5 The Laplacian
The Laplacian of a function [maths rendering] is written as [maths rendering] and is defined as: Laplacian [maths rendering] = div grad [maths rendering] , that is
[maths rendering]The equation [maths rendering] , that is [maths rendering] is known as Laplace’s equation and has applications in many branches of engineering including Heat Flow, Electrical and Magnetic Fields and Fluid Mechanics.
Example 15
Find the Laplacian of [maths rendering] .
Solution
[maths rendering]