What does laplace's equation mean?
Definitions for laplace's equation
laplace's equa·tion
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Wikipedia
Laplace's equation
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties. This is often written as ∇ 2 f = 0 or Δ f = 0 , {\displaystyle \nabla ^{2}\!f=0\qquad {\mbox{or}}\qquad \Delta f=0,} where Δ = ∇ ⋅ ∇ = ∇ 2 {\displaystyle \Delta =\nabla \cdot \nabla =\nabla ^{2}} is the Laplace operator, ∇ ⋅ {\displaystyle \nabla \cdot } is the divergence operator (also symbolized "div"), ∇ {\displaystyle \nabla } is the gradient operator (also symbolized "grad"), and f ( x , y , z ) {\displaystyle f(x,y,z)} is a twice-differentiable real-valued function. The Laplace operator therefore maps a scalar function to another scalar function. If the right-hand side is specified as a given function, h ( x , y , z ) {\displaystyle h(x,y,z)} , we have Δ f = h . {\displaystyle \Delta f=h.} This is called Poisson's equation, a generalization of Laplace's equation. Laplace's equation and Poisson's equation are the simplest examples of elliptic partial differential equations. Laplace's equation is also a special case of the Helmholtz equation. The general theory of solutions to Laplace's equation is known as potential theory. The solutions of Laplace's equation are the harmonic functions, which are important in multiple branches of physics, notably electrostatics, gravitation, and fluid dynamics. In the study of heat conduction, the Laplace equation is the steady-state heat equation. In general, Laplace's equation describes situations of equilibrium, or those that do not depend explicitly on time.
Numerology
Chaldean Numerology
The numerical value of laplace's equation in Chaldean Numerology is: 3
Pythagorean Numerology
The numerical value of laplace's equation in Pythagorean Numerology is: 9
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"laplace's equation." Definitions.net. STANDS4 LLC, 2024. Web. 27 Apr. 2024. <https://www.definitions.net/definition/laplace%27s+equation>.
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