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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 Sciences
Àâòîðû: 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: 1988
Êîëè÷åñòâî ñòðàíèö: 629
Äîáàâëåíà â êàòàëîã: 06.03.2016
Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
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
Elasticity 349
Emergent osmolarity 248
Emergent osmolarity 248
Energy 45 480
Energy 45 480
Energy balance 476
Engel, A. 33
Engineering, applied mathematics in 8
Engineering, applied mathematics in 8
Ensemble average 78 179
Ensemble average 78 179
entropy 478—481 496—501
entropy 478—481 496—501
Enzymes 304—306
Enzymes 304—306
Equilibrium 321 515
Equilibrium 321 515
Equilibrium thermodynamics 474
Equilibrium thermodynamics 474
Equilibrium, stability of 322—324
Equilibrium, stability of 322—324
Error, formula 68
Error, formula 68
Error, least squared 144
Error, weighted 145
Euler expansion formula 355 432
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
Euler’s laws of mechanics 413 503—504
Existence 57 61
Existence 57 61
Exotic materials 487
Exotic materials 487
Expected value 75
Expected value 75
Falling sphere, dimensional analysis of flow 205
Falling sphere, dimensional analysis of flow 205
Ferguson, N. 194
Feynman, R. 496
Fick’s law 101 255
Fick’s law 101 255
Field equations 365 440 485—486
Field equations 365 440 485—486
Field point 574
Finite differences 66—68
Finite differences 66—68
Finlayson, B. 194 466
First passage time 97 104
First passage time 97 104
Flux 24 100 104
Flux 24 100 104
Focus 341
Focus 341
Formal calculation 59
Formal calculation 59
Fourier identity 169
Fourier series 77 131—139
Fourier theorems 137
Fourier transform 167—172
Fourier transform 167—172
Fourier’s book on mathematical theory of heat 114—115
Free will 43
Free will 43
frequency 380
frequency 380
Fresnel integrals 90
Fresnel integrals 90
Friedrichs, K. 121
Frog skin 260—261
Frog skin 260—261
Froude number 201
Froude number 201
Function space 63
Function space 63
Functional relationship, nondimensionalization of 198—200
Fundamental solution 103—106 160
Fundamental solution 103—106 160
Fundamental solution of Laplace equation 575
Fundamental solution of Laplace equation 575
Fundamental term 127
Fundamental term 127
Fundamental units 196
Fundamental units 196
Gadd, G. 202
Gal-Or, B. 500
Galactic spirals 19—20
Galactic spirals 19—20
Galaxies 10—14
Galaxies 10—14
Gamma function 86—89
Gamma function 86—89
Gasparoux, H. 466
Gauss’ Theorem 568
Gauss’ Theorem 568
Generating function 76—77 80
Generating function 76—77 80
Gibbs phenomenon 141—143
Gibbs phenomenon 141—143
Gibbs relations 477
Gibbs relations 477
Goldgraben, J.R. 275
Gompertz equation 325
Gompertz equation 325
Gram molecular weight 247
Gram molecular weight 247
Gram — Schmidt process 161—162
Gram — Schmidt process 161—162
Gravitation 39
Gravitation 39
Gravitational potential 15 566
Gravitational potential 15 566
Green’s formula 108
Green’s formula 108
Green’s functions 574—579
Green’s functions 574—579
Grenander, U. 34
Ground, temperature in 151—153
Ground, temperature in 151—153
Gupta, A. 537
Harmonic analysis, generalized 172—180
Harmonic functions 570—572
Harmonic functions 570—572
Harmonics 127
Harmonics 127
Heat conduction 115—129
Heat conduction 115—129
Heat conduction in ground 151
Heat conduction in ground 151
Heat conduction in nonuniform medium 156
Heat conduction, geophysical 158—159
Heat conduction, geophysical 158—159
Heat conduction, three-dimensional 120
Heat conduction, three-dimensional 120
Heat conductivity 116
Heat content 496
Heat content 496
Heat equation see "Diffusion equation"
Heat equation see "Diffusion equation"
Heat flux density 116 477
Heaviside function 175
Heaviside function 175
Heineken, F.G. 305
Helmholtz equation 578—581
