An introductory treatment of electrostatics usually begins with Coulomb's law, the concepts of charge, the electric field and energy stored in the field, potential, capacitance, and so on. Poisson's and Laplace's equations soon appear.
Unfortunately, almost no real world problem can be solved in closed form using the latter equations. The most basic of electrostatic device analysis, the electric fields surrounding and the capacitance of a simple parallel plate capacitor, cannot be found.
Typically, a few interesting solution techniques, such as the separation of variables, are presented. Then the author has to choose a path. Other solution techniques such as conformal mapping can be shown; if the book is to be more than an introductory text, more formal materials such as Greene's functions can be introduced. In any case, the practitioner with real world geometries to be analyzed has been abandoned.
A book about numerical analysis techniques typically presents just that – numerical analysis techniques. The few examples presented are usually based as much on the ease of their presentation as on their ultimate usefulness.
My goal in writing this book is to present enough basic electrostatic theory as necessary to get into real world problems, then to present several of the available numerical techniques that are applicable to these problems, and finally to present numerous, detailed, examples showing how these techniques are applied. In other words, I am presenting ...