1. Occurrence and Derivation of Laplace's Equation. - 1. Situations in which Laplace's equation arises. - 2. Laplace's equation in orthogonal curvilinear co-ordinates. - 3. Laplace's equation in particular co-ordinate systems. - 2. The Method of Separation of Variables. - 1. Rectangular Cartesian co-ordinates. - 2. Temperature distribution in a rectangular metal block. - 3. The analogous electrostatic problem. - 4. Cylindrical polar co-ordinates. - 5. Spherical polar co-ordinates. - 3. Bessel Functions. - 1. An infinite series solution of Bessel's equation. - 2. Bessel functions of the second kind. - 3. Derivatives of Bessel functions and recurrence formulae. - 4. Modified Bessel functions. - 5. Behaviour of Bessel functions at zero and infinity. - 6. Series of zero order Bessel functions. - 4. Solutions using Cylindrical Polar Co-ordinates. - 1. Form of solutions of Laplace's equation. - 2. An infinite cylinder in a uniform field. - 3. A particular solid of revolution in a uniform field. - 4. Axi-symmetric temperature distributions in a cylinder. - 5. Legendre Polynomials. - 1. Solution in series of Legendre's equation. - 2. Associated Legendre functions. - 3. Derivatives and recurrence formulae for Legendre polynomials. - 4. Series of Legendre polynomials. - 6. Solutions using Spherical Polar Co-ordinates. - 1. Form of solutions of Laplace's equation. - 2. Sphere moving in a liquid at rest at infinity. - 3. A charged conducting sphere in a uniform electric field. - 4. Dielectric sphere in a uniform electric field. - 5. Axi-symmetric temperature distributions in a hollow sphere. - 6. Flow past a nearly spherical body. - 7. Sources sinks and doublets. - 8. Doublet in a fluid bounded by a sphere. - 9. Doublet in a cavity in a dielectric medium. Language: English