Waves and Distributions

Höfundar: T Jonsson;J Yngvason; (Útgáfa: 0)
Waves and Distributions

Kaup valmöguleikar

This book begins with an introduction on continuum mechanics and a derivation of the linear partial differential equations for sound waves in fluids and elastic waves in solids. There is a brief chapter on the wave equations of electrodynamics. This is followed by a description of plane wave solutions and a discussion of concepts like reflection, refraction, polarization and the role of boundary conditions.

The second part of the book deals with the theory and applications of distributions and Fourier transforms. Furthermore, dispersion, the method of stationary phase, Kramers-Kronig relations and various examples including surface waves on liquids are discussed. This text is unique because it emphasizes the use of distributions to analyze the solutions of the wave equation. The treatment of continuum mechanics is self-contained, as well as the discussion on distributions and Fourier transforms.

Nánar um bókina

Útgefandi
World Scientific Publishing
ISBN
9789813104525
Print ISBN
9789810209742
Format
Page Fidelity (PDF)
Útgáfa
0
Höfundar
T Jonsson;J Yngvason;
Tungumál
English
Útgefið
05/09/1995
Prent takmörkun á líftíma
100
Prent takmörkun
2
Afritunar takmörkun
2

Kaflar

  • Contents
  • Preface
  • Chapter 1 Mechanics of Continua and Elastic Waves
  • 1.1 Kinematics of Continuous Media
  • 1.2 Elements of Fluid Mechanics
  • 1.2.1 Euler's Equation of Motion
  • 1.2.2 Bernoulli's Equation
  • 1.3 Linear Wave Equations for Fluids
  • 1.3.1 Linearization of the Equations of Motion
  • 1.3.2 General Remarks on Linearizations of Differential Equations
  • 1.4 The Equations of Motion for Continuous Media
  • 1.4.1 The Stress Tensor
  • 1.4.2 The General Equation of Motion and Conservation of Momentum
  • 1.4.3 The Stress-Momentum Tensor
  • 1.4.4 Conservation of Angular Momentum
  • 1.5 Stress and Strain
  • 1.5.1 The Strain Tensor
  • 1.5.2 Hooke's Law, Conservation of Energy
  • 1.5.3 Isotropic Elastic Media
  • 1.5.4 Simple Examples of Stress and Strain
  • 1.6 Elastic Waves in Isotropic Solids
  • 1.7 Exercises
  • Chapter 2 Maxwell's Equations and Electromagnetic Waves
  • 2.1 Maxwell's Equations
  • 2.2 Electromagnetic Waves
  • 2.3 The Electromagnetic Potentials
  • 2.4 Wave Equations for the Potentials
  • 2.5 Exercises
  • Chapter 3 Plane Waves
  • 3.1 General Plane Waves
  • 3.2 Harmonic Waves
  • 3.3 Polarization
  • 3.4 Boundary Conditions
  • 3.4.1 Sound Waves in Fluids
  • 3.4.2 Seismic Waves
  • 3.4.3 Electromagnetic Waves
  • 3.5 Reflection and Refraction of Sound Waves
  • 3.6 The Reflection of a p-Wave from a Free Surface
  • 3.7 Exercises
  • Chapter 4 Distributions and Fourier Analysis
  • 4.1 Introduction
  • 4.2 The Test Function Space D and Distributions
  • 4.3 Operations with Distributions
  • 4.3.1 Differentiation
  • 4.3.2 Support of Distributions
  • 4.3.3 Multiplication by C°°-Functions
  • 4.3.4 Change of Variables
  • 4.3.5 Tensor Product of Distributions
  • 4.3.6 Convolutions and Approximations by C∞-Functions
  • 4.4 The Test Function Space S and Tempered Distributions
  • 4.5 Fourier Analysis in S
  • 4.6 Fourier Analysis in S'
  • 4.7 Green Functions and Fundamental Solutions
  • • Elliptic operators.
  • • Hyperbolic or parabolic operators.
  • 4.8 Exercises
  • Chapter 5 Waves in Homogeneous Media
  • 5.1 Fundamental Solutions of the Wave Equation
  • 5.2 The General Solution of the Wave Equation
  • 5.3 The Initial Value Problem
  • 5.4 Huygens's Principle and Asgeirsson's Mean Value Theorem
  • 5.5 Spherical Waves
  • 5.6 Multipole Expansions
  • 5.6.1 The Helmholtz Equation
  • Spherical Harmonics
  • Spherical Bessel Functions
  • The General Solution to the Helmholtz Equation
  • 5.6.2 Multipoles
  • Asymptotic Behaviour
  • Multipole Moments
  • Point Multipoles
  • 5.7 Wave Propagation in Bounded Regions
  • 5.7.1 Cavity Waves
  • 5.7.2 Wave Guides
  • 5.7.3 Green Functions
  • The Method of Images
  • The Mode Expansion
  • 5.8 Exercises
  • Chapter 6 Dispersion
  • 6.1 Introduction
  • 6.2 Phase Velocity and Group Velocity
  • 6.3 Electromagnetic Waves in Dispersive Media
  • 6.3.1 The Equations of Kramers and Kronig
  • 6.3.2 Attenuation of Electromagnetic Waves
  • 6.3.3 A Model of a Dispersive Medium
  • 6.3.4 Progagation Speed of Electromagnetic Waves
  • 6.4 The Deformation and Dispersion of Wave Packets
  • 6.4.1 The Method of Stationary Phase
  • 6.4.2 The Dispersion of a Klein-Gordon Wave-Packet
  • 6.4.3 The Deformation of a Wave-Packet
  • 6.5 Waves on a Liquid Surface
  • 6.5.1 Gravity Waves
  • Liquid of Constant Depth
  • Shallow Liquid (Long Waves)
  • Deep Liquid (Short Waves)
  • 6.5.2 The Cauchy Problem
  • 6.5.3 The Motion of the Material Particles
  • 6.5.4 Surface Tension
  • 6.6 Exercises
  • Further Reading
  • Bibliography
  • Index