Oliver Dimon Kellogg was an American mathematician recognized for his significant contributions to potential theory. This field formed the basis of his doctoral research and his seminal 1929 textbook. In collaboration with George David Birkhoff, he extended the Brouwer fixed-point theorem, leading to the development of the Birkhoff–Kellogg theorem.
Introduction to fundamentals of potential functions covers the force of gravity, fields of force, potentials, harmonic functions, electric images and Green's function, sequences of harmonic functions, fundamental existence theorems, the logarithmic potential, and much more. Detailed proofs rigorously worked out. 1929 edition.
A classic text on the applications of calculus to mechanics, this book presents the fundamental principles of classical physics and their mathematical expressions in a clear and comprehensive manner. With numerous examples and exercises, it offers a rigorous and intuitive introduction to the calculus of variations and the dynamics of particles and systems, and provides a solid foundation for further study in physics, engineering, and related fields.