Author | Bland, D. R. author |
---|---|
Title | Solutions of Laplace's Equation [electronic resource] / by D. R. Bland |
Imprint | Dordrecht : Springer Netherlands, 1961 |
Connect to | http://dx.doi.org/10.1007/978-94-011-7694-1 |
Descript | VIII, 98 p. online resource |
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