Coverart for item
The Resource Mathematics of wave propagation, Julian L. Davis

Mathematics of wave propagation, Julian L. Davis

Label
Mathematics of wave propagation
Title
Mathematics of wave propagation
Statement of responsibility
Julian L. Davis
Creator
Subject
Genre
Language
eng
Cataloging source
JSTOR
http://library.link/vocab/creatorName
Davis, Julian L
Illustrations
illustrations
Index
index present
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/subjectName
  • Welle, ..
  • Wave-motion, Theory of
  • Théorie du mouvement ondulatoire
  • MATHEMATICS / Applied
  • Wave-motion, Theory of
  • Mathematische Physik
  • Wellenausbreitung
  • WAVES
  • WAVE PROPAGATION
  • DIFFERENTIAL EQUATIONS
  • WAVE EQUATIONS
  • VISCOUS FLUIDS
  • Welle
Label
Mathematics of wave propagation, Julian L. Davis
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 389-390) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 5
  • 125
  • Reduced Wave Equation in Two Dimensions
  • 126
  • Eigenvalues Must Be Negative
  • 127
  • Rectangular Membrane
  • 127
  • Circular Membrane
  • 131
  • Three-Dimensional Wave Equation
  • Wave Equation for a Bar
  • 135
  • Chapter 4
  • Wave Propagation in Fluids
  • 145
  • Part I
  • Inviscid Fluids
  • 145
  • Lagrangian Representation of One-Dimensional Compressible Gas Flow
  • 146
  • Eulerian Representation of a One-Dimensional Gas
  • 5
  • 149
  • Solution by the Method of Characteristics: One-Dimensional Compressible Gas
  • 151
  • Two-Dimensional Steady Flow
  • 157
  • Bernoulli's Law
  • 159
  • Method of Characteristics Applied to Two-Dimensional Steady Flow
  • 161
  • Supersonic Velocity Potential
  • Transverse Oscillations of a String
  • 163
  • Hodograph Transformation
  • 163
  • Shock Wave Phenomena
  • 169
  • Part II
  • Viscous Fluids
  • 183
  • Elementary Discussion of Viscosity
  • 183
  • 9
  • Conservation Laws
  • 185
  • Boundary Conditions and Boundary Layer
  • 190
  • Energ Dissipation in a Viscous Fluid
  • 191
  • Wave Propagation in a Viscous Fluid
  • 193
  • Oscillating Body of Arbitrary Shape
  • 196
  • Speed of a Transverse Wave in a Siting
  • Similarity Considerations and Dimensionless Parameters; Reynolds'Law
  • 197
  • Poiseuille Flow
  • 199
  • Stokes'Flow
  • 201
  • Oseen Approximation
  • 208
  • Chapter 5
  • Stress Waves in Elastic Solids
  • 10
  • 213
  • Fundamentals of Elasticity
  • 214
  • Equations of Motion for the Stress
  • 223
  • Navier Equations of Motion for the Displacement
  • 224
  • Propagation of Plane Elastic Waves
  • 227
  • General Decomposition of Elastic Waves
  • Traveling Waves in General
  • 228
  • Characteristic Surfaces for Planar Waves
  • 229
  • Time-Harmonic Solutions and Reduced Wave Equations
  • 230
  • Spherically Symmetric Waves
  • 232
  • Longitudinal Waves in a Bar
  • 234
  • Curvilinear Orthogonal Coordinates
  • 11
  • 237
  • Navier Equations in Cylindrical Coordinates
  • 239
  • Radially Symmetric Waves
  • 240
  • Waves Propagated Over the Surface of an Elastic Body
  • 243
  • Chapter 6
  • Stress Waves in Viscoelastic Solids
  • 250
  • Sound Wave Propagation in a Tube
  • Internal Ftiction
  • 251
  • Discrete Viscoelastic Models
  • 252
  • Continuous Marwell Model
  • 260
  • Continuous Voigt Model
  • 263
  • Three-Dimensional VE Constitutive Equations
  • 264
  • Chapter 1
  • 16
  • Equations of Motion for a VE Material
  • 265
  • One-Dimensional Wave Propagation in VE Media
  • 266
  • Radially Symmetric Waves for a VE Bar
  • 270
  • ElectromechanicalAnalogy
  • 271
  • Chapter 7
  • Wave Propagation in Thermoelastic Media
  • Superposition Principle
  • 282
  • Duhamel-Neumann Law
