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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
Projectile problem, nondimensionalization of 195—198 Projectile problem, parametric differentiation in 237—238 Projectile problem, parametric differentiation in 237—238 Projectile problem, perturbation theory in 233—240 Projectile problem, scaling of 211—213 Propeller thrust 204 Propeller thrust 204 Proust, J. 466 Pure mathematics, relation to applied mathematics 68—69 115 Pure mathematics, relation to applied mathematics 68—69 115 Quasi-linear equation 545 Quasi-linear equation 545 Radiation 147 Radiation 147 Radiation condition 384 583 Radiation condition 384 583 Railroad track, strain in 365 Railroad track, strain in 365 Random motion 25 Random motion 25 Random processes 71 Random walk 73—77 91—97 100—101 Random walk 73—77 91—97 100—101 Rate constant 303 Rate constant 303 Rate of deformation tensor 479 Rate of deformation tensor 479 Rayleigh quotient 404—409 Rayleigh quotient 404—409 Rayleigh — Ritz method 407—409 Rayleigh — Ritz method 407—409 Reciprocity property 575 Reciprocity property 575 Recurrence property 108—110 Recurrence property 108—110 Reflected wave 381 Reflected wave 381 Reflecting barrier 95—96 Regular perturbation theory 240 Regular perturbation theory 240 Reiner, M. 510 Relative error 191 Relative error 191 Relativity 41 Relativity 41 Residual 190—119 Residual 190—119 Resonant term 53 Resonant term 53 Reversible processes 493 Reynolds number 201 Reynolds number 201 Reynolds transport theorem 374 443 Reynolds transport theorem 374 443 Riemann method 544 Riemann method 544 Riesz — Fischer theorem 147 Riesz — Fischer theorem 147 Rigid body 487 Rigid body 487 Rigor 34 Rigor 34 Rubinow, S. 311 Ruffner, J.A. 487 Saddle point 340 Saddle point 340 Scale models 200—203 253 Scale models 200—203 253 Scale-up problems 202 Scaling 209—223 226 284 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 Scaling, regular perturbation theory and 236 Scattering 384 Scattering 384 Schey, H.M. viii Secondary quantities 206 Secondary quantities 206 Secular equation see "Characteristic equation" Secular equation see "Characteristic equation" Secular term 53 Secular term 53 Segel, L. 24 112 185 246 277 Selwyn, Ph. 491 Semipermeable membrane 247 Semipermeable membrane 247 Sensitivity 71 189 193 Sensitivity 71 189 193 Separation constant 125 Separation constant 125 Separation of variables 123—127 553—555 Separation of variables 123—127 553—555 Separatrix 337 Separatrix 337 Shaffer, D. 34 Shear stress 506 Shear stress 506 Ship design 201—202 Ship design 201—202 Shock strength 551 Shock strength 551 Shock waves 547—549 Shock waves 547—549 Silent rings 587 Silent rings 587 Silly Putty 506 Silly Putty 506 Silver, D. 466 Similar regions 436—439 Similar regions 436—439 Simple waves 544 Simple waves 544 Sine integral function 143 Sine integral function 143 Sine series see "Fourier series" Sine series see "Fourier series" Singular perturbation theory 277—301 Singular perturbation theory 277—301 Singular perturbation theory, applied to biochemical kinetics 302—320 Singular perturbation theory, applied to biochemical kinetics 302—320 Singular perturbation theory, higher approximations in 311—316 Singularity, excluded by small sphere 568—569 Singularity, excluded by small sphere 568—569 Skin effect 153 Skin effect 153 Slime mold amebae, aggregation of 22—31 Slime mold amebae, aggregation of 22—31 Small box method 444—446 Small box method 444—446 Small terms, neglect of 210 Small terms, neglect of 210 Smith, G.M. 222 Smith, J.M. 345 Smith, W. 106 Smoothness, piecewise 131 Smoothness, piecewise 131 Sobolev, S.L. 170 Sound speed 377 542 Sound speed 377 542 Source point 574 Source point 574 Source solution 103 Spatial description 420 Spatial description 420 Spatial variables 357 420 Spatial variables 357 420 Specific heat 481 