Foundations of Potential Theory

1. Front Matter

   Pages I-IX

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2. The Force of Gravity

   • Oliver Dimon Kellogg

   Pages 1-28

3. Fields of Force

   • Oliver Dimon Kellogg

   Pages 28-48

4. The Potential

   • Oliver Dimon Kellogg

   Pages 48-84

5. The Divergence Theorem

   • Oliver Dimon Kellogg

   Pages 84-121

6. Properties of Newtonian Potentials at Points of Free Space

   • Oliver Dimon Kellogg

   Pages 121-146

7. Properties of Newtonian Potentials at Points Occupied by Masses

   • Oliver Dimon Kellogg

   Pages 146-175

8. Potentials as Solutions of Laplace’s Equation; Electrostatics

   • Oliver Dimon Kellogg

   Pages 175-211

9. Harmonic Functions

   • Oliver Dimon Kellogg

   Pages 211-228

10. Electric Images; Green’s Function

    • Oliver Dimon Kellogg

    Pages 228-248

11. Sequences of Harmonic Functions

    • Oliver Dimon Kellogg

    Pages 248-277

12. Fundamental Existence Theorems

    • Oliver Dimon Kellogg

    Pages 277-338

13. The Logarithmic Potential

    • Oliver Dimon Kellogg

    Pages 338-376

14. Back Matter

    Pages 377-386

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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. It is inherent in the nature of the subject that physical intuition and illustration be appealed to freely, and this has been done. However, that the book may present sound ideals to the student, and in order also serve the mathematician, both for purposes of reference and as a basis for further developments, the proofs have been given by rigorous methods. This has led, at a number of points, to results either not found elsewhere, or not readily accessible. Thus, Chapter IV contains a proof for the general regular region of the divergence theorem (Gauss', or Green's theorem) on the reduction of volume to surface integrals. The treatment of the fundamental existence theorems in Chapter XI by means of integral equations meets squarely the difficulties incident to ·the discontinuity of the kernel, and the same chapter gives an account of the most recent developments with respect to the Dirichlet problem.

• Fourier series
• Green's theorem
• Microsoft Access
• Potential
• Potential theory
• Potentialtheorie
• Vector field
• boundary value problem
• derivative
• development
• differential equation
• eXist
• electrostatics
• proof
• solution

• Harvard University, Cambridge, USA

  Oliver Dimon Kellogg

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