  • 282
  • Equations of Motion
  • 285
  • Plane Harmonic Waves
  • 287
  • Three-Dimensional Thermal Waves; Generalized Navier Equation
  • 293
  • Chapter 8
  • 19
  • Water Waves
  • 297
  • Irrotational, Incompressible, Inviscid Flow; Velocity Potential and Equipotential Surfaces
  • 297
  • Euler's Equations
  • 299
  • Two-Dimensional Fluid Flow
  • 300
  • Complec Variable Treatment
  • 302
  • Sinusoidal Waves
  • Vortex Motion
  • 309
  • Small-Amplitude Gravity Waves
  • 311
  • Water Waves in a Straight Canal
  • 311
  • Kinematics of the Free Surface
  • 316
  • Vertical Acceleration
  • 317
  • 19
  • Standing Waves
  • 319
  • Two-Dimensional Waves of Finite Depth
  • 321
  • Boundary Conditions
  • 322
  • Formulation of a Typical Surface Wave Problem
  • 324
  • Example of Instability
  • 325
  • Interference Phenomena
  • Approximation Aeories
  • 327
  • Tidal Waves
  • 337
  • Chapter 9
  • Variational Methods in Wave Propagation
  • 344
  • Introduction; Fermat's PKnciple
  • 344
  • Calculus of Variations; Euler's Equation
  • 21
  • 345
  • Configuration Space
  • 349
  • Cnetic and Potential Eneigies
  • 350
  • Hamilton's Variational Principle
  • 350
  • PKnciple of Virtual Work
  • 352
  • Transformation to Generalized Coordinates
  • Reflection of Light Waves
  • 354
  • Rayleigh's Dissipation Function
  • 357
  • Hamilton's Equations of Motion
  • 359
  • Cyclic Coordinates
  • 362
  • Hamilton-Jacobi Theory
  • 364
  • Extension of W to 2 n Degrees of Freedom
  • 25
  • 370
  • H-J Aeory and Wave P[similar]vpagation
  • 372
  • Quantum Mechanics
  • 376
  • An Analog between Geometric Optics and Classical Mechanics
  • 377
  • Asymptotic Theory of Wave Propagation
  • 380
  • Appendix
  • Reflection of Waves in a String
  • Principle of Least Action
  • 384
  • Physics of Propagating Waves
  • 27
  • Sound Waves
  • 29
  • Doppler Effect
  • 33
  • Dispersion and Group Velocity
  • 36
  • Chapter 2
  • Partial Differential Equations of Wave Propagation
  • 41
  • 3
  • Types of Partial Differential Equations
  • 41
  • Geometric Nature of the PDEs of Wave Phenomena
  • 42
  • Directional Derivatives
  • 42
  • Cauchy Initial Value Problem
  • 44
  • Parametric Representation
  • 49
  • Discrete Wave-Propagating Systems
  • Wave Equation Equivalent to Two First-Order PDEs
  • 51
  • Characteristic Equations for First-Order PDEs
  • 55
  • General Treatment of Linear PDEs by Characteristic Theory
  • 57
  • Another Method of Characteristics for Second-Order PDEs
  • 61
  • Geometric Interpretation of Quasilinear PDEs
  • 63
  • 3
  • Integral Surfaces
  • 65
  • Nonlinear Case
  • 67
  • Canonical Form of a Second-Order PDE
  • 70
  • Riemann's Method of Integration
  • 73
  • Chapter 3
  • Wave Equation
  • Approximation of Stress Wave Propagation in a Bar by a Finite System of Mass-Spring Models
  • 85
  • Part I
  • One-Dimensional Wave Equation
  • 85
  • Factorization of the Wave Equation and Characteristic Curves
  • 85
  • Vibrating String as a Combined IV and B V Problem
  • 90
  • D'Alembert's Solution to the IV Problem
  • 97
  • 4
  • Domain of Dependence and Range of Influence
  • 101
  • Cauchy IV Problem Revisited
  • 102
  • Solution of Wave Propagation Problems by Laplace Transforms
  • 105
  • Laplace Transforms
  • 108
  • Applications to the Wave Equation
  • 111
  • Limiting Form of a Continuous Bar
  • Nonhomogeneous Wave Equation
  • 116
  • Wave Propagation through Media with Different Velocities
  • 120
  • Electrical Transmission Line
  • 122
  • Part II
  • Wave Equation in two and Three Dimensions
  • 125
  • Two-Dimensional Wave Equation
Control code
on1231563353
