# 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

#### applications-harmonic-functions

By Juan Carlos Ponce Campuzano

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