Solutions of Laplace's Equation (Paperback)

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.