Spherical harmonics and tensors for classical field theory

the long version

Presents the theory of spherical harmonics in a form suitable for the analysis of non-separable, nonlinear, partial differential equations, defined in a spherical or infinite domain. Describes and develops those aspects of group theory that are relevant to classical field theory. Each harmonic is labeled by a particular irreducible representation of the three-dimensional rotation group. Shows how to apply tensor harmonic techniques to all branches of classical field theory, including fluid mechanics, electromagnetism, geophysics and the atmospheric sciences.