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Lin C., Segel L. — Mathematics Applied to Deterministic Problems in the Natural Sciences
Lin C., Segel L. — Mathematics Applied to Deterministic Problems in the Natural Sciences

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Название: Mathematics Applied to Deterministic Problems in the Natural Sciences

Авторы: Lin C., Segel L.

Аннотация:

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.



Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 629

Добавлена в каталог: 06.03.2016

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absorbing barrier      96
Acrivos, A.      305
Action and reaction      361 457—458
Active transport      245
Adam, G.      109
Adiabatic process      494
AMP      23
Analyticity      59
Analyticity      59
Andronov, A.      344
angular momentum      466
angular momentum      466
Angular momentum, conservation of      37
Angular momentum, conservation of      37
Anharmonic periodic behavior      178
Anharmonic periodic behavior      178
Anomaly      45
Anomaly      45
Aphelion      45
Aphelion      45
Applied mathematics      4—8 31—33
Applied mathematics      4—8 31—33
Aris, R.      305
Astronomical unit      11
Astronomical unit      11
Asymptotic approximations      81—89 230 232
Asymptotic approximations      81—89 230 232
Asymptotic approximations to eigenfunctions and eigenvalues      163—165
Asymptotic series      230 232
Asymptotic series      230 232
Asymptotic stability      324
Asymptotic stability      324
Attenuated wave      386
Attenuated wave      386
Autocorrelation function      178
Autocorrelation function      178
Autonomous systems      339
Autonomous systems      339
Availability of energy      501
Availability of energy      501
Average value      76
Average value      76
Axial strain      363
Axial strain      363
Balance law      24 see
Balance law      24 see
Balancing procedure      282
Balancing procedure      282
Barber, M.      74
Barotropic fluid      512 541
Barotropic fluid      512 541
Basic simplification procedure      186—194
Basic simplification procedure      186—194
Batchelor, G.K.      200
Bell, E.T.      5 114
Bernoulli equation      513—514 556
Bernoulli equation      513—514 556
Bessel equation      164—165
Bessel equation      164—165
Bessel function      80
Bessel function      80
Bessel inequality      146
Bessel inequality      146
Binomial coefficient      75
Binomial coefficient      75
Binomial expansion, use in perturbation theory      234
Binomial expansion, use in perturbation theory      234
Birds, salt glands of      273
Birds, salt glands of      273
Bode’s law      37
Bode’s law      37
Body force      358 454
Body force      358 454
Bok, B.J.      20
Boltzmann's constant      78
Boltzmann's constant      78
Bond number      202
Bond number      202
Bonner, J.T.      22
Bossert, W.      245
boundary conditions      119 121
boundary conditions      119 121
Boundary conditions, elastic bar      366—368 372
Boundary conditions, elastic bar      366—368 372
Boundary conditions, homogeneous      124 126
Boundary layer      288
Boundary layer      288
Bowen, J.R.      305
Brockett, R.W.      32
Brownian motion      73—74 78—79
Brownian motion      73—74 78—79
Brownian motion, recurrence property in      108—110
Brownian motion, recurrence property in      108—110
Buckingham Pi theorem      207
Buckingham Pi theorem      207
Buoyancy      556
Buoyancy      556
Carrier, G.F.      35 298 530
Cauchy’s differential equations      461
Center      341
Center      341
Chain rule      433—434
Chandrasekhar, S.      15 531
Chang, C.T.      530
Change of units rule      205
Characteristic curves      17
Characteristic curves      17
Characteristic equations      17 160
Characteristic equations      17 160
Characteristics, Lagrange’s method of      17
Characteristics, Lagrange’s method of      17
Chemical engineering, scale models in      202—203
Chemical engineering, scale models in      202—203
Chemotaxis      26
Chemotaxis      26
Chinnaswamy, A.V.      583
Circular cylinder, flow past      551—558
Circular cylinder, flow past      551—558
Circulation      555
Circulation      555
Clausius — Duhem inequality      479
Clausius — Duhem inequality      479
Coagulation      97
Coagulation      97
Cohen, H.      32
coin tossing      72 74
coin tossing      72 74
col      340
col      340
Collisions      491
Collisions      491
Completeness      163
Completeness, dimensional      207
COMPLEX      304
COMPLEX      304
Complex representation      379—380
Complex representation      379—380
Compression waves      539—549
Compression waves      539—549
Computation      32
Computation      32
Condensation      541
Condensation      541
Conservation laws      see "Mass conservation"
Conservation laws      see "Mass conservation"
Consistency      188 189
Consistency      188 189
Constitutive equations, heat flux      117
Contact force      456
Contact force      456
Continuity equation      357 442
Continuity equation      357 442
Continuous dependence      63
Continuous medium      414
Continuous medium      414
Continuum      3 24 417—418
Continuum      3 24 417—418
