Kellogg O.D. Foundations of Potential Theory

Springer-Verlag Berlin Heidelberg, 1929 — 384p. — (Grundlehren der mathematischen Wissenschaften 31) — ISBN: 978-3-642-90850-7 (eBook), 978-3-642-88995-0 (Softcover).The present volume gives a systematic treatment of potential functions. It takes its origin in two courses, one elementary and one advanced, which the author has given at intervals during the last ten years, and has a two-fold purpose: first, to serve as an introduction for students whose attainments in the Calculus include some knowledge of partial derivatives and multiple and line integrals; and secondly, to provide the reader with the fundamentals of the subject, so that he may proceed immediately to the applications, or to the periodical literature of the day.The Force of Gravity
Fields of Force
The Potential
The Divergence Theorem
Properties of Newtonian Potentials at Points of Free Space
Properties of Newtonian Potentials at Points Occupied by Masses
Potentials as Solutions of Laplace’s Equation; Electrostatics
Harmonic Functions
Electric Images; Green’s Function
Sequences of Harmonic Functions
Fundamental Existence Theorems
The Logarithmic Potential