Laplace's equation: Difference between revisions
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'''Laplace's equation''' is a [[partial differential equation]] named after its discoverer [[Pierre-Simon Laplace]]. |
'''Laplace's equation''' is a [[partial differential equation]] named after its discoverer [[Pierre-Simon Laplace]]. |
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Laplace's equation for a scalar variable in a 3D space can be written as |
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 |
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:∇<sup>2</sup> φ = 0 |
:∇<sup>2</sup> φ = 0 |
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Revision as of 01:50, 29 January 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)
Solutions of Laplace's equation are important in many fields of science, notably the fields of electromagnetism and astronomy.
- This is a stub