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図書
図書
1. Initial value methods for boundary value problems : theory and application of invariant imbedding
Gunter H. Meyer
出版情報: New York : Academic Press, 1973  xiii, 220 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 100
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2.

図書
図書
2. Separation of variables for partial differential equations : an eigenfunction approach
George Cain, Gunter H. Meyer
出版情報: Boca Raton, FL : Chapman & Hall/CRC, c2006  xv, 281 p. ; 25 cm
シリーズ名: Studies in advanced mathematics
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目次情報: 続きを見る
Acknowledgments
Preface
Potential, Heat, and Wave Equation / 1：
Overview / 1.1：
Classification of second order equations / 1.2：
Laplace's and Poisson's equation / 1.3：
The heat equation / 1.4：
The wave equation / 1.5：
Basic Approximation Theory / 2：
Norms and inner products / 2.1：
Projection and best approximation / 2.2：
Important function spaces / 2.3：
Sturm-Liouville Problems / 3：
Sturm-Liouville problems for o" = [mu]o / 3.1：
Sturm-Liouville problems for [pound]o = [mu]o / 3.2：
A Sturm-Liouville problem with an interface / 3.3：
Fourier Series / 4：
Introduction / 4.1：
Convergence / 4.2：
Convergence of Fourier series / 4.3：
Cosine and sine series / 4.4：
Operations on Fourier series / 4.5：
Partial sums of the Fourier series and the Gibbs phenomenon / 4.6：
Eigenfunction Expansions for Equations in Two Independent Variables / 5：
One-Dimensional Diffusion Equation / 6：
Applications of the eigenfunction expansion method / 6.1：
How many terms of the series solution are enough? / Example 6.1：
Determination of an unknown diffusivity from measured data / Example 6.2：
Thermal waves / Example 6.3：
Matching a temperature history / Example 6.4：
Phase shift for a thermal wave / Example 6.5：
Dynamic determination of a convective heat transfer coefficient from measured data / Example 6.6：
Radial heat flow in a sphere / Example 6.7：
A boundary layer problem / Example 6.8：
The Black-Scholes equation / Example 6.9：
Radial heat flow in a disk / Example 6.10：
Heat flow in a composite slab / Example 6.11：
Reaction-diffusion with blowup / Example 6.12：
Convergence of u[subscript N](x, t) to the analytic solution / 6.2：
Influence of the boundary conditions and Duhamel's solution / 6.3：
One-Dimensional Wave Equation / 7：
A vibrating string with initial displacement / 7.1：
A vibrating string with initial velocity / Example 7.2：
A forced wave and resonance / Example 7.3：
Wave propagation in a resistive medium / Example 7.4：
Oscillations of a hanging chain / Example 7.5：
Symmetric pressure wave in a sphere / Example 7.6：
Controlling the shape of a wave / Example 7.7：
The natural frequencies of a uniform beam / Example 7.8：
A system of wave equations / Example 7.9：
Eigenfunction expansions and Duhamel's principle / 7.2：
Potential Problems in the Plane / 8：
The Dirichlet problem for the Laplacian on a rectangle / 8.1：
Preconditioning for general boundary data / Example 8.2：
Poisson's equation with Neumann boundary data / Example 8.3：
A discontinuous potential / Example 8.4：
Lubrication of a plane slider bearing / Example 8.5：
Lubrication of a step bearing / Example 8.6：
The Dirichlet problem on an L-shaped domain / Example 8.7：
Poisson's equation in polar coordinates / Example 8.8：
Steady-state heat flow around an insulated pipe I / Example 8.9：
Steady-state heat flow around an insulated pipe II / Example 8.10：
Poisson's equation on a triangle / Example 8.11：
Eigenvalue problem for the two-dimensional Laplacian / 8.2：
The eigenvalue problem for the Laplacian on a rectangle / Example 8.12：
The Green's function for the Laplacian on a square / Example 8.13：
The eigenvalue problem for the Laplacian on a disk / Example 8.14：
The eigenvalue problem for the Laplacian on the surface of a sphere / Example 8.15：
Convergence of u[subscript N](x, y) to the analytic solution / 8.3：
Multidimensional Problems / 9：
A diffusive pulse test / 9.1：
Standing waves on a circular membrane / Example 9.2：
The potential inside a charged sphere / Example 9.3：
Pressure in a porous slider bearing / Example 9.4：
The eigenvalue problem for the Laplacian in R[subscript 3] / 9.2：
An eigenvalue problem for quadrilaterals / Example 9.5：
An eigenvalue problem for the Laplacian in a cylinder / Example 9.6：
Periodic heat flow in a cylinder / Example 9.7：
An eigenvalue problem for the Laplacian in a sphere / Example 9.8：
The eigenvalue problem for Schrodinger's equation with a spherically symmetric potential well / Example 9.9：
Bibliography
Index
Acknowledgments
Preface
Potential, Heat, and Wave Equation / 1：
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