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Billingham J., King A.C. — Wave Motion
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Название: Wave MotionАвторы: Billingham J., King A.C. Аннотация: Waves are a ubiquitous and important feature of the physical world, and, throughout history, it has been a major challenge to understand them. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymp totic expansions as well as with fluid mechanics, elasticity, and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers.
Язык: Рубрика: Физика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1 editionГод издания: 2000Количество страниц: 464Добавлена в каталог: 09.04.2010Операции: Положить на полку |
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Предметный указатель
Absolute temperature 38 239 Acoustic energy flux 63 Acoustic intensity 44 Acoustic intensity vector 62 Acoustic source 44 59 64 Acoustic velocity potential 39 Acoustically compact 61 69 73 393 Added damping 91 Added mass 91 Adiabatic flow 39 Admittance 46 70 Advection-diffusion equation 324 358 Air 38 174 198 240 256 305 378 Air entrainment 305 Aircraft 378 AKNS method 436 Ampere’s Law 179 217 Amplitude 9 60 77 Amplitude-dependence, nonlinear 424 Analytic continuation 388 Angle of incidence 50 Angle of reflection 51 Angular frequency 9 21 199 Antenna 33 208 213 218 Anvil 42 Aperture 3 70 391 394 401 404 Associated Legendre equation 409 Asymptotic balance 147 Asymptotic expansion 281 288 308 322 323 329 351 371 427 Asymptotic method 2 152 285 Asymptotic solution 307 357 370 377 446 Atmospheric pressure 76 Attenuation 425 Autocatalysis 311 316 326 350 351 Avogadro’s number 239 310 Axisymmetric solution 54 Axon 335 340 Axoplasmic material 335 Barrier 378 379 403 Basis function 23 Beach 87 97 114 121 Bed 124 269 289 Bed condition 77 87 99 Bed topography 74 97 Belousov — Zhabotinskii (BZ) reaction 308 Bending deformation 145 Bendixson’s negative criterion, Dulac’s extension to 343 352 Benjamin — Feir instability 285 297 431 Bernoulli condition 284 301 Bernoulli condition, linearised 91 Bernoulli constant 281 Bernoulli’s equation 76 289 Bernoulli’s equation, linearised 95 Bessel function 55 166 400 Bessel function, modified 160 204 Bessel’s equation 55 115 151 Biot — Savart law 176 217 Boltzmann’s constant 239 Bore 269 270 275 Bore, Severn 275 Bore, undular 280 Boundary condition 20 23 45 48 50 55 60 64 66 93 132 135 189 201 221 Boundary condition, dynamic 98 Boundary condition, impedance 403 Boundary condition, kinematic 98 Boundary layer, viscous 383 Boundary value problem 77 88 152 217 379 411 Boundary value problem, nonlinear 298 Brain 334 Breakers 305 Breaking waves 115 Brewster’s angle 198 Burgers’ equation 3 355 Cagniard — de Hoop technique 166 Canal 297 Capacitance 340 Capillary length 94 Capillary surface 94 Capillary wave spectroscopy 306 CAR 130 Car density 222 Car flowrate 223 358 Car velocity 222 Cartesian coordinates 451 Cauchy — Riemann equations 300 Causality 425 Central nervous system (c.n.s) 334 Centrosymmetric crystal 425 Chaos 308 313 350 Chapman — Jouguet point 257 Characteristic coordinates 366 Characteristic curve 2 219 221 226 245 270 358 371 Characteristic curves 367 Characteristics, intersection of 232 247 Characteristics, neighbouring 232 247 Charge 173 395 Charge density 176 209 Charge, surface 188 Chemical concentration 310 Chemical reaction 220 256 258 308 349 Chemical species 2 Cladding 202 Clarinet 49 Clock reaction 312 coating 33 Coefficients of normalisation 412 Cole — Hopf transformation 355 358 375 Combined free surface condition 86 87 99 106 Combustion 310 Compact disc 378 Compact source 65 Complex potential 300 Complex variable theory 220 269 Complex velocity 300 Compressible gas 219 Computer algebra 416 421 442 Conduction, saltatory 340 Conductivity 188 Conductor 186 Conductor, perfect 188 191 378 Conformal mapping 285 Connection coefficients 406 Connection problem 406 Conservation equation 223 Conservation law, integral 277 Conservation laws, systems of 238 Conservation of cars 223 237 248 314 Conservation of charge 177 340 Conservation of chemical 314 Conservation of current 314 Conservation of energy 243 249 261 Conservation of horizontal momentum 110 Conservation of mass 37 42 43 74 110 244 248 261 276 314 315 Conservation of momentum 37 42 49 74 243 249 261 277 Conservation of total mass 310 Conservation of