What is the Laplace equation?
Understand the Problem
The question is asking for a definition or explanation of the Laplace equation, which is a fundamental equation in the field of mathematics and physics, particularly in the study of differential equations and potential theory.
Answer
The Laplace equation is ∇²u = 0.
The Laplace equation is a second-order partial differential equation written as ∇²u = 0.
Answer for screen readers
The Laplace equation is a second-order partial differential equation written as ∇²u = 0.
More Information
Laplace's equation is significant in many fields of science and engineering, particularly in problems of electrostatics, gravity, and fluid dynamics, where it describes the behavior of potentials.
Tips
A common mistake is confusing Laplace's equation with Poisson's equation, which has a similar form but includes a source term.
Sources
- Laplace's equation - Wikipedia - en.wikipedia.org
- Laplace's equation | Definition, Uses, & Facts - Britannica - britannica.com
- 9.7: The Laplace Equation - Mathematics LibreTexts - math.libretexts.org
Thank you for voting!
