Higher-Dimensional Boundary-Value Problems
The treatment of problems in more than two space variables is much more involved than problems in two space variables. Here a number of multidimensional problems involving the Laplace equation, wave and heat equations with various boundary conditions will be presented. Included are the Dirichlet problem for a cube, for a cylinder and for a sphere, wave and heat equations in three dimensional rectangular, cylindrical polar and spherical polar coordinates. The solution of the three-dimensional Schrödinger equation in a central field with applications to hydrogen and helium atoms is discussed. We also consider the forced vibration of a rectangular membrane described by the three-dimensional, nonhomogeneous wave equation with moving boundaries.
KeywordsDirichlet Problem Laplace Equation Homogeneous Boundary Condition Double Fourier Series Rectangular Membrane
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