Question

A function v is called a conjugate harmonic function u in w whenever​

Answer 1

Answer:

A function u in relation to v is called a conjugate harmonic function whenever uv is harmonic in nature.

Step-by-step explanation:

Harmonic functions seem often and play a essential role in math, physics and engineering.

A characteristic u(x,a) is referred to as harmonic if it's far two times constantly differentiable and satisfies the subsequent partial differential equation:

                                        ∇²u = uₓₓ + uₐₐ = 0.

This equation is referred to as Laplace’s equation. So a function is harmonic if it satisfies Laplace’s equation. The operator ∇² is referred to as the Laplacian and ∇²u is referred to as the Laplacian of u.

For a function u(x, a) and a vector field F(x,a) = (u,v), we have

1. grad u = ∇u = (uₓ,uₐ)
2. curl F = ∇ × F = (vₓ − uₐ)
3. div F = ∇ · F = uₓ + vₐ
4. div grad u = ∇ · ∇u = ∇²u = uₓₓ + uₐₐ
5. curl grad u = ∇ × ∇u = 0
6. div curl F = ∇ · ∇ × F = 0