Helmholtz equation 578—581
Herman, P. 32
Heurism 34
Heurism 34
Higher harmonics 53
Higher harmonics 53
Homogeneity 159
Homogeneity 159
Homogeneity, dimensional 208
Homogeneity, dimensional 208
Homogeneity, spatial 217
Homogeneity, spatial 217
Homogeneous boundary condition 124 126
Homogeneous boundary condition 124 126
Homogeneous function 43
Homogeneous function 43
Hooke, R. 34
Hooke’s law 364
Hooke’s law 364
Hoppenstead, F.C. 316
Horizontal wave number 522
Horizontal wave number 522
Hourglass 515
Hourglass 515
House, C.R. 261
Huygen’s principle 584
Hydrostatic equation 509
Hydrostatic equation 509
Ideal gas 471
Ideal gas 471
Ill-conditioned problem 189
Ill-conditioned problem 189
Images, method of 103 576—577
Images, method of 103 576—577
Impedance boundary conditions 368
Impedance boundary conditions 368
Impenetrability of matter 419
Impenetrability of matter 419
Incompressibility 357 426
Incompressibility 357 426
Infinite plane, Green’s function for 576
Infinite plane, Green’s function for 576
Inhomogeneous function 43
Inhomogeneous function 43
Initial conditions 119
Initial conditions 119
Initial layer 308
Initial layer 308
Initial value problem 42 46 57 104
Initial value problem 42 46 57 104
Initial value problem, singular perturbation approximation to 308—316
Initial value problem, singular perturbation approximation to 308—316
Inner approximation 290
Inner approximation 290
Inner equation 293
Inner equation 293
Inner solution 308
Inner solution 308
Instability 28 see
Instability 28 see
Instability Kelvin — Helmholtz 536
Instability Kelvin — Helmholtz 536
Instability of stratified fluid 515—530
Instability Taylor 536
Instability Taylor 536
Integral equation 61
Integral mean value theorem 435—436
Integral of differential equations 17 40 56
Integral of differential equations 17 40 56
Integrals, asymptotic approximation of 84
Integrals, asymptotic approximation of 84
Intermediate expansion 312—313
Intermediate region 293—294
Intermediate region 293—294
Internal energy 476
Interphase 22
Interphase 22
Intrinsic reference quantities 197—198
Intrinsic reference quantities 197—198
Inviscid fluid, constitutive equation for 510
Inviscid fluid, constitutive equation for 510
Irreversible processes 493
Irreversible processes 493
Irrotational motion 482 513
Irrotational motion 482 513
Isentropic processes 498
Isentropic processes 498
Isochoric motion 427
Isochoric motion 427
Iteration 50—51 61
Iteration 50—51 61
Iteration for perturbation calculations 238—240
Iteration for perturbation calculations 238—240
Iteration for polynomial roots 280
Iteration for polynomial roots 280
Jacobian 355
Jacobian 355
Jacobian, material derivative of 429—432
Jacobian, material derivative of 429—432
James, M.L. 222
Johnstone, R.E. 203
Joseph, D. 241
Jump conditions 391—395 484 548—549
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
Kelvin — Helmholtz instability 536
Kepler’s laws 37
Kepler’s laws 37
Khaikin, S. 344
Kinematic boundary condition 425
Kinematic boundary condition 425
Kinematics 38
Kinematics 38
Kinematics of deformable media 418—425
Kinematics of deformable media 418—425
Kinetic energy in elastic bars 401
Kinetic energy in elastic bars 401
Kinetics, reaction 305
Kinetics, reaction 305
Klamkin, M.S. 208
Kutta — Joukowsky theorem 557
Kutta — Joukowsky theorem 557
Lagrangian strain 375
Lagrangian strain 375
Lagrangian variables 420
Lagrangian variables 420
Lanczos, C. 141 187
Landahl, M. 537
Langevin’s equation 78
Langevin’s equation 78
Laplace equation 107 552 567
Laplace equation 107 552 567
Laplace method 84
Laplace method 84
Large box method 446—448
Large box method 446—448
Large numbers, laws of 71
Large numbers, laws of 71
Lebowitz, J. 311
Lefever, R. 537
Lefschetz, S. 339
Legendre equation 560
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