Laplace’s equation A classical equation of mathematics is Laplace’s equation, which arises in both theory and applications. It governs ideal fluid flow, electrostatic potentials, and the steady-state distribution of heat in a conducting medium. In two dimensions, Laplace’s equation is
Show that the following functions are harmonic; that is, they satisfy Laplace’s equation.
82. u(x, y) = eax cos ay, for any real number a
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