Foundations of Potential Theory by Oliver Dimon Kellogg, published in 1929, is a systematic treatment of potential functions. It serves as an introduction for students with knowledge of partial derivatives and integrals, and provides the fundamentals for further study or application. The book emphasizes physical intuition and illustration, while also presenting rigorous proofs to ensure sound mathematical ideals for both students and mathematicians. It includes exercises to reinforce understanding and covers topics such as fields of force, potentials, the divergence theorem, Newtonian potentials, harmonic functions, electric images, and fundamental existence theorems. The text also discusses the Dirichlet and Neumann problems, integral equations, and the properties of potentials in various contexts. The book is structured into chapters that explore the mathematical foundations of potential theory, including its applications in electrostatics, heat flow, and fluid dynamics. It includes detailed discussions on the logarithmic potential, its relation to Newtonian potentials, and the use of Green's function in solving boundary value problems. The work is a comprehensive resource for understanding the theoretical and practical aspects of potential theory.Foundations of Potential Theory by Oliver Dimon Kellogg, published in 1929, is a systematic treatment of potential functions. It serves as an introduction for students with knowledge of partial derivatives and integrals, and provides the fundamentals for further study or application. The book emphasizes physical intuition and illustration, while also presenting rigorous proofs to ensure sound mathematical ideals for both students and mathematicians. It includes exercises to reinforce understanding and covers topics such as fields of force, potentials, the divergence theorem, Newtonian potentials, harmonic functions, electric images, and fundamental existence theorems. The text also discusses the Dirichlet and Neumann problems, integral equations, and the properties of potentials in various contexts. The book is structured into chapters that explore the mathematical foundations of potential theory, including its applications in electrostatics, heat flow, and fluid dynamics. It includes detailed discussions on the logarithmic potential, its relation to Newtonian potentials, and the use of Green's function in solving boundary value problems. The work is a comprehensive resource for understanding the theoretical and practical aspects of potential theory.