Berlin: Julius Springer, 1929. 8vo. xi, [i], 384 pp., plus leaf of publisher’s advertisements. FIRST EDITION. With 30 text figures. Original publisher’s yellow cloth, a bit rubbed; ownership signature dated London, 1930 on fly-leaf. A very good copy. Item #2590
First edition. Kellogg was a professor of mathematics known for his work on potential theory. His work here presents a very good overview of the study of harmonic functions, or potential theory. It includes much of the past development of the theory of partial differential equations and its applications to “classical” mathematical physics and is most important in its relations to functions of a complex variable, but also continues to introduce readers to new issues (of the time) in mathematical problems. Chapters include the force of gravity; fields of force; the divergence theorem; properties of Newtonian potentials at points of free space and at points occupied by masses; potentials as solutions of Laplace’s equation, electrostatics; harmonic functions; fundamental existence theorems; and the logarithmic potential, among others. The final section is devoted to the explicit formulas required for the mapping of polygons.
Kellogg (1878-1932) was known among mathematicians for his skillful and clear expositions, as well as for his original contributions and scholarship. The exposition here is reinforced by a number of important exercises, some of them given for the sake of review and drill, but many also in order to present interesting facts and illustrations. The work is unusually rich in scholarly bibliographical data.