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# Laplace Transforms watch

1. Okay so I'm just looking at this and something's not making sense here:

say I have a simple first order ODE and I want to solve this using the laplace method e.g.

now we take laplace transforms of each of the terms (which i get and because these are all assumed to be casual functions we can look up some of these in the table)....now the bit I don't understand is how is the laplace transform of is equal to:

??

i tried to work it out using the original definition of the laplace transform equation but you end up with the exponential to the power t but integrating w.r.t. dx

Someone explain this to me please
2. (Original post by TeeEm)
.
3. (Original post by a10)
apply the laplace transform definition as an integral to F'(t)

integrate by parts and the answer is practically the next line
4. (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

is this right so far?
5. (Original post by a10)

is this right so far?
there should be no f dash in the integral and there should be limits in the "integrated bit"
6. (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?

Edit: Ahhhhhhh I've spotted my mistake when i chose v it was supposed to be dv
7. (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?
you differentiate the e-st
you integrate the derivative with respect to t, so it goes back to f
8. (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

Thank you
9. (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

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.
10. (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 :/
11. (Original post by a10)
Do you have any resources on the convolution theorum? I'm only just learning it it seems so long :/

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
12. (Original post by TeeEm)

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
13. (Original post by a10)
we have covered the PDE's but im kinda behind trying to catch up quickly
what course are you doing?
14. (Original post by TeeEm)
what course are you doing?
mechanical engineering
15. (Original post by a10)
mechanical engineering
2nd year I take it and what place?
16. (Original post by TeeEm)
2nd year I take it and what place?
Yeah, second year advanced engineering maths module

University of Sussex.
17. (Original post by a10)
Yeah, second year advanced engineering maths module

University of Sussex.
all the best
18. Ah, this brings back some memories a10. Been very quiet lately, bogged down with uni work?
19. (Original post by Smack)
Ah, this brings back some memories a10. Been very quiet lately, bogged down with uni work?
Hi Smack, hope life is treating you well? How are you?

Yeah I've just been really busy; applying for some one year placements, having interviews and what not (which made me get behind on my course a bit so basically playing catch up now lol). Also TSR is getting a bit old, I will only really use it for help on studies or maybe having a look at the careers sections for some info cba answering all these noob/childish questions on the engineering forum

p.s. Had a look at your workout blog you been slacking I'm catching up to your lifts
20. (Original post by a10)
Hi Smack, hope life is treating you well? How are you?
Yeah okay for someone in oil & gas really.

Yeah I've just been really busy; applying for some one year placements, having interviews and what not (which made me get behind on my course a bit so basically playing catch up now lol). Also TSR is getting a bit old, I will only really use it for help on studies or maybe having a look at the careers sections for some info cba answering all these noob/childish questions on the engineering forum

p.s. Had a look at your workout blog you been slacking I'm catching up to your lifts
Yeah definitely make use of the study resources here, there are some really fantastic people willing to help. I kinda wish I made better use of here when I was studying.

I also cba with the same repetitive stuff usually seen in the engineering forum any more. Most of the time.

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Updated: October 31, 2015
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