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Title:Solutions of Laplace's equation
Author(s): D. R. Bland
Walter Ledermann (ed.)
Publisher:New York : Dover
Size:96 p
Contents:Preface I 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 II The Method of Separati on 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 III Bessel Functions 1. An infinite ser ies 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 IV 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 V Lege ndre 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 VI Solutions using Spherical Polar Co-ordinates 1. Form of sol utions 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
Series:Library of mathematics
Keywords: Harmonic functions
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