Foundations Of Potential Theory

Book Details:

• Author: Kellogg Oliver Dimon

• Publisher: Barman Press

• Binding: Paperback

• Format: Import

• Number of Pages: 396

• ISBN: 9780486601441

• Release Date: 15-03-2007

• Languages: English

• Package Dimensions: 8.5 x 5.3 x 0.8 inches

About the Book:

Potential Functions by Kellogg Oliver Dimon is an important work in the field of mathematics, particularly focused on the systematic treatment of potential functions. Originally based on two courses—one elementary and one advanced—that the author taught over ten years, this book serves a dual purpose. It is intended both as an introduction for students with knowledge of partial derivatives, multiple, and line integrals, and as a foundation for those looking to dive deeper into applications and contemporary literature on the subject.

This work stands out for its appeal to physical intuition and illustration, which is essential for grasping complex mathematical concepts. While the text includes physical applications, it does not compromise on rigor. The author provides carefully constructed proofs for key theorems, ensuring that students are equipped with both theoretical and practical knowledge. For instance, Chapter IV contains a proof for the divergence theorem (Gauss's theorem) and Green's theorem on the reduction of volume to surface integrals.

In Chapter XI, Dimon discusses the fundamental existence theorems and uses integral equations to address challenges related to discontinuity in the kernel. This chapter also provides insight into the latest developments regarding the Dirichlet problem, making it a valuable reference for advanced mathematicians and students alike.

The book includes exercises to reinforce the theory and extend the learning process. These exercises not only illustrate the concepts but also provide concrete numerical results, helping students solidify their understanding of the material. This edition, republished by Barman Press, brings a classic text back into circulation, making it affordable and accessible to a new generation of mathematicians and students.