Haberman was a standard text when I was studying the analytical solution of linear partial differential equations. In the main these are the heat, wave and Laplace equations. These equations form the backbone of much of older mathematical physics and appear in all manner of physical/engineering problems, e.g. electromagnetics, fluid mechanics, continuum mechanics, diffusion phenomena and so on.
In each case there is a basic introduction to the physical models needed to know how these equations are arrived at. This starts with the heat equation followed by the wave equation and then Laplace's equation. The analytical techniques studied include separation of variables in Cartesian, polar, cylindrical and spherical coordinates followed by work on the Sturm-Louiville equation, Fourier series, Eigenfunction expansions, Green's functions, Laplace and Fourier transforms. there is also a small section on numerical methods and the method of characteristics.
The character of explanation is at a high level, much work is done to make it possible for the student to understand the techniques in a deep sense, all steps are properly justified with a good degree of clarity. Although this text is now quite old and is no longer the preferred university text for many courses in say engineering mathematics or a second year course on an introduction to PDE's it nevertheless was the bedrock upon which all modern texts of this nature are based.
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