Continuum mechanics, validity of      490—491
Convection      353
Convection      353
Convergence      52
Convergence      52
Convergence of perturbation series      232—233
Convergence, absolute      62
Convergence, absolute      62
Convergence, uniform      62
Convergence, uniform      62
Convergent series, compared to asymptotic      84
Cosine series      see "Fourier series"
Cosine series      see "Fourier series"
Courant, R.      33 121
Covariance      487
Covariance      487
Critical points      338
Critical points      338
Critical points, behavior of trajectories near      339—341
Critical points, behavior of trajectories near      339—341
Crocodiles, kidney tubules of      273
Crocodiles, kidney tubules of      273
Cross-section paths      350
Cross-section paths      350
Cylindrical coordinates      565
Cylindrical coordinates      565
Dainty, J.      261
Daly, B.J.      530
Darvey, I.G.      344
Deborah number      510
Deborah number      510
Deformation rate      479—480
Degree of freedom      344
Degree of freedom      344
Delbruck, M.      109
Delta function      416
Delta function      416
Den Hartog, J.P.      323
density      355 see
density      355 see
Deterministic system      42
Deterministic system      42
Diamond, J.      245
Difference equation      91 153
Difference equation      91 153
Differentiability      60 64—65
Differentiability      60 64—65
Differential equations      see also "Laplace equation" "Wave
Differential equations      see also "Laplace equation" "Wave
Differential equations, nondimensionalization of      195—198
Differential equations, nondimensionalization of      195—198
Differential equations, residuals for      191—193
Differential equations, system of      42
Differential equations, system of      42
Diffraction integral      584—586
Diffraction integral      584—586
Diffraction of acoustic waves      580—587
Diffraction of acoustic waves      580—587
Diffusion coefficient      78
Diffusion coefficient      78
Diffusion equation      26 93 100 118 120—129 151 156
Diffusion equation      26 93 100 118 120—129 151 156
Diffusion equation, fundamental facts concerning      129
Diffusion equation, fundamental facts concerning      129
Diffusion equation, numerical integration of      153
Diffusion equation, solution by Fourier transform      170—171
Diffusivity      26 255
Diffusivity      26 255
Dilatation      431
Dilatation      431
Dimensional analysis      195—204
Dimensional analysis      195—204
Dimensional analysis of functional relationship      249—252
Dimensional analysis of functional relationship      249—252
Dimensional analysis, comparison of physical and mathematical approaches      259
Dimensional analysis, comparison of physical and mathematical approaches      259
Dimensional analysis, practical examples of      204—205
Dimensional analysis, practical examples of      204—205
Dimensional homogeneity      208 257
Dimensional homogeneity      208 257
Dimensionless groups      197
Dimensionless groups      197
Dimensionless parameters, estimating the size of      264
Dimensionless parameters, estimating the size of      264
Dimensionless parameters, physical interpretation of      272—274
Dimensionless parameters, physical interpretation of      272—274
Dimensionless variables      128 196 517
Dimensionless variables      128 196 517
Dirac delta function      176
Dirac delta function      176
Direct notation      460
Direct notation      460
Dirichlet problem      573
Dirichlet problem      573
Discontinuous solutions      549
Discontinuous solutions      549
Discontinuous solutions for elastic bars      381—384 388—399
Discontinuous solutions for elastic bars      381—384 388—399
Discontinuous solutions for general media      482—485
Discontinuous solutions for general media      482—485
Discrete spectrum      160
Discrete spectrum      160
Displacement      352
Displacement      352
Dissipation function      481
Dissipation function      481
Dissociation      247
Dissociation      247
Distortion, measure of      363
Distortion, measure of      363
Distribution function      15—16
Distribution function      15—16
DNA molecules, collision of      106
DNA molecules, collision of      106
Doherty, R.E.      204
Drag      556
Drag      556
Drew, D.      221
Dubois — Reymond lemma      121 441
Dubois — Reymond lemma      121 441
Dynamics      418
Dynamics      418
D’Alembert’s paradox      557 560—563
D’Alembert’s paradox      557 560—563
Edson, L.      8
Effective radius      260
Effective radius      260
Eiconal equation      396
Eiconal equation      396
Eigenfunctions      157
Eigenfunctions      157
Eigenfunctions, asymptotic approximation      163—165
Eigenfunctions, asymptotic approximation      163—165
Eigenfunctions, completeness      163
Eigenfunctions, completeness      163
Eigenfunctions, linear independence      161
Eigenfunctions, orthogonality      161
Eigenfunctions, properties      405
Eigenfunctions, properties      405
Eigenvalue problem      522
Eigenvalue problem      522
Eigenvalue problem, perturbation theory for      242
Eigenvalues      157
1 2 3 4 5
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