Potential Theory is a branch of theoretical physics that deals with phenomena having to do with attraction or the distribution of physical effects through space. It has additionally grown to be a lucrative branch of Mathematics as well, but the context of the information available on this page is confined to a physical interpretation involving the discussion of mutual Newtonian Attraction, i.e., gravitational attraction. Many other interesting applications of potential theory can be made in the areas of electromagnetism, heat propagation and nuclear physics.

The content found on this page largely deals with the classical theory involved. Potential theory is applied in studies of the gravitational attractions of the Earth and other terrestrial planetary bodies. Physical geodesy, a subdiscipline of geophysics, relies heavily on concepts arising in potential theory. The gravitational attraction of stars, galaxies and other large-scale celestial bodies is more properly treated in a study of astrophysics, which is not included on this web site.


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Potential Theory, specifically:

• Related Mathematical Texts:

• Contents from Selected books:

Contents of Kellogg's Foundations of Potential Theory
Contents of MacMillan's Theory of the Potential
  1. The Force of Gravity
  2. Fields of Force
  3. The Potential
  4. The Divergence Theorem
  5. Properties of Newtonian Potentials at Points of Free Space
  6. Properties of Newtonian Potentials at Points Occupied by Masses
  7. Potentials as Solutions of Laplace's Equation; Electrostatics
  8. Harmonic Functions
  9. Electric Images; Green's Functions
  10. Sequences of Harmonic Functions
  11. Fundamental Existence Theorems
  12. The Logarithmic Potential
  1. The Attraction of Finite Bodies
  2. The Newtonian Potential Function
  3. Vector Fields. Theorems of Green and Gauss
  4. The Attractions of Surfaces and Lines
  5. Surface Distributions of Matter
  6. Two-Layer Surfaces
  7. Spherical Harmonics
  8. Ellipsoidal Harmonics

Contents of MacRobert's Spherical Harmonics
Contents of Hobson's Spherical & Ellipsoidal Harmonics
  1. Fourier Series
  2. Conduction of Heat
  3. Transverse Vibrations of Stretched Strings
  4. Spherical Harmonics: The Hypergeometric Function
  5. The Legendre Polynomials
  6. The Legendre Functions
  7. The Associated Legendre Functions of Integral Order
  8. Applications of Legendre Coefficients to Potential Theory
  9. Potentials of Spherical Shells, Spheres and Spheroids
  10. Applications to Electrostatics
  11. Ellipsoids of Revolution
  12. Eccentric Spheres
  13. Clerk Maxwell's Theory of Spherical Harmonics
  14. Bessel Functions
  15. Asymptotic Expansions and Fourier-Bessel Expansions
  16. Application of Bessel Functions
  17. The Hypergeometric Function
  18. Associated Legendre Functions of General Order
  1. The Transformation of Laplace's Equation
  2. The Solution of Laplace's Equation in Polar Coordinates
  3. The Legendre's Associated Functions
  4. Spherical Harmonics
  5. Spherical Harmonics of General Type
  6. Approximate Values of the Generalized Legendre's Functions
  7. Representation of Functions by Series
  8. The Addition Theorems for General Legendre's Functions
  9. The Zeros of Legendre's Functions and Associated Functions
  10. Harmonics for Spaces Bounded by Surfaces of Revolution
  11. Ellipsoidal Harmonics