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| Lin C.C., Segel L.A. — Mathematics Applied to Deterministic Problems in the Natural Sciences |
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| Ïðåäìåòíûé óêàçàòåëü |
Inner equation 293
Inner solution 308
Instability 28 see
Instability of stratified fluid 515—530
Instability, Kelvin — Helmholtz 536
Instability, Taylor 536
Integral equation 61
Integral mean value theorem 435—436
Integral of differential equations 17 40 56
Integrals, asymptotic approximation of 84
Intermediate expansion 312—313
Intermediate expansion, region 293—94
Internal energy 476
Interphase 22
Intrinsic reference quantities 197—198
Inviscid fluid, constitutive equation for 510
Irreversible processes 493
Irrotational motion 482 513
Isentropic processes 498
Isochoric motion 427
Iteration 50—51 61
Iteration for perturbation calculations 238—240
Iteration for polynomial roots 280
Jacobian 355
Jacobian, material derivative of 429—432
James, M. L. 222
Johnstone, R. E. 203
Joseph, D. 241
Jump conditions 391—395 484 548—549
Kac, M. 278
Kanwal, R. P. 583
Keller, E. F. 24 112
Keller, E. G. 204
Keller, H. B. 34
Kelvin — Helmholtz instability 536
Kepler’s laws 37
Khaikin, S. 344
Kinematic boundary condition 425
Kinematics 38
Kinematics of deformable media 418—425
Kinetic energy in elastic bars 401
Kinetics, reaction 305
Klamkin, M. S. 208
Kutta — Joukowsky theorem 557
Lagrangian strain 375
Lagrangian variables 420
Lanczos, C 141 187
Landahl, M. 537
Langevin’s equation 78
Laplace equation 107 552 567
Laplace method 84
Large box method 446—448
Large numbers, laws of 71
Least squared error see Error
Lebowitz. J. 311
Lefever, R. 537
Lefschetz, S. 339
Legendre equation 560
Length scale 128 215
Lewy, H. 121
Liapunov stability 324
Lift 556
Lighthill, M. J. 68
Limit cycles 339
Lin, C. C. 14 20
Line integrals, in thermodynamics 494—495
linear combination 44 59
Linearity 43
Linearization 29 322 368—371 519
Lineweaver — Burke plot 319
Liouville’s normal form 164
Lipschitz condition 57
Local determinism 490
Local equilibrium assumption 475
Local moment equilibrium 467
Local stress equilibrium 456—457
Logistic equation 324
Lorentz transformation 488—490
Mach number 542
Mass action, law of 302—304
Mass conservation 16 254—255 356—358 440—449
Mass distribution function 416—417 451—452
Matching 293—294 297 312—315
Material derivative 353 426—428
Material description 420
Material region 429
Material variables 357
Mathematical model, Brownian motion 73—74 78—79
Mathematical model, chemotactic amoebae 24—27
Mathematical model, conceptual versus descriptive 278
Mathematical model, diffraction of acoustic waves 583
Mathematical model, DNA collision 106
Mathematical model, enzyme-substrate chemical reaction 302—307
Mathematical model, one-dimensional elastic bar 371—372
Mathematical model, planetary motion 37—40
Mathematical model, simple pendulum 48
Mathematical model, standing gradient flow 244—268
Mathematical model, stellar system 14
Matlak, R. F. 344
Maximum principle 123 571—572
McBride, E. B. 76
Mean displacement 76
Mean free path 491
Mean square displacement 76
Mean value theorem 571
Michaelis constant 319
Michaelis — Menten approximation 308
Michelson Fourier analyzer 141
Model equation 278
Model, mathematical see Mathematical model
Models, scale 200—203
Mole 247
Molecular average 414—415
Molecular model 506
Mollo—Christensen, E. 537
moment 76
Moment, force 465
Moment, momentum 466
Momentum balance, angular 465—469
Momentum balance, linear 360—362 454—461
Momentum flux tensor 463
Momentum transfer equation 462
Montroll, E. W. 34
Morphogenetic motion 4
Morrison, P. 14
Motility 26
Motionless fluid, constitutive equation for 506—508
Multiple scale expansions 325—331
Munson, Z. Z. 241
Naive approximations 279
Natural boundary conditions 407
Nemenyi, P. F. 502
Neumann problem 573
Neutral stability 324 523
Newton — Euler sound speed 543
Newton — Fourier law of cooling 101
Newton’s contributions to mechanics 412 502—503
Newton’s laws 412
Ninham, B. 74
Node 340
Nonlinearity 16 27 53 539—540
Nonlinearity in stability theory 530
Nonlinearity in waves 544—547
Nonuniqueness 66
Nordtvedt, K. 41
Norm 63
Normal modes 158 530
Normal stress 506
Normalization 145
