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| Авторизация |
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| Logan J. — Applied Mathematics: A Contemporary Approach |
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| Предметный указатель |
![$C^{n}[a,b]$](/math_tex/284ab6e0bb17ccd9e28d3122c7121a7d82.gif) 92
Abel’s integral equation 223
Acceleration of iterative schemes 540
Acoustic equations 283 441
Action integral 128
Adiabatic process 278 281
Admissible functions 86
Admissible variations 96
Advection equation 231 234 554
Approximation for differential equation 47
Approximation, difference 491 501
Approximation, inner 57
Approximation, outer 56
Approximation, uniform singular perturbation 64
Approximation, uniformly valid 46
Asymptotic expansion 48
Asymptotic power series 48
Asymptotic sequence 48
Attractor 394
Benard problem 400
Bernoulli’s theorem 336
Bifurcation diagram 358
Bifurcation in tank reactor 376
Bifurcation of bead on hoop 347 401
Bifurcation point 358
Bifurcation, Hopf 396 400
Bifurcation, pitchfork 346
Boundary layer in singular perturbation 55 66
Boundary layer, over airfoil 29
Boundary layer, width 62
Brachistochrone problem 87 88 107
Breaking time 240 250
Buckingham Pi theorem 3 7
Buckingham pi theorem, proof 10
Burgers’ equation 243 262 441
Canonical coordinates 423 468 480
Catenary 147
Cauchy — Euler method 491
Cauchy’s equations 329
Cauchy’s stress principle 324 329
Cauchy’s Theorem 326
Characteristic schemes 558
Characteristic system 255
Characteristics for wave equation 294
Characteristics of advection equation 235
Characteristics of hyperbolic systems 559
Characteristics of linear equations 236
Characteristics of nonlinear equations 237
Chemical reactor 373
Chemotaxis 351
Clausius — Duhem inequality 334
Cole — Hopf transformation 262
Conductivity 8 9 21 160
Configuration space 127
Conservation laws across discontinuity 251 314
Conservation laws for mass 271 272 305 306 313 322
Conservation laws in differential form 248 306 562
Conservation laws in integral form 249
Conservation laws in mechanics 128 435
Consistent scheme 501
Constraint, algebraic 149
Constraint, isoperimetric 144
Continuity equation 272 306 323
Convection theorem 320
Convective derivative 270 319
Convergence in-the-mean 182
Convergence of finite difference scheme 501
Convergence of Fourier series 180 182
Convergence pointwise 45
Convergence uniform 45
Convergent matrix 522
Convolution 189
Coordinates, canonical 423 468 480
Coordinates, cylindrical 170
Coordinates, eulerian 266
Coordinates, Lagrangian 267
Coordinates, phase 136 379
Coordinates, shock-fixed 290
Coordinates, spherical 171
Courant — Friedrichs — Levy criterion 549 555 556 558
Crank — Nicolson scheme 508
Critical point 380
Critical point, center 383
Critical point, node 383 387 388 389
Critical point, saddle 383 387
Critical point, spiral 383 389
Derivative of functional 95 96
Derivative, directional 97
Derivative, discrete approximation of 494
Derivative, ordinary 90 95
Difference approximation of boundary conditions 510 534
Difference approximation, backward 495
Difference approximation, centered 496
Difference approximation, forward 494
Diffusion equation, fundamental solution 158 194
Diffusion equation, initial value problem 193
Diffusion equation, linear 20 152 154 156 158 162 282
Diffusion equation, nonlinear 162 455
Diffusion equation, similarity solution 417 444 455
Diffusion equation, spherically symmetric 444 447
Diffusion equation, three dimensional 168
Diffusivity 8 19 21 162 168
Dimensional analysis, blast wave problem 3
Dimensional analysis, damped oscillator 71
Dimensional analysis, diffusion problem 7 445
Dimensional analysis, projectile problem 23
Dimensional matrix 6
Dirichlet problem 174 518
Discretization error see "Truncation error"
dispersion relation 245
Dissipation function 333
Distortion 285
Divergence theorem 166 321 534
Domain of dependence, analytical 297 550
Domain of dependence, numerical 550
Duffing equation 40
DuFort — Frankel scheme 509
Eigenvalues, Freholm integral equation 210 212
Eigenvalues, Sturm — Liouville problem 183
Eigenvalues, Volterra integral equation 220
Elliptic equation 155 157
Emden — Fowler equation 143 461
Energy conservation in diffusion 19 160
Energy conservation in fluids 278 280 332
Energy conservation in mechanics 128 435 437
Energy integral 164 302
Energy transport theorem 337
Enthalpy 279 290
entropy 278 281
Equation of state, Abel 279
Equation of state, barotropic 276
Equation of state, caloric 281
Equation of state, ideal gas 277 279
Equation of state, Tait 279
Equation of state, thermal 281
Equation of state, Van der Waals 279
Equilibrium solution 358 380
Erf function 192
Euler equation for fluid 332
Euler equation, isoperimetric problem 146
Euler equation, multiple integrals 116 118
Euler equation, nth order problem 112
