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Math Help - Level curve

  1. #1
    Junior Member
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    Level curve

    working through some problems on complex analysis and have no idea what's going on here if someone can give an explanation i may be able to solve,

    If f(z) = u(x,y) +iv(x,y), where z = x + iy,

    A level curve is a curve of the form u(x,y) = c , c= constant

    I don't understand this concept of the level curve any explanation would be greatly appreciated,

    Cheers
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  2. #2
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    Here is an example of level curves that i got from a site:



    This is a topographical map of some mountain. The contours are the level curves i.e. they are the curves of constant elevation. If f(x,y) = height of mountain at point (x,y), f(x) = c are the level curves of height c.

    It is similar for a complex number, except that you are mapping 2 dimensions onto 2 dimension whereas in the above example you are mapping 2 dimensions to 1 dimension. It is somewhat analogous.
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