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Lin C., Segel L. — Mathematics applied to deterministic problems in the natural sciences
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Íàçâàíèå: Mathematics applied to deterministic problems in the natural sciencesÀâòîðû: Lin C., Segel L. Àííîòàöèÿ: Addresses the construction, analysis, and interpretation of mathematical models that shed light on significant problems in the physical sciences.
The authors' case studies approach leads to excitement in teaching realistic problems. The exercises reinforce, test and extend the reader's understanding. This reprint volume may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers working on fluid mechanics, elasticity, perturbation methods, dimensional analysis, numerical analysis, continuum mechanics and differential equations.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1988Êîëè÷åñòâî ñòðàíèö: 634Äîáàâëåíà â êàòàëîã: 28.03.2015Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
Inner solution 308 Instability 28 see Instability of stratified flnid 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 region 293—294 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 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 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 for eigenvalues 165—166 Numerical analysis of stratified fluid layer 531 Numerical analysis, compared with analytical approach 155 157 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 Polya, G. 76 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—569 Power spectrum 179—180 Prager, W. 31 Pressure 478 506 Prigogine, L 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 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 Singular perturbation theory, higher approximations in 311—316 Singularity, excluded by small sphere 568—569 Skin effect 153
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