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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: 629Äîáàâëåíà â êàòàëîã: 06.03.2016Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
Legendre equation 560 Length scale 128 215 Length scale 128 215 Lewy, H. 121 Liapunov stability 324 Liapunov stability 324 Lift 556 Lift 556 Lighthill, M.J. 68 Limit cycles 339 Limit cycles 339 Lin, C.C. 14 20 Line integrals, in thermodynamics 494—495 Line integrals, in thermodynamics 494—495 linear combination 44 59 linear combination 44 59 Linearity 43 Linearity 43 Linearization 29 322 368—371 519 Linearization 29 322 368—371 519 Lineweaver — Burke plot 319 Lineweaver — Burke plot 319 Liouville’s normal form 164 Liouville’s normal form 164 Lipschitz condition 57 Local determinism 490 Local determinism 490 Local equilibrium assumption 475 Local moment equilibrium 467 Local moment equilibrium 467 Local stress equilibrium 456—457 Logistic equation 324 Logistic equation 324 Lorentz transformation 488—490 Lorentz transformation 488—490 Mach number 542 Mach number 542 Mass action, law of 302—304 Mass conservation 16 254—255 356—358 440—449 Mass conservation 16 254—255 356—358 440—449 Mass distribution function 416—417 451—452 Mass distribution function 416—417 451—452 Matching 293—294 297 312—315 Matching 293—294 297 312—315 Material derivative 353 426—428 Material derivative 353 426—428 Material description 420 Material description 420 Material region 429 Material variables 357 Material variables 357 Mathematical model, Brownian motion 73—74 78—79 Mathematical model, chemotactic amoebae 24—27 Mathematical model, chemotactic amoebae 24—27 Mathematical model, conceptual versus descriptive 278 Mathematical model, conceptual versus descriptive 278 Mathematical model, diffraction of acoustic waves 583 Mathematical model, diffraction of acoustic waves 583 Mathematical model, DNA collision 106 Mathematical model, enzyme-substrate chemical reaction 302—307 Mathematical model, enzyme-substrate chemical reaction 302—307 Mathematical model, one-dimensional elastic bar 371—372 Mathematical model, planetary motion 37—40 Mathematical model, planetary motion 37—40 Mathematical model, simple pendulum 48 Mathematical model, standing gradient flow 244—268 Mathematical model, standing gradient flow 244—268 Mathematical model, stellar system 14 Mathematical model, stellar system 14 Matlak, R.F. 344 Maximum principle 123 571—572 Maximum principle 123 571—572 McBride, E.B. 76 Mean displacement 76 Mean displacement 76 Mean free path 491 Mean free path 491 Mean square displacement 76 Mean square displacement 76 Mean value theorem 571 Mean value theorem 571 Michaelis constant 319 Michaelis constant 319 Michaelis — Menten approximation 308 Michaelis — Menten approximation 308 Michelson Fourier analyzer 141 Michelson Fourier analyzer 141 Model equation 278 Model equation 278 Models, scale 200—203 Mole 247 Mole 247 Molecular average 414—415 Molecular model 506 Molecular model 506 Mollo-Christensen, E. 537 moment 76 moment 76 Moment, force 465 Moment, force 465 Moment, momentum 466 Moment, momentum 466 Momentum balance, angular 465—469 Momentum balance, angular 465—469 Momentum balance, linear 360—362 454—461 Momentum flux tensor 463 Momentum flux tensor 463 Momentum transfer equation 462 Montroll, E.W. 34 Morphogenetic motion 4 Morphogenetic motion 4 Morrison, P. 14 Motility 26 Motility 26 Motionless fluid, constitutive equation for 506—508 Motionless fluid, constitutive equation for 506—508 Multiple scale expansions 325—331 Multiple scale expansions 325—331 Munson, Z.Z. 241 Naive approximations 279 Naive approximations 279 Natural boundary conditions 407 Nemenyi, P.F. 502 Neumann problem 573 Neumann problem 573 Neutral stability 324 523 Neutral stability 324 523 Newton — Euler sound speed 543 Newton — Euler sound speed 543 Newton — Fourier law of cooling 101 Newton’s contributions to mechanics 412 502—503 Newton’s contributions to mechanics 412 502—503 Newton’s laws 412 Newton’s laws 412 Ninham, B. 74 Node 340 Node 340 Nonlinearity 16 27 53 539—540 Nonlinearity 16 27 53 539—540 Nonlinearity in stability theory 530 Nonlinearity in stability theory 530 Nonlinearity in waves 544—547 Nonlinearity in waves 544—547 Nonuniqueness 66 Nonuniqueness 66 Nordtvedt, K. 41 Norm 63 Norm 63 Normal modes 158 530 