Laplace's equation: Difference between revisions
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where the operator ∇ stands for (∂/∂x '''i''' + ∂/∂y '''j''' + ∂/∂z '''k''') |
where the operator ∇ stands for (∂/∂x '''i''' + ∂/∂y '''j''' + ∂/∂z '''k''') |
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Expanding this into its full component form, we have: |
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:∂<sup>2</sup>/∂x<sup>2</sup> φ(x,y,z) + ∂<sup>2</sup>/∂y<sup>2</sup> φ(x,y,z) + ∂<sup>2</sup>/∂z<sup>2</sup> φ(x,y,z) = 0 |
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Solutions of Laplace's equation are important in many fields of science, notably the fields of [[electromagnetism]] and [[astronomy]]. |
Solutions of Laplace's equation are important in many fields of science, notably the fields of [[electromagnetism]] and [[astronomy]]. |
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:''This is a stub'' |
:''This is a stub'' |
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External links: |
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* [http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Laplace.html Biography of Pierre-Simon Laplace] |
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Revision as of 15:51, 25 February 2002
Laplace's equation is a partial differential equation named after its discoverer Pierre-Simon Laplace.
Laplace's equation for a scalar variable φ(x,y,z) in a 3D space with unit basis vectors i, j and k can be written as
- ∇2 φ = 0
where the operator ∇ stands for (∂/∂x i + ∂/∂y j + ∂/∂z k)
Expanding this into its full component form, we have:
- ∂2/∂x2 φ(x,y,z) + ∂2/∂y2 φ(x,y,z) + ∂2/∂z2 φ(x,y,z) = 0
Solutions of Laplace's equation are important in many fields of science, notably the fields of electromagnetism and astronomy.
- This is a stub
External links: