Introduction
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 largescale celestial bodies is more properly treated in a study of astrophysics, which is not included on this web site.
Resources:
Hard Copy:
• Potential Theory, specifically:
 Blakely, R., Potential Theory in Gravity and Magnetic Applications, Cambridge U. Press, Cambridge, 1995.
 Günter, N. M., Potential Theory and its Applications to Basic Problems of Mathematical Physics, F. Ungar, New York, 1967.
 Kellogg, O. D., Foundations of Potential Theory, F. Ungar Publishing, New York, 1929 (also in Dover reprint).
 MacMillan, W. D., The Theory of the Potential, Dover reprint, New York, 1958.
 Ramsey, A. S., Newtonian Attraction, Cambridge U. Press, Cambridge, 1981.
 Sigl, R., Introduction to Potential Theory, Abacus Press, Tunbridge Wells, Kent, UK, 1985.
 Sternberg, W. J. & T. L. Smith, The Theory of Potential and Spherical Harmonics, 2nd ed., U. of Toronto Press, Toronto, 1952.
 Wangerin, A., Theorie des Potentials und der Kugelfunktionen, 2 vols., Walter de Gruyter, Berlin, 1922.
• Related Mathematical Texts:
 Barton, G., Elements of Green's Functions and Propagation: Potentials, Diffusion and Waves, Oxford U. Press, Oxford, 1989.
 Bland, D. R., Solutions of Laplace's Equation, The Free Press, Glencoe, IL, 1961.
 Borisenko, A. I. & I. E. Tarapov, Vector and Tensor Analysis with Applications, Dover, New York, 1979.
 Byerly, W. E., An Elementary Treatise on Fourier Series and Spherical, Cylyndrical, and Ellipsoidal Harmonics with Applications to Problems in Mathematical Physics, Dover reprint, New York, 1893.
 Hobson, E. W., Spherical and Ellipsoidal Harmonics, Cambridge Univ. Press, Cambridge, 1931.
 Lebedev, N. N., Special Functions & Their Applications, Dover, New York, 1972.
 Lense, J., Kugelfunktionen, Akademische Verlagsgesellschaft, Leipzig, 1950.
 MacRobert, T. M., Spherical Harmonics, 3rd ed.,Pergamon Press, Oxford, 1967.
 Wangerin, A., Theorie des Potentials und der Kugelfunktionen, Walter de Gruyter, Berlin, 1922.
• Contents from Selected books:
Contents of Kellogg's Foundations of Potential Theory  Contents of MacMillan's Theory of the Potential 
 The Force of Gravity
 Fields of Force
 The Potential
 The Divergence Theorem
 Properties of Newtonian Potentials at Points of Free Space
 Properties of Newtonian Potentials at Points Occupied by Masses
 Potentials as Solutions of Laplace's Equation; Electrostatics
 Harmonic Functions
 Electric Images; Green's Functions
 Sequences of Harmonic Functions
 Fundamental Existence Theorems
 The Logarithmic Potential
  The Attraction of Finite Bodies
 The Newtonian Potential Function
 Vector Fields. Theorems of Green and Gauss
 The Attractions of Surfaces and Lines
 Surface Distributions of Matter
 TwoLayer Surfaces
 Spherical Harmonics
 Ellipsoidal Harmonics

Contents of MacRobert's Spherical Harmonics  Contents of Hobson's Spherical & Ellipsoidal Harmonics 
 Fourier Series
 Conduction of Heat
 Transverse Vibrations of Stretched Strings
 Spherical Harmonics: The Hypergeometric Function
 The Legendre Polynomials
 The Legendre Functions
 The Associated Legendre Functions of Integral Order
 Applications of Legendre Coefficients to Potential Theory
 Potentials of Spherical Shells, Spheres and Spheroids
 Applications to Electrostatics
 Ellipsoids of Revolution
 Eccentric Spheres
 Clerk Maxwell's Theory of Spherical Harmonics
 Bessel Functions
 Asymptotic Expansions and FourierBessel Expansions
 Application of Bessel Functions
 The Hypergeometric Function
 Associated Legendre Functions of General Order
  The Transformation of Laplace's Equation
 The Solution of Laplace's Equation in Polar Coordinates
 The Legendre's Associated Functions
 Spherical Harmonics
 Spherical Harmonics of General Type
 Approximate Values of the Generalized Legendre's Functions
 Representation of Functions by Series
 The Addition Theorems for General Legendre's Functions
 The Zeros of Legendre's Functions and Associated Functions
 Harmonics for Spaces Bounded by Surfaces of Revolution
 Ellipsoidal Harmonics