Normal modes 158 530 Normal stress 506 Normalization 145 Normalization 145 Notation, theoretical vs. particular 421 Numerical analysis 41 Numerical analysis 41 Numerical analysis for eigenvalues 165—166 Numerical analysis of stratified fluid layer 531 Numerical analysis of stratified fluid layer 531 Numerical analysis, compared with analytical approach 155 157 Numerical analysis, compared with analytical approach 155 157 O and o symbols 112—113 227 O and o symbols 112—113 227 Observer invariance 476 Observer invariance 476 Oppenheim, A.K. 305 Oppenheim, I. 491 Orbits, planetary and cometary 40 Order 52 Order 52 Order of magnitude 213—214 Order of magnitude 213—214 Order symbols 112—113 Order symbols 112—113 Orthodoxy 218—221 Orthodoxy 218—221 Orthogonal functions 145 Orthogonal functions 145 Orthogonality 161 Orthogonality 161 Oscillation theorems 163 Oscillation theorems 163 Osmol 247 Osmol 247 Osmosis 247 Osmosis 247 Outer approximation 289 Outer approximation 289 Outer approximation, solution 308 Outer approximation, solution 308 Overall wave number 522 Overall wave number 522 O’Malley, R.E. 300 Parameter dependence, continuity of 58 Parameter dependence, continuity of 58 Parametric differentiation 59 236 Parametric differentiation 59 236 Parsec 11 Parsec 11 Parseval’s theorem 146 Parseval’s theorem 146 Partial differential equations, classification of 10 Partial differential equations, classification of 10 Partial differential equations, first order 17 Particle 419 Particle 419 Particle path 419 423—424 Pendulum problem 48 55 Pendulum problem 48 55 Pendulum problem, dimensional analysis applied to 204 Pendulum problem, dimensional analysis applied to 204 Pendulum problem, multiple scale method applied to 326—330 Pendulum problem, multiple scale method applied to 326—330 Pendulum problem, phase plane behavior for 335—338 342—343 Pendulum problem, phase plane behavior for 335—338 342—343 Pendulum problem, residuals for 193 Pendulum problem, residuals for 193 Pendulum problem, series method for 226—233 Pendulum problem, series method for 226—233 Pendulum problem, stability of 322—324 Pendulum problem, stability of 322—324 Perihelion 45 Perihelion 45 Perihelion, advance of 41 56 Perihelion, advance of 41 56 Period 380 Period 380 Permeability 248 Permeability 248 Perturbation 29 515 Perturbation 29 515 Perturbation theory 41 45—55 Perturbation theory 41 45—55 Perturbation theory, multiple scale methods 325—331 Perturbation theory, multiple scale methods 325—331 Perturbation theory, Poincare's 53—55 Perturbation theory, Poincare's 53—55 Perturbation theory, series method 225—236 Perturbation theory, series method 225—236 Perturbation theory, two-parameter 265—267 Perturbation theory, unsuccessful use of 265 Perturbation theory, unsuccessful use of 265 Phase 381 Phase 381 Phase plane 334—344 Phase plane 334—344 Phase space number density 15 Pi theorem 207 Pi theorem 207 Piecewise smoothness 131 Piecewise smoothness 131 Pipe flow 205 Pipe flow 205 Piston 492—493 Piston 492—493 Pitts, R.F 247 Plane waves 542 Plane waves 542 Planets 36 Planets 36 Point-particle interchangeability 420 Point-particle interchangeability 420 Poisson equation 18 568 Poisson equation 18 568 Poisson integral formulas 577 Poisson integral formulas 577 Polar coordinates 563—564 Polar coordinates 563—564 Polar fluids 466 Polar fluids 466 Pollack, H.O. 55 Polya, G. 76 Polynomial equations, singular perturbations applied to 278—284 Polynomial, zeros of 188 Polynomial, zeros of 188 Polytropic state equation 541 Polytropic state equation 541 Potential energy, in elastic bars 402—403 Potential theory, gravitational 566—569 Potential theory, gravitational 566—569 Power spectrum 179—180 Power spectrum 179—180 Prager, W. 31 Pressure 478 506 Pressure 478 506 Prigogine, I. 537 Primary quantities 205 Primary quantities 205 Pritulo method 332 Pritulo method 332 probability 73 probability 73 Probability density function 93 Probability density function 93 Projectile problem, air resistance in 224 Projectile problem, air resistance in 224 Projectile problem, basic simplification procedures for 187 193 Projectile problem, basic simplification procedures for 187 193 Projectile problem, iteration method in 239 Projectile problem, nondimensionalization of 195—198
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