Applications

Harmonic functions & Conformal mapping

Heat conduction

Physical laws tells us that if a two-dimensional region is maintained at a steady state temperature \(T,\) then \(T\) should be harmonic.

Electrostatics

If an electric potential \(\phi\) is determined by static eletric charges, \(\phi\) must satisfy Laplace's equation. 

Hydrodynamics

If we have a (steady-sate) incompressible, nonviscous fluid, we are interested in finding its velocity field: \(\mathbf V(x,y)\)

Hydrodynamics

Joukowsky airfoil

🔗 Source

applications-harmonic-functions

By Juan Carlos Ponce Campuzano