| Solutions, in the form H/r, of the homogeneous linear partial differential equation of the second order with constant coefficients are used as generalized potential functions. With the aid of generalized Green's theorems and the methods developed by Erhardt Schmidt, it is possible to obtain the breaks in the derivatives of the generalized potentials due to a volume, simple surface and double surface distribution.; When the functions involved satisfy certain differetiability and continuity conditions, it is shown that the breaks in the (n + 1)st order derivatives of these generalized potentials are given by recursion. For example, the breaks in the (n + 1)st order derivatives of the generalized volume potential are obtained from the breaks in the nth order derivatives of potential due to a volume and simple surface distribution. Similar relations are shown to exist for the breaks in the (n + 1)st order derivatives of the generalized potential due to simple surface and double surface distribution.; In chapter IV the theory has been applied to two problems and the breaks in the potentials and their first and second order derivatives have been found for the case of the x3 axis parallel to the normal at the point. |
