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| Lin C.C., Segel L.A. — Mathematics Applied to Deterministic Problems in the Natural Sciences |
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| Предметный указатель |
Absorbing barrier 96
Acrivos, A. 305
Action and reaction 361 457—458
Active transport 245
Adam, G. 109
Adiabatic process 494
AMP 23
Analyticity 59
Andronov, A. 344
Angular momentum, conservation of 37
Anharmonic periodic behavior 178
Anomaly 45
Aphelion 45
Applied mathematics 4—8 31—33
Aris, R. 305
Astronomical unit 11
Asymptotic approximations 81—89 230 232
Asymptotic approximations to eigenfunctions and eigenvalues 163—165
Asymptotic series 230 232
Asymptotic stability 324
Attenuated wave 386
Autocorrelation function 178
Autonomous systems 339
Availability of energy 501
Average value 76
Axial strain 363
Balance law 24 see Energy
Balancing procedure 282
Barber, M. 74
Barotropic fluid 512 541
Basic simplification procedure 186—194
Batchelor, G. K. 200
Bell, E. Т. 5 114
Bernoulli equation 513—514 556
Bessel equation 164—165
Bessel function 80
Bessel inequality 146
Binomial coefficient 75
Binomial expansion use in perturbation theory 234
Birds, salt glands of 273
Bode’s law 37
Body force 358 454
Bok, B. J. 20
Boltzmann’s constant 78
Bond number 202
Bonner, J. T. 22
Bossert, W. 245
boundary conditions 119 121
Boundary conditions, elastic bar 366—368 372
Boundary conditions, homogeneous 124 126
Boundary layer 288
Bowen, J. R. 305
Brockett, R. W. 32
Brownian motion 73—74 78—79
Brownian motion, recurrence property in 108—110
Buckingham Pi theorem 207
Buoyancy 556
Carrier, G. F. 35 298 530
Cauchy’s differential equations 461
Center 341
Chain rule 433—434
Chandrasekhar, S. 15 531
Chang, C. T. 530
Change of units rule 205
Characteristic curves 17
Characteristic equations 17 160
Characteristics, Lagrange’s method of 17
Chemical engineering, scale models in 202—203
Chemotaxis 26
Chinnaswamy, A. V. 583
Circular cylinder, flow past 551—558
Circulation 555
Clausius — Duhem inequality 479
Coagulation 97
Cohen, H. 32
coin tossing 72 74
col 340
Collisions 491
Completeness 163
Completeness, dimensional 207
COMPLEX 304
Complex representation 379—380
Compression waves 539—549
Computation 32
Condensation 541
Conservation laws see Mass conservation Linear
Consistency 188 189
Constitutive equations 363 487 see such Inviscid
Constitutive equations, heat flux 117
Contact force 456
Continuity equation 357 442
Continuous dependence 63
Continuous medium 414
Continuum 3 24 417—418
Continuum mechanics, validity of 490—491
Convection 353
Convergence 52
Convergence of perturbation series 232—233
Convergence, absolute 62
Convergence, uniform 62
Convergent series, compared to asymptotic 84
Cosine series see Fourier series
Courant, R. 33 121
Covariance 487
Critical points 338
Critical points, behavior of trajectories near 339—341
Crocodiles, kidney tubules of 273
Cross-section paths 350
Cylindrical coordinates 565
Dainty, J. 261
Daly, B. J. 530
Darvey, I. G. 344
Deborah number 510
Deformation rate 479—480
Degree of freedom 344
Delbruck, M. 109
Delta function 416
Den Hartog, J. P. 323
density 355 see
Deterministic system 42
Diamond, J. 245
Difference equation 91 153
Differentiability 60 64—65
Differential equations see also Laplace equation Wave
Differential equations, nondimensionalization of 195—198
Differential equations, residuals for 191—193
Differential equations, system of 42
Diffraction integral 584—586
Diffraction of acoustic waves 580—587
Diffusion coefficient 78
Diffusion equation 26 93 100 118 120—129 151 156
Diffusion equation, fundamental facts concerning 129
Diffusion equation, numerical integration of 153
Diffusion equation, solution by Fourier transform 170—171
Diffusivity 26 255
Dilatation 431
Dimensional analysis 195—204
Dimensional analysis of functional relationship 249—252
Dimensional analysis, comparison of physical and mathematical approaches 259
Dimensional analysis, practical examples of 204—205
Dimensional homogeneity 208 257
Dimensionless groups 197
Dimensionless parameters, estimating the size of 264