vertical momentum 109 Conserved quantity 12 Continuity of normal velocity 87 Continuum approximation 222 Convective acceleration 40 75 Convective derivative 43 Convolution theorem 160 Core 202 Crapper, G.D. 299 Critical angle 196 Current 337 Current density 179 209 340 current loop 179 Current, localised distribution 212 Current, surface 188 Current, time-varying 208 Curvature 299 Cut-off frequency 50 53 57 151 Cylindrical polar coordinates 54 201 451 Dam break problem 270 Damper 92 Decibel 44 Deep water 79 90 97 99 104 124 125 220 269 399 Degrees of freedom 239 Dendritic cell body 335 Density discontinuity 29 Detonation 256 Detonation adiabatic 257 Detonation, over-driven 261 268 dielectric constant 187 199 Differential-difference equation 405 Diffraction 3 17 70 100 355 378 401 Diffraction pattern 378 397 404 Diffraction pattern, optical 394 Diffraction, Fraunhofer 393 Diffraction, Fresnel 393 Diffraction, geometrical theory of 398 Diffraction, scalar 379 391 397 Diffraction, Sommerfeld 379 Diffraction, vector 379 394 Diffusion 220 308 314 355 Diffusion coefficient 314 316 Diffusion equation 349 367 376 Diffusion equation, linear 314 Diffusion equation, nonlinear 314 Dilatation 131 Dimensional analysis 143 Dipole moment 210 Dipole, harmonic electric 218 Directivity 57 398 Directivity function 69 73 Discontinuity 221 234 Discrete spectrum 407 438 dispersion 10 77 99 111 189 205 220 269 285 307 424 430 dispersion relation 10 15 77 79 84 88 93 96 99 100 111 121 146 148 156 286 295 304 Dispersion, anomalous 434 Dispersion, material 207 431 Dispersion, normal 433 Dispersion, waveguide 207 431 Dispersive system 10 15 Displacement current 179 180 Displacement vector 130 Dissipation 362 367 Distributed circuit theory 308 Divergence theorem 43 177 185 190 316 453 Drift 284 Duck 99 Dynamic boundary condition 76 95 106 Dynamic free surface condition 80 86 Dynamo 180 d’Alembert’s solution 26 34 368 Ear 42 44 Earthquake 1 74 115 130 139 156 EDGE 378 390 401 Eigenfrequency 53 72 217 Eigensolution 22 204 Eigenvalue 406 Eigenvalue, bound state 407 Eikonal equation 153 Elastic body, finite 143 Elastic body, infinite 132 157 Elastic body, semi-infinite 135 161 Elastic body, unbounded 172 Elastic half-space 169 Elastic solid 130 219 Elasticity 2 Electric circuit theory 340 Electric current 174 Electric current density 177 Electric Dipole 210 electric dipole moment 187 Electric dipole, time-harmonic 210 Electrical permittivity 174 Electromagnetic induction 180 Electromotive force 181 Electron 173 187 216 425 Electrostatics 177 Elliptic function 294 296 Energy 11 15 16 19 23 27 29 31 33 53 56 57 62 81 100 109 124 148 197 206 276 278 281 Energy density 12 186 Energy extraction 91 Energy flux 44 46 73 186 211 214 243 252 Energy loss 252 Energy transmission 44 Energy, acoustic 42 Energy, acoustic potential 43 Energy, compressive potential 44 81 Energy, dissipation of 280 Energy, elastic potential 12 Energy, electrical 91 Energy, equipartition of 25 27 45 125 186 Energy, hydrodynamic 91 Energy, hydrostatic potential 278 Energy, incident 93 Energy, internal 239 243 249 Energy, kinetic 12 19 25 44 71 83 243 278 Energy, mechanical 241 Energy, potential 12 20 25 71 Energy, thermal 241 Energy, wave 126 Enthalpy 241 entropy 241 244 246 248 252 262 280 363 365 Envelope 9 13 21 424 449 envelope function 426 Enzyme reaction 329 Equal areas rule 236 248 266 361 Evanescent mode 151 Expansion fan 230 369 371 374 Explosion 252 Far field 60—62 65 73 210 212 213 380 393 397 Faraday resonance 128 Faraday’s law 180 Feedback 337 Fick’s law of diffusion 314 Field, axial component 201 203 217 Field, dipole 208 Field, electric 173 183 Field, electromagnetic 177 185 Field, magnetic 173 183 Field, transverse components 201 203 217 Fisher’s Equation 323 Fitzhugh — Nagumo equations 308 334 342 352 Flexural deformation 145 Flow, irrotational 281 Flow, one-dimensional 244 Flow, subsonic 251 Flow, supersonic 251 Fluid mechanics 131 222 314 405 Fluid particle 76 81 Force, electric 173 Force, electromagnetic 185 Force, gravitational 36 Force, hydrodynamic 91 93 401 Force, intermolecular 94 Force, internal line 157 Force, localised 156 Force, magnetic 173 Force, point 161 Force, restoring 74 Force, viscous 36 364 Ford Fiesta 85 Fossil fuel 91 Fourier component 48 107 109 Fourier integral 171 Fourier integral transform 66 105
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