Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    19
    ReputationRep:
    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.

    \frac {dx}{dt} +4x =8

    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 \frac{dx}{dt} is equal to:

     -x(0) + sX(s) ??

    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 :confused:

    Someone explain this to me please
    • Thread Starter
    Offline

    19
    ReputationRep:
    (Original post by TeeEm)
    .
    I need your expertise
    Offline

    19
    ReputationRep:
    (Original post by a10)
    I need your expertise
    apply the laplace transform definition as an integral to F'(t)

    integrate by parts and the answer is practically the next line
    • Thread Starter
    Offline

    19
    ReputationRep:
    (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
    F'(s)= $$\int_{0}^{\infty} e^{-st} . f'(t) dt

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

    v= f'(t)

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

    is this right so far?
    Offline

    19
    ReputationRep:
    (Original post by a10)
    F'(s)= $$\int_{0}^{\infty} e^{-st} . f'(t) dt

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

    v= f'(t)

     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"
    • Thread Starter
    Offline

    19
    ReputationRep:
    (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
    Offline

    19
    ReputationRep:
    (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
    • Thread Starter
    Offline

    19
    ReputationRep:
    (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
    Offline

    19
    ReputationRep:
    (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.
    • Thread Starter
    Offline

    19
    ReputationRep:
    (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 :/
    Offline

    19
    ReputationRep:
    (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
    • Thread Starter
    Offline

    19
    ReputationRep:
    (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
    Offline

    19
    ReputationRep:
    (Original post by a10)
    we have covered the PDE's but im kinda behind trying to catch up quickly
    what course are you doing?
    • Thread Starter
    Offline

    19
    ReputationRep:
    (Original post by TeeEm)
    what course are you doing?
    mechanical engineering
    Offline

    19
    ReputationRep:
    (Original post by a10)
    mechanical engineering
    2nd year I take it and what place?
    • Thread Starter
    Offline

    19
    ReputationRep:
    (Original post by TeeEm)
    2nd year I take it and what place?
    Yeah, second year advanced engineering maths module :ahee:

    University of Sussex.
    Offline

    19
    ReputationRep:
    (Original post by a10)
    Yeah, second year advanced engineering maths module :ahee:

    University of Sussex.
    all the best
    • TSR Support Team
    Offline

    20
    ReputationRep:
    TSR Support Team
    Ah, this brings back some memories a10. Been very quiet lately, bogged down with uni work?
    • Thread Starter
    Offline

    19
    ReputationRep:
    (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 :lol:

    p.s. Had a look at your workout blog you been slacking I'm catching up to your lifts :lol:
    • TSR Support Team
    Offline

    20
    ReputationRep:
    TSR Support Team
    (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 :lol:

    p.s. Had a look at your workout blog you been slacking I'm catching up to your lifts :lol:
    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.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: October 31, 2015
Poll
Are you going to a festival?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.