Dimensionless parameters, physical interpretation of 272—274
Dimensionless variables 128 196 517
Dirac delta function 176
Direct notation 460
Dirichlet problem 573
Discontinuous solutions 549
Discontinuous solutions for elastic bars 381—384 388—399
| Discontinuous solutions for general media 482—485
Discrete spectrum 160
Displacement 352
Dissipation function 481
Dissociation 247
Distortion, measure of 363
Distribution function 15—16
DNA molecules, collision of 106
Doherty, R. E. 204
Drag 556
Drew, D. 221
Dubois — Reymond lemma 121 441
Dynamics 418
D’Alembert’s paradox 557 560—563
Edson, L. 8
Effective radius 260
Eiconal equation 396
Eigenfunctions 157
Eigenfunctions, asymptotic approximation 163—165
Eigenfunctions, completeness 163
Eigenfunctions, linear independence 161
Eigenfunctions, orthogonality 161
Eigenfunctions, properties 405
Eigenvalue problem 522
Eigenvalue problem, perturbation theory for 242
Eigenvalues 157
Eigenvalues, asymptotic approximations to 163—165
Eigenvalues, multiplicity of 162
Eigenvalues, numerical determination of 165—166
Eigenvalues, properties of 405
Einstein, A. 5
Elasticity 349
Emergent osmolality 248
Energy 45 480
Energy balance 476
Engel, A. 33
Engineering, applied mathematics in 8
Ensemble average 78 179
entropy 478—481 496—501
Enzymes 304—306
Equations, heat see Heat equation
Equilibrium 321 515
Equilibrium thermodynamics 474
Equilibrium, stability of 322—324
Error, formula 68
Error, least squared 144
Error, weighted 145
Euler expansion formula 355 432
Euler momentum equation 510
Eulerian strain 375
Eulerian variables 357 420
Euler’s contributions to mechanics 413 503—504
Euler’s laws of mechanics 413 503—504
Existence 57 61
Exotic materials 487
Expected value 75
Falling sphere, dimensional analysis of flow 205
Ferguson, N. 194
Feynman, R. 496
Fick’s law 101 255
Field equations 365 440 485—486
Field point 574
Finite differences 66—68
Finlayson, B. 194 466
First passage time 97 104
Flux 24 100 104
Focus 341
Formal calculation 59
Fourier identity 169
Fourier series 77 131—139
Fourier theorems 137
Fourier transform 167—172
Fourier’s book on mathematical theory of heat 114—115
Free will 43
frequency 380
Fresnel integrals 90
Friedrichs, K. 121
Frog skin 260—261
Froude number 201
Function space 63
Functional relationship, nondimensionalization of 198—200
Fundamental solution 103—106 160
Fundamental solution of Laplace equation 575
Fundamental term 127
Fundamental units 196
Gadd, G. 202
Galactic spirals 19—20
Galaxies 10—14
Gal—or, B. 500
Gamma function 86—89
Gasparoux, H. 466
Gauss’ Theorem 568
Generating function 76—77 80
Gibbs phenomenon 141—143
Gibbs relations 477
Goldgraben, J. R. 275
Gompertz equation 325
Gram molecular weight 247
Gram — Schmidt process 161—162
Gravitation 39
Gravitational potential 15 566
Green’s formula 108
Green’s functions 574—579
Grenander, U. 34
Ground, temperature in 151—153
Gupta, A. 537
Harmonic analysis, generalized 172—180
Harmonic functions 570—572
Harmonics 127
Heat conduction 115—129
Heat conduction in nonuniform medium 156
Heat conduction, geophysical 158—159
Heat conduction, in ground 151
Heat conduction, three-dimensional 120
Heat conductivity 116
Heat content 496
Heat equation see Diffusion equation
Heat flux density 116 477
Heaviside function 175
Heineken, F. G. 305
Helmholtz equation 578—581
Herman, P. 32
Heurism 34
Higher harmonics 53
Homogeneity 159
Homogeneity, dimensional 208
Homogeneity, spatial 217
Homogeneous boundary condition 124 126
Homogeneous function 43
Hooke, R. 34
Hooke’slaw 364
Hoppenstead, F. C. 316
Horizontal wave number 522
Hourglass 515
House, C. R. 261
Huygen’s principle 584
Hydrostatic equation 509
Ideal gas 471
Ill-conditioned problem 189
Images, method of 103 576—577
Impedance boundary conditions 368
Impenetrability of matter 419
Incompressibility 357 426
Infinite plane, Green’s function for 576
Inhomogeneous function 43
Initial conditions 119
Initial layer 308
Initial value problem 42 46 57 104
Initial value problem, singular perturbation approximation to 308—316
Inner approximation 290
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