Dimensions
unknown
Extent
1 online resource (xv, 395 pages)
File format
unknown
Form of item
online
Isbn
9780691223377
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
22573/ctv1826hdk
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)1231563353
Label
Mathematics of wave propagation, Julian L. Davis
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references (pages 389-390) and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 5
  • 125
  • Reduced Wave Equation in Two Dimensions
  • 126
  • Eigenvalues Must Be Negative
  • 127
  • Rectangular Membrane
  • 127
  • Circular Membrane
  • 131
  • Three-Dimensional Wave Equation
  • Wave Equation for a Bar
  • 135
  • Chapter 4
  • Wave Propagation in Fluids
  • 145
  • Part I
  • Inviscid Fluids
  • 145
  • Lagrangian Representation of One-Dimensional Compressible Gas Flow
  • 146
  • Eulerian Representation of a One-Dimensional Gas
  • 5
  • 149
  • Solution by the Method of Characteristics: One-Dimensional Compressible Gas
  • 151
  • Two-Dimensional Steady Flow
  • 157
  • Bernoulli's Law
  • 159
  • Method of Characteristics Applied to Two-Dimensional Steady Flow
  • 161
  • Supersonic Velocity Potential
  • Transverse Oscillations of a String
  • 163
  • Hodograph Transformation
  • 163
  • Shock Wave Phenomena
  • 169
  • Part II
  • Viscous Fluids
  • 183
  • Elementary Discussion of Viscosity
  • 183
  • 9
  • Conservation Laws
  • 185
  • Boundary Conditions and Boundary Layer
  • 190
  • Energ Dissipation in a Viscous Fluid
  • 191
  • Wave Propagation in a Viscous Fluid
  • 193
  • Oscillating Body of Arbitrary Shape
  • 196
  • Speed of a Transverse Wave in a Siting
  • Similarity Considerations and Dimensionless Parameters; Reynolds'Law
  • 197
  • Poiseuille Flow
  • 199
  • Stokes'Flow
  • 201
  • Oseen Approximation
  • 208
  • Chapter 5
  • Stress Waves in Elastic Solids
  • 10
  • 213
  • Fundamentals of Elasticity
  • 214
  • Equations of Motion for the Stress
  • 223
  • Navier Equations of Motion for the Displacement
  • 224
  • Propagation of Plane Elastic Waves
  • 227
  • General Decomposition of Elastic Waves
  • Traveling Waves in General
  • 228
  • Characteristic Surfaces for Planar Waves
  • 229
  • Time-Harmonic Solutions and Reduced Wave Equations
  • 230
  • Spherically Symmetric Waves
  • 232
  • Longitudinal Waves in a Bar
  • 234
  • Curvilinear Orthogonal Coordinates
  • 11
  • 237
  • Navier Equations in Cylindrical Coordinates
  • 239
  • Radially Symmetric Waves
  • 240
  • Waves Propagated Over the Surface of an Elastic Body
  • 243
  • Chapter 6
  • Stress Waves in Viscoelastic Solids
  • 250
  • Sound Wave Propagation in a Tube
  • Internal Ftiction
  • 251
  • Discrete Viscoelastic Models
  • 252
  • Continuous Marwell Model
  • 260
  • Continuous Voigt Model
  • 263
  • Three-Dimensional VE Constitutive Equations
  • 264
  • Chapter 1
  • 16
  • Equations of Motion for a VE Material
  • 265
  • One-Dimensional Wave Propagation in VE Media
  • 266
  • Radially Symmetric Waves for a VE Bar
  • 270
  • ElectromechanicalAnalogy
  • 271
  • Chapter 7
  • Wave Propagation in Thermoelastic Media
  • Superposition Principle
  • 282
  • Duhamel-Neumann Law
  • 282
  • Equations of Motion
  • 285
  • Plane Harmonic Waves
  • 287
  • Three-Dimensional Thermal Waves; Generalized Navier Equation
  • 293
  • Chapter 8
  • 19
  • Water Waves
  • 297
  • Irrotational, Incompressible, Inviscid Flow; Velocity Potential and Equipotential Surfaces
  • 297
  • Euler's Equations
  • 299
  • Two-Dimensional Fluid Flow
  • 300
  • Complec Variable Treatment
  • 302
  • Sinusoidal Waves
  • Vortex Motion
  • 309
  • Small-Amplitude Gravity Waves
