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Solution to Laplaces equation

  1. Oct 28, 2005 #1
    The Laplace's equations in 2-dimensions if V is the electric potential is given by:
    [tex]\frac{\partial^2 V}{\partial x^2} + \frac{\partial^2 V}{\partial y^2} = 0[/tex]
    Since this is a second order partial differential equation, the simple rules of an ordinary differential do not apply. The solution will not contain a definite number of arbitrary constants. So how is a general solution obtained for this equation?
  2. jcsd
  3. Oct 28, 2005 #2
  4. Nov 1, 2005 #3
    see Introduction to Electrodynamics by David J Griiffiths....
    there is a very good introiduction to Partial differential equations in it....
  5. Nov 1, 2005 #4


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    Or see Mary Boas "Mathematical Methods in the Physical Science". Chances are, if you're having problems with this, you may need to look at a bunch of other mathematical techniques in 2nd order partial differential equation and how they are used in physics. This book covers such a thing.

  6. Nov 2, 2005 #5


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    1.Bring it to canonical form.
    2.Identify the type of problem you're dealing with depending on the initial/boundary conditions.
    3.Using the separation of variables is the easiest way to get a particular solution.

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