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]