Laplace Transforms

OP

Original post by TeeEm

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I need your expertise :biggrin:

Reply 2

Original post by a10

I need your expertise :biggrin:

apply the laplace transform definition as an integral to F'(t)

integrate by parts and the answer is practically the next line

Reply 3

OP

Original post by TeeEm

apply the laplace transform definition as an integral to F'(t)

integrate by parts and the answer is practically the next line

Unparseable latex formula:

F'(s)= $$\int_{0}^{\infty} e^{-st} . f'(t) dt

u = e^{-st}, \frac{du}{dt} = -se^{-st}

v= f'(t)

Unparseable latex formula:

e^{-st} f'(t) + s $$\int_{0}^{\infty} e^{-st} . f'(t) dt

is this right so far?

Reply 4

Original post by a10

Unparseable latex formula:

F'(s)= $$\int_{0}^{\infty} e^{-st} . f'(t) dt

u = e^{-st}, \frac{du}{dt} = -se^{-st}

v= f'(t)

Unparseable latex formula:

e^{-st} f'(t) + s $$\int_{0}^{\infty} e^{-st} . f'(t) dt

is this right so far?

there should be no f dash in the integral and there should be limits in the "integrated bit"

Reply 5

OP

Original post by TeeEm

there should be no f dash in the integral and there should be limits in the "integrated bit"

I get the second part about the limits but I don't understand the first part?

how does the f dash go away? :colondollar:

Edit: Ahhhhhhh I've spotted my mistake when i chose v it was supposed to be dv

(edited 8 years ago)

Reply 6

Original post by a10

I get the second part about the limits but I don't understand the first part?

how does the f dash go away? :colondollar:

you differentiate the e^-st
you integrate the derivative with respect to t, so it goes back to f

Reply 7

OP

Original post by TeeEm

you differentiate the e^-st
you integrate the derivative with respect to t, so it goes back to f

Yeah i made the mistake of using v as f'(t) it was supposed to be dv and then integrate to get v. My integration is rusty :lol:

Thank you

Reply 8

Original post by a10

Yeah i made the mistake of using v as f'(t) it was supposed to be dv and then integrate to get v. My integration is rusty :lol:

Thank you

no worries

I will upload the proof in my Laplace file
Usually my resources tend to be comprehensive, I do not believe I actually did not include this standard proof.

Reply 9

OP

Original post by TeeEm

no worries

I will upload the proof in my Laplace file
Usually my resources tend to be comprehensive, I do not believe I actually did not include this standard proof.

Do you have any resources on the convolution theorum? I'm only just learning it it seems so long :/

Reply 10

Original post by a10

Do you have any resources on the convolution theorum? I'm only just learning it it seems so long :/

download the latest version of Laplace from my site.

in the various Laplace question section
The proof is there
then there are some very simple inversions using it.

Then there are some applications in solving Standard PDEs in the last section but that might be a bit too advanced if you have just started this

Reply 11

OP

Original post by TeeEm

download the latest version of Laplace from my site.

in the various Laplace question section
The proof is there
then there are some very simple inversions using it.

Then there are some applications in solving Standard PDEs in the last section but that might be a bit too advanced if you have just started this

we have covered the PDE's but im kinda behind trying to catch up quickly :redface:

Reply 12

Original post by a10

we have covered the PDE's but im kinda behind trying to catch up quickly :redface:

what course are you doing?

Reply 13

OP

Original post by TeeEm

what course are you doing?

mechanical engineering

Reply 14

Original post by a10

mechanical engineering

2nd year I take it and what place?

Reply 15

OP

Original post by TeeEm

2nd year I take it and what place?

Yeah, second year advanced engineering maths module :ahee:

University of Sussex.

Reply 16

Original post by a10

Yeah, second year advanced engineering maths module :ahee:

University of Sussex.

all the best

Ah, this brings back some memories a10. Been very quiet lately, bogged down with uni work?

Reply 18

OP