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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.
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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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