Synopses & Reviews
Focusing on applications rather than theory, this book examines the theory of Fourier transforms and related topics. Suitable for students and researchers interested in the boundary value problems of physics and engineering, its accessible treatment assumes no specialized knowledge of physics; however, a background in advanced calculus is assumed. 1951 edition.
Synopsis
Text presents theory of Fourier transforms and related topics applicable to boundary value problems of physics and engineering.
Synopsis
Focusing on applications rather than theory, this book examines the theory of Fourier transforms and related topics. Suitable for students and researchers interested in the boundary value problems of physics and engineering, its accessible treatment assumes no specialized knowledge of physics; however, a background in advanced calculus is assumed. 1951 edition.
Table of Contents
Preface
Chapter 1. Fourier Transforms
Integral transforms. Fourier kernels. Fourier's integral theorem. Laplace transform. Foundations of operator calculus. Mellin transform. Multiple Fourier transforms
Chapter 2. Hankel Transforms
Hankel inversion theorem. Parseval's theorem for Hankel transforms. Hankel transforms of the derivatives of a function.
Relation between Hankel transforms and Fourier transforms. Dual integral equations
Chapter 3. Finite Transforms
Finite Fourier transforms. Finite Hankel transforms
Chapter 4. The Theory of Vibrations
Electrical oscillations in simple circuits. Transverse vibrations of a continuous string. Oscillations of a heavy chain. Transverse oscillations of an elastic beam.
Transverse vibrations of a thin membrane. Vibrations of a thin elastic plate. Elastic vibrations of thick cylinders and spheres
Chapter 5. The Conduction of Heat in Solids
General theory. Conduction of heat when there are no sources present. Two- and three-dimensional boundary value problems. Diffusion of heat in a solid medium which is generating heat
Chapter 6. The Slowing Down of Neutrons in Matter
Fundamental equations. Age theory. Diffusion of thermal neutrons with sources given by the age theory. Exact solutions of the transport equation
Chapter 7. Hydrodynamic Problems
Hydrodynamic equations. Irrotational flow of a perfect fluid. Surface waves. Slow motion of a viscous fluid. Motion of a viscous fluid contained between two infinite coaxial cylinders.
Motion of a viscous fluid under a surface load. Harmonic analysis of nonlinear viscous flow
Chapter 8. Applications to Atomic and Nuclear Physics
Theory of radioactive transformations. Van der Waals attraction between spherical particles. Interaction of radiation with an electron. Cascade theory of cosmic ray showers.
Distribution of momentum in atomic and molecular systems. Binding energies of the lightest nuclei
Chapter 9. Two-Dimensional Stress Systems
Equations of motion. Infinite elastic solid with body forces. Application of pressure to the surfaces of a two-dimensional elastic solid.
Distribution of stress due to a force in the interior of a semiinfinite elastic medium. Distribution of stress in the neighborhood of a Griffith crack.
Indentation problems. Two-dimensional problems in polar coordinates. Dynamical problems
Chapter 10. Axially Symmetrical Stress Distributions
Equations of equilibrium. Stresses produced by the indentation of the plane surface of a semiinfinite elastic medium by a rigid punch. Application of pressure to the faces of a thick plate.
Distribution of stress in the neighborhood of a circular crack in an elastic body. Distribution of stress in a semiinfinite elastic medium due to a torsional displacement of the surface.
Stress distribution in a long circular cylinder when a discontinuous pressure is applied to the curved surface
Appendix A. Some Properties of Besell Functions
Bessel's differential equation. Recurrence relations for Bessel functions of the first kind. Definite integrals involving Bessel functions. Infinite integrals involving Bessel functions.
Relation between the Bessel functions and circular functions. Integral expression for the Bessel function J subscript n (x)
Appendix B. Approximate Methods of Calculating Integral Transforms
Method of steepest descents for contour integrals. Numerical calculations of Fourier integrals
Appendix C. Tables of Integral Transforms
Fourier transforms. Fourier cosine transforms. Fourier sine transforms. Laplace transforms. Mellin transforms. Hankel transforms.
Finite Fourier cosine transforms. Finite Fourier sine transforms. Finite Hankel transforms
Index