Specific heat 481 Sphere, cooling of 129 Sphere, flow past 559—560 Sphere, Green's function for 576—577 Sphere, Green's function for 576—577 Spherical waves 543 Spherical waves 543 Stability 16 28 58 322—324 Stability 16 28 58 322—324 Stability in numerical analysis 154 Stability in population dynamics 533—534 Stability of reaction-diffusion equations 537—539 Stability of two-layer inviscid flow 535—536 Stability of viscous flow model 531 534—535 Stability of viscous flow model 531 534—535 Stagnation points 558 Stagnation points 558 Stakgold, I. 296 Standing gradient flow 245 Standing wave 381 403 544 Star-shaiped regions 436 Star-shaiped regions 436 state variables 492 state variables 492 Stationary time sequence 176—178 Stationary time sequence 176—178 Steady flows 421 423 Steady flows 421 423 Stefan’s law 149 Stefan’s law 149 Stieltjes integral 176 Stieltjes integral 176 Stirling’s approximation 81 86—89 102 Stirling’s approximation 81 86—89 102 Stoker, J. 344 Stokes' Law 78 204—205 Stokes' Law 78 204—205 strain 363 strain 363 Stratified fluid 516 Stratified fluid 516 Stream function 511 Stream function 511 Streamlines 422—424 Streamlines 422—424 Stress 358—360 454 Stress 358—360 454 Stress component 361 Stress in motionless fluids 505—510 Stress in one-dimensional elastic bar 364 Stress in one-dimensional elastic bar 364 Stress tensor 458—461 Stress tensor 458—461 Stress-strain relation 364 Sturm — Liouville theory 159 167 404—405 521 529 Sturm — Liouville theory 159 167 404—405 521 529 Substantial derivative see "Material derivative" Substantial derivative see "Material derivative" Substrate 304 Substrate 304 Successive approximations see "Iteration" Successive approximations see "Iteration" Superposition 39 103 114 Superposition 39 103 114 Surface traction 358 Surface traction 358 Symmetry, in perturbation calculations 232 Symmetry, in perturbation calculations 232 Systems of ordinary differential equations, theorems for 57—65 Systems of ordinary differential equations, theorems for 57—65 Taylor instability 536 Taylor instability 536 Taylor series 46 47 Taylor series 46 47 Tensors 449 Tensors 449 Term-by-term integration 89 Term-by-term integration 89 Theoretical science, contrasted with applied mathematics 7 Thermal diffusivity 118 Thermal diffusivity 118 Thermodynamics 491—501 Thermostatics 474 Thermostatics 474 Thring, M.W. 203 Time scale 128 Time scale 128 Titchmarsh, E.C. 147 Tormey, J. 245 torque 465 torque 465 Trajectories 336 Trajectories 336 Transient 124 Transient 124 Translation invariance 103 Translation invariance 103 Transmitted wave 381 Trial and error 222 Triangle, diffusion from 106—108 Triangle, diffusion from 106—108 Trigonometric identities 229 Trigonometric identities 229 Trivial solution 125 157 Trivial solution 125 157 Truesdell, C. 22 33 412 501 Truncated sinusoid, Fourier analysis of 173—176 Truncated sinusoid, Fourier analysis of 173—176 Tseng, H. 466 Tsuchiya, H.M. 305 Turing, A. 537 Uniform approximation 294—295 310 Uniform approximation 294—295 310 Uniform validity 289—290 Uniqueness 58 60 122—123 Uniqueness 58 60 122—123 Unorthodoxy 218—221 Unorthodoxy 218—221 Unstable equilibrium 515 Unstable equilibrium 515 Unstirred layers 261 Unstirred layers 261 van Ness, H.C. 491 Variance 76—77 Vasil’eva, A.B. 315 Vector 488 Vector 488 Vector product 465 Vector product 465 Velocity 352 420 Velocity 352 420 Velocity potential 512—513 558 Velocity potential 512—513 558 Velocity scale 214 Velocity scale 214 Verhulst — Pearl equation 324 Verhulst — Pearl equation 324 Virtual displacement 407 Virtual displacement 407 Vitt, A. 344 von Karman, T. 8 von Neumann, J. 32 Watson, G.S. 106 Wave equation 377—378 542 Wave equation 377—378 542 Wave function 396 Wave function 396 wave number 380 wave number 380 Wave number vector 522 Wavelength 380
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