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.

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

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

Joukowsky airfoil

By Juan Carlos Ponce Campuzano

Independent Mathematics Educator