Euler equation, second order problem 112
Euler equation, several functions 113 114
Euler equation, simplest problem 104
Euler expansion formula 270 320
Explicit scheme for diffusion equation 497
Explicit scheme for wave equation 547
Explicit scheme, BASIC program 499
Explicit scheme, Lax — Wendroff 555 557 563
| Extremal 99 116
False boundary 510 530
Fermat’s principle 108
First integral for differential equation 106 107 429
First integral of characteristic system 255
Flow, adiabatic 281
Flow, incompressible 323
Flow, irrotational 336
Flow, isentropic 282
Flow, plane Couette 339
Flow, plane Poiseuille 339
Flow, potential 336
Flow, steady 318
Fluid motion in one dimension 267
Fluid motion in three dimensions 316
Force on object in fluid 330
Force, body 273 323
Force, surface 273 324
Fourier coefficients 180 185
Fourier cosine series 181
Fourier series 180 185
Fourier sine series 181
Fourier transform 192
Fourier’s heat law 19 161 167 281
Fredholm alternative theorem 209
Froude number 15
Functional 86
Functional, continuous 100
Functional, linear 100
Fundamental frequencies 291
Fundamental Lemma of Calculus of Variations see "Lagrange’s lemma"
Gateaux variation 96
Gauss — Seidel method 524
Gauss — Seidel method, applied to Laplace’s equation 525
Gauss — Seidel method, convergence of 532
Gauss — Seidel method, SOR 540
Generators of extended group 472 475
Graph, connected 531
Graph, directed 531
Green’s function 194 229
Green’s identity 167 173
Green’s Theorem 116
Gronwall’s inequality 360
Gurney energy 15
Hadamard’s example 165
Hamiltonian 128 133 136 435 437
Hamilton’s equations 134
Hamilton’s principle 127
heat capacity 8
Helmholtz equation 304
Hilbert — Schmidt theorem 214
Hooke’s law 286 482
Hugoniot curve 315
Hyperbolic equation 155 157
Hyperbolic system 552 558
Ideal fluid 331
Implicit scheme for diffusion equation 503
Implicit scheme for wave equation 551
Implicit scheme, BASIC program 507
Implicit scheme, Crank — Nicolson 508
Implicit scheme, DuFoit — Frankel 509
Integral equation, Abel’s 223
Integral equation, convolution type 221
Integral equation, Fredholm 200
Integral equation, Volterra 200
Integral surface 255
Internal energy 278 280 332
Invariance of function 439
Invariance of functional 428
Invariance of ordinary differential equation 457 461
Invariance of partial differential equation 450 453 470
Invariance, conformal 440 450 470
Invariant surface condition 452 481
Inverse problem in integral equations 203
Inverse problem, calculus of variations 137
Inverse problem, scattering 298
Inviscid fluid 331
Isoperimetric problem 143 144 149
Iteration for Fredholm equations 228
Iteration for Volterra equations 218
Iteration, fixed point 216
Iteration, Gauss — Seidel 524
Iteration, Jacobi 522
Iteration, matrix 521
Iteration, Picard 217
Iteration, rate of convergence 530
Jacobi method 522
Jacobi method, convergence of 532
Kelvin’s theorem 338
Kernel, convolution 221
kernel, resolvent 216 221 228
Kernel, separable 208
Kernel, singular 200 222
kernel, symmetric 200 212
Kinetic energy in generalized coordinates 127
Kinetic energy of fluid 280 332 337
Korteweg — de Vries equation 246
Lagrange multiplier rule 143
Lagrange’s equations 128 435 436
Lagrange’s lemma 103 112 116
Lagrangian 90 127 436
Laplace transforms 188
Laplace transforms, table of 190
Laplace’s equation 170 517
Laplace’s equation, difference approximation 518 520
Lax — Wendroff method 555 563
Leibniz’ formula 224 322
Lennard-Jones potential 16
Lie derivative 473
Lie plane 457
Linear space 91
Linear system 385
Local Lie group 420 466
Local Lie group in n dimensions 475
Local Lie group, determining equations 434
Local Lie group, dynamical system of 423
Local Lie group, extended 426 473
Local Lie group, generators of 422 466 473
Local Lie group, global representation 422
Local Lie group, infinitesimal representation 422 466
Local Lie group, operator of 439 473
Mach number 284
Magnitude of function 27
Magnitude, order of 27
Matching 62 63
Material derivative see "Convective derivative"
Matrix stability analysis 513
Matrix, diagonally dominant 531
Matrix, irreducible 532
Matrix, strictly diagonally dominant 531
Matrix, tridiagonal 504 517
Maximum principle 168
Maxwell’s equations 123 301
Momentum angular 338
Momentum of fluid 272 323
Momentum, balance of 272 306 324
Momentum, canonical 133 136 435
Momentum, conservation of 436 437
Natural boundary conditions 119
Natural boundary conditions for multiple integrals 124
Natural boundary conditions for simplest problem 120
Navier — Stokes equations 335
Neumann problem 174 518
Neumann problem, BASIC program 534 539
Neumann problem, difference approximation 534
Neumann series 219
Newtonian fluid 334
Noether’s theorem 430 436
Norm, definition 93 527
Norm, matrix 527
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