' = uv - ∫uv' (which is what he did)

All 3 are the same.

Hope that's what you were referring to.

[dibser]

such a great resource, helped me so much so far

[alundraman]

this lectures would be ten times better if it is in wide screen... more space

ps. I love your lectures please do more

[TimpBizkit]

Is it possible to evaluate L(cos(at))

as a x L(sin(at)) - sin 0, thus ridding yourself of the second integration by parts stage?

[TimpBizkit]

Forget that last comment, if you do that, the equation becomes the utterly useless y = 0+y

[hammad506]

im studying digital signal processing n this helps a lot.. gr8 work!

god bless!

[bordenw]

I did the problem my way and your way and it is the same answer. I did not realize that int by parts is the opposite form of the product rule. Thank you for clarfying that for me. Do you have any videos on work and energy on an incline and partial differential equations?

[khanacademy]

Depends on what you pick for u and v. I rederive the formula from the product rule everytime (it's the only way you'll remember it 15 years after taking calculus)

[bordenw]

the integration by parts formula is uv-integral v du not dv.