The Most Important Linear Partial Differential Equations of Physics

Abstract

Of all the partial differential equations we encountered last chapter, we will consider three in some detail because of their particular importance. These three equations are the wave equation

$$ (\frac{1}{{{{c}^{2}}}}\frac{{{{\partial }^{2}}}}{{\partial {{t}^{2}}}} - \Delta )u(t,r) = 0, $$

the heat conduction equation

$$ (\frac{\partial }{{\partial t}} - \lambda \Delta )u(t,r) = 0 $$

and Laplace’s equation

$$ \Delta u(r) = 0. $$

.