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

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

Published $1961$, **Routledge & Kegan Paul**.

### Subject Matter

### 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*

- 1.

- 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*

- 1.

- 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*

- 1.

- 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*

- 1.

- 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*

- 1.

- 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*

- 1.