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Math Help - understanding PDE's

  1. #1
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    understanding PDE's

    Hi im new to Pde's , a few key concepts I am trying to get a better understanding of, : integrals, characteristic curves and a envelopes for a pde. I understand they are key components in constructing a general solution. If we stick to 3 dimensions, the solution is a surface(?), then is there a visual interpretation for those other parts aswell? many thanks in advance
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    I am pretty certain

    Quote Originally Posted by Richyie View Post
    Hi im new to Pde's , a few key concepts I am trying to get a better understanding of, : integrals, characteristic curves and a envelopes for a pde. I understand they are key components in constructing a general solution. If we stick to 3 dimensions, the solution is a surface(?), then is there a visual interpretation for those other parts aswell? many thanks in advance
    That an integral curve is a curve that fits all the directions in a direction field..ergo being a solution to the partial differntial equation
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  3. #3
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    in not sure what you mean by a direction field ?
    say we had a quasilinear pde a*du/dx+b*du/dy = c . Lecture notes say: charactaristics satisfy dx/a = dy/b = du/c
    from the above we can deduct integrals I, J such that I=constant and J = constant.. fair enough
    and when these integrals intersect we get a charactaristic curve.. . ..
    or am i understanding this incorrectly, just trying to picture it, its confusing what does it look like geometrically ? ?
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Maybe I am getting my ODE's and PDE's mixed up

    Quote Originally Posted by Richyie View Post
    in not sure what you mean by a direction field ?
    say we had a quasilinear pde a*du/dx+b*du/dy = c . Lecture notes say: charactaristics satisfy dx/a = dy/b = du/c
    from the above we can deduct integrals I, J such that I=constant and J = constant.. fair enough
    and when these integrals intersect we get a charactaristic curve.. . ..
    or am i understanding this incorrectly, just trying to picture it, its confusing what does it look like geometrically ? ?
    but if you assigned the two derivatives a value c and d...then you assign them numbers and graphed them you would get a three dimensional graph which shows the slope at each point
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  5. #5
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    hmmm i think im going to try this on matlab , thnx anyway
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