Originally published in 1957, this book was written to provide physicists and engineers with a means of solving partial differential equations subject to boundary conditions. The text gives a systematic and unified approach to a wide class of problems, based on the fact that the solution may be viewed as a point in function-space, this point being the intersection of two linear subspaces orthogonal to one another. Using this method the solution is located on a hypercircle in function-space, and the approximation is improved by reducing the radius of the hypercircle. The complexities of calculation are illuminated throughout by simple, intuitive geometrical pictures. This book will be of value to anyone with an interest in solutions to boundary value problems in mathematical physics.
Contents
Preface; Introduction; Part I. No Metric: 1. Geometry of function-space without a metric; Part II. Positive-Definite Metric: 2. Geometry of function-space with positive-definite metric; 3. The dirichlet problem for a finite domain in the Euclidean plane; 4. The torsion problem; 5. Various boundary value problems; Part III. Indefinite Metric: 6. Geometry of function-space with indefinite metric; 7. Vibration problems; Note A. The torsion of a hollow square; Note B. The Green's tensor or fundamental solution for the equilibrium of an anistropic elastic body; Bibliography; Index.
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