Boundary Value Problems/Main PDE's to be addressed in course

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Heat Equation

$u_t-{\alpha }^2{\mathrm{\nabla }}^{2}u=F$

Poisson's Equation

${\mathrm{\nabla }}^{2}u=F$

The Wave Equation

$u_{tt}-c^2{\mathrm{\nabla }}^{2}u=F$

Maxwell's Equations

$div(E)=4\pi \rho$

$curl(E)+\frac{1}{c}\frac{\partial B}{\partial t}=0$

$curl(B)-\frac{1}{c}\frac{\partial E}{\partial t}=\frac{4\pi }{c}J$

$div(B)=0$