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

## D.R. Bland: Solutions of Laplace's Equation

Published $\text {1961}$, Routledge & Kegan Paul.

### 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