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Logan J. — Applied Mathematics: A Contemporary Approach
Logan J. — Applied Mathematics: A Contemporary Approach

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Название: Applied Mathematics: A Contemporary Approach

Автор: Logan J.

Аннотация:

This text presents, for the first time at an elementary level, current topics in applied mathematics such as singular perturbation, nonlinear wave propagation, bifurcation, similarity methods and the numerical solution of partial differential equations. It emphasizes the interdependency of mathematics and its application to physical phenomena, and is written in a style accessible to readers with a wide range of interests and backgrounds. There is also coverage of scaling and dimensional analysis, calculus of variations, Fourier and transform methods for partial differential equations and intergral equations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 588

Добавлена в каталог: 23.11.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^{n}[a,b]$      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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