Degree Type

Dissertation

Date of Award

1939

Degree Name

Doctor of Philosophy

Department

Mathematics

Abstract

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.

DOI

https://doi.org/10.31274/rtd-180813-14158

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Arthur W. Davis

Language

en

Proquest ID

AAIDP11956

File Format

application/pdf

File Size

43 pages

Included in

Mathematics Commons

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