Use of index or tensor notation in mathematical analysis of the equations that govern continuum mechanics.
Separation of Variables
Employing separation of variables to the solution of classical (heat, Laplace, and wave equations) PDE's.
Transforms and Series
Applying Fourier transforms and series to the solution of PDE's and analysis of data.
Applying the principle of superposition to PDE's with nonhomogeneities.
Cartesian and Cylindrical Coordinates
Solution of PDE's in Cartesian and Cylindrical coordinates.