  • 311
  • Water Waves in a Straight Canal
  • 311
  • Kinematics of the Free Surface
  • 316
  • Vertical Acceleration
  • 317
  • 19
  • Standing Waves
  • 319
  • Two-Dimensional Waves of Finite Depth
  • 321
  • Boundary Conditions
  • 322
  • Formulation of a Typical Surface Wave Problem
  • 324
  • Example of Instability
  • 325
  • Interference Phenomena
  • Approximation Aeories
  • 327
  • Tidal Waves
  • 337
  • Chapter 9
  • Variational Methods in Wave Propagation
  • 344
  • Introduction; Fermat's PKnciple
  • 344
  • Calculus of Variations; Euler's Equation
  • 21
  • 345
  • Configuration Space
  • 349
  • Cnetic and Potential Eneigies
  • 350
  • Hamilton's Variational Principle
  • 350
  • PKnciple of Virtual Work
  • 352
  • Transformation to Generalized Coordinates
  • Reflection of Light Waves
  • 354
  • Rayleigh's Dissipation Function
  • 357
  • Hamilton's Equations of Motion
  • 359
  • Cyclic Coordinates
  • 362
  • Hamilton-Jacobi Theory
  • 364
  • Extension of W to 2 n Degrees of Freedom
  • 25
  • 370
  • H-J Aeory and Wave P[similar]vpagation
  • 372
  • Quantum Mechanics
  • 376
  • An Analog between Geometric Optics and Classical Mechanics
  • 377
  • Asymptotic Theory of Wave Propagation
  • 380
  • Appendix
  • Reflection of Waves in a String
  • Principle of Least Action
  • 384
  • Physics of Propagating Waves
  • 27
  • Sound Waves
  • 29
  • Doppler Effect
  • 33
  • Dispersion and Group Velocity
  • 36
  • Chapter 2
  • Partial Differential Equations of Wave Propagation
  • 41
  • 3
  • Types of Partial Differential Equations
  • 41
  • Geometric Nature of the PDEs of Wave Phenomena
  • 42
  • Directional Derivatives
  • 42
  • Cauchy Initial Value Problem
  • 44
  • Parametric Representation
  • 49
  • Discrete Wave-Propagating Systems
  • Wave Equation Equivalent to Two First-Order PDEs
  • 51
  • Characteristic Equations for First-Order PDEs
  • 55
  • General Treatment of Linear PDEs by Characteristic Theory
  • 57
  • Another Method of Characteristics for Second-Order PDEs
  • 61
  • Geometric Interpretation of Quasilinear PDEs
  • 63
  • 3
  • Integral Surfaces
  • 65
  • Nonlinear Case
  • 67
  • Canonical Form of a Second-Order PDE
  • 70
  • Riemann's Method of Integration
  • 73
  • Chapter 3
  • Wave Equation
  • Approximation of Stress Wave Propagation in a Bar by a Finite System of Mass-Spring Models
  • 85
  • Part I
  • One-Dimensional Wave Equation
  • 85
  • Factorization of the Wave Equation and Characteristic Curves
  • 85
  • Vibrating String as a Combined IV and B V Problem
  • 90
  • D'Alembert's Solution to the IV Problem
  • 97
  • 4
  • Domain of Dependence and Range of Influence
  • 101
  • Cauchy IV Problem Revisited
  • 102
  • Solution of Wave Propagation Problems by Laplace Transforms
  • 105
  • Laplace Transforms
  • 108
  • Applications to the Wave Equation
  • 111
  • Limiting Form of a Continuous Bar
  • Nonhomogeneous Wave Equation
  • 116
  • Wave Propagation through Media with Different Velocities
  • 120
  • Electrical Transmission Line
  • 122
  • Part II
  • Wave Equation in two and Three Dimensions
  • 125
  • Two-Dimensional Wave Equation
Control code
on1231563353
Dimensions
unknown
Extent
1 online resource (xv, 395 pages)
File format
unknown
Form of item
online
Isbn
9780691223377
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
JSTOR
Other physical details
illustrations
http://library.link/vocab/ext/overdrive/overdriveId
22573/ctv1826hdk
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
(OCoLC)1231563353

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      32.771354 -117.193327
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