Book:D.R. Bland/Solutions of Laplace's Equation

Subject Matter

 * Laplace's Equation

Contents

 * Preface


 * 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