Question #11273

describe poisson and laplas equation.

Expert's answer

In mathematics, Poisson's (<img class="tex" alt="\Delta\varphi=f" src="https://upload.wikimedia.org/wikipedia/en/math/5/c/1/5c1eca5688ddbfe8e4df96b205f652ed.png">)equation

is a partial differential equation of elliptic type with broad utility in

electrostatics, mechanical engineering and theoretical physics.In mathematics,

Laplace's(<img style="BORDER-BOTTOM-STYLE: none; LINE-HEIGHT: 19px; BORDER-LEFT-STYLE: none; FONT-FAMILY: sans-serif; BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; FONT-SIZE: 13px; VERTICAL-ALIGN: middle" class="tex" alt="\nabla^2 \varphi = 0 \," src="https://upload.wikimedia.org/wikipedia/en/math/4/2/6/42635da1dea70ee9c2f855a7c52573c9.png" data-mce-style="border-style: none; vertical-align: middle; font-family: sans-serif; font-size: 13px; line-height: 19px;" data-mce-src="https://upload.wikimedia.org/wikipedia/en/math/4/2/6/42635da1dea70ee9c2f855a7c52573c9.png">)

equation is a second-order partial differential equation.Laplace's equation and

Poisson's equation are the simplest examples of elliptic partial differential

equations. Solutions of Laplace's equation are called harmonic functions.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 many fields of science, notably the fields of electromagnetism,

astronomy, and fluid dynamics, because they can be used to accurately describe

the behavior of electric, gravitational, and fluid potentials. In the study of

heat conduction, the Laplace equation is the steady-state heat equation.

is a partial differential equation of elliptic type with broad utility in

electrostatics, mechanical engineering and theoretical physics.In mathematics,

Laplace's(<img style="BORDER-BOTTOM-STYLE: none; LINE-HEIGHT: 19px; BORDER-LEFT-STYLE: none; FONT-FAMILY: sans-serif; BORDER-TOP-STYLE: none; BORDER-RIGHT-STYLE: none; FONT-SIZE: 13px; VERTICAL-ALIGN: middle" class="tex" alt="\nabla^2 \varphi = 0 \," src="https://upload.wikimedia.org/wikipedia/en/math/4/2/6/42635da1dea70ee9c2f855a7c52573c9.png" data-mce-style="border-style: none; vertical-align: middle; font-family: sans-serif; font-size: 13px; line-height: 19px;" data-mce-src="https://upload.wikimedia.org/wikipedia/en/math/4/2/6/42635da1dea70ee9c2f855a7c52573c9.png">)

equation is a second-order partial differential equation.Laplace's equation and

Poisson's equation are the simplest examples of elliptic partial differential

equations. Solutions of Laplace's equation are called harmonic functions.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 many fields of science, notably the fields of electromagnetism,

astronomy, and fluid dynamics, because they can be used to accurately describe

the behavior of electric, gravitational, and fluid potentials. In the study of

heat conduction, the Laplace equation is the steady-state heat equation.

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