Notation, theoretical vs. particular 421
| Numerical analysis 41
Numerical analysis compared with analytical approach 155 157
Numerical analysis for eigenvalues 165—166
Numerical analysis of stratified fluid layer 531
O and o symbols 112—113 227
Observer invariance 476
Oppenheim, A. K. 305
Oppenheim, I. 491
Orbits, planetary and cometary 40
Order 52
Order of magnitude 213—214
Order symbols 112—113
Orthodoxy 218—221
Orthogonal functions 145
Orthogonality 161
Oscillation theorems 163
Osmol 247
Osmosis 247
Outer approximation 289
Outer approximation, solution 308
Over-all wave number 522
O’Malley, R. E. 300
Parameter dependence, continuity of 58
Parametric differentiation 59 236
Parsec 11
Parseval’s theorem 146
Partial differential equations, classification of 10
Partial differential equations, first order 17
Particle 419
Particle path 419 423—424
Pendulum problem 48 55
Pendulum problem, dimensional analysis applied to 204
Pendulum problem, multiple scale method applied to 326—330
Pendulum problem, phase plane behavior for 335—338 342—343
Pendulum problem, residuals for 193
Pendulum problem, series method for 226—233
Pendulum problem, stability of 322—324
Perihelion 45
Perihelion, advance of 41 56
Period 380
Permeability 248
Perturbation 29 515
Perturbation theory 41 45—55
Perturbation theory, multiple scale methods 325—331
Perturbation theory, Poincare’s 53—55
Perturbation theory, series method 225—236
Perturbation theory, two-parameter 265—267
Perturbation theory, unsuccessful use of 265
Phase 381
Phase plane 334—344
Phase space number density 15
Pi theorem 207
Piecewise smoothness 131
Pipe flow 205
Piston 492—493
Pitts, R. F. 247
Plane waves 542
Planets 36
Point-particle interchangeability 420
Poisson equation 18 568
Poisson integral formulas 577
Polar coordinates 563—564
Polar fluids 466
Pollack, H. O. 55
Polynomial equations, singular perturbations, applied to 278—284
Polynomial, zeros of 188
Polytropic state equation 541
Potential energy, in elastic bars 402—403
Potential theory, gravitational 566—69
Power spectrum 179—180
Prager, W. 31
Pressure 478 506
Prigogine, I. 537
Primary quantities 205
Pritulo method 332
probability 73
Probability density function 93
Projectile problem, air resistance in 224
Projectile problem, basic simplification procedures for 187 193
Projectile problem, iteration method in 239
Projectile problem, nondimensionalization of 195—198
Projectile problem, parametric differentiation in 237—238
Projectile problem, perturbation theory in 233—240
Projectile problem, scaling of 211—213
Propeller thrust 204
Proust, J. 466
Pure mathematics, relation to applied mathematics 68—69 115
Quasi-linear equation 545
Radiation 147
Radiation condition 384 583
Railroad track, strain in 365
Random motion 25
Random processes 71
Random walk 73—77 91—97 100—101
Rate constant 303
Rate of deformation tensor 479
Rayleigh quotient 404—409
Rayleigh-Ritz method 407—409
Reciprocity property 575
Recurrence property 108—110
Reflected wave 381
Reflecting barrier 95—96
Regular perturbation theory 240
Reiner, M. 510
Relative error 191
Relativity 41
Residual 190—194
Resonant term 53
Reversible processes 493
Reynolds number 201
Reynolds transport theorem 374 443
Riemann method 544
Riesz-Fischer theorem 147
Rigid body 487
Rigor 34
Rubinow, S. 311
Ruffner, J. A. 487
Saddle point 340
Scale models 200—203 253
Scale-up problems 202
Scaling 209—223 226 284
Scaling in chemical kinetics 306—307
Scaling in standing gradient flow problem 262—264
Scaling, regular perturbation theory and 236
Scattering 384
Schey, H. M. viii
Secondary quantities 206
Secular equation see Characteristic equation
Secular term 53
Segel, L. 24 112 185 246 277
Selwyn, Ph. 491
Semipermeable membrane 247
Sensitivity 71 189 193
Separation constant 125
Separation of variables 123—127 553—555
Separatrix 337
Shaffer, D. 34
Shear stress 506
Ship design 201—202
Shock strength 551
Shock waves 547—549
Silent rings 587
Silly Putty 506
Silver, D. 466
Similar regions 436—439
Simple waves 544
Sine integral function 143
Sine series see Fourier series
Singular perturbation theory 277—301
Singular perturbation theory applied to biochemical kinetics 302—320
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