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Riley, Hobson Ч Mathematical Methods for Physics and Engineering
Riley, Hobson Ч Mathematical Methods for Physics and Engineering



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Ќазвание: Mathematical Methods for Physics and Engineering

јвторы: Riley, Hobson

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: 2-d edition

 оличество страниц: 1253

ƒобавлена в каталог: 17.02.2013

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ѕредметный указатель
Spur of a matrix      263Ч264
Spur, of a matrix      see "Trace of
Square matrices      254
Square, symmetries of      942
Square-wave, Fourier series for      424 425
Stagnation points of fluid flow      727
Standard deviation $\sigma$      988
Standard deviation $\sigma$ of sample      1067
standing waves      626
Stationary values of functions of one real variable      51Ч53
Stationary values of functions of several real variables      165Ч170
Stationary values of integrals      835
Stationary values under constraints      see "Lagrange undetermined multipliers"
Statistical tests, and hypothesis testing      1120
Statistics      961 1064Ч1140
Statistics, describing data      1065Ч1072
Statistics, estimating parameters      1072Ч1097 1140
Stirling's approximation      1027 1203
Stirling's asymptotic series      1203
Stokes' equation      858
Stokes' theorem      394 412Ч415
Stokes' theorem for tensors      804
Stokes' theorem, physical applications      414
Stokes' theorem, related theorems      413
Strain tensor      802
Stratified sampling, in Monte Carlo methods      1172
Streamlines and complex potentials      727
Stress tensor      802
Stress waves      829
String, loaded      857
String, plucked      705
String, transverse vibrations of      609 848
Student's t-distribution, comparison of means      1131
Student's t-distribution, critical points table      1130
Student's t-distribution, normalisation      1128
Student's t-distribution, one/two-tailed confidence limits      1130
Student's t-distribution, plots      1129
Student's t-test      1126Ч1132
Sturm Ч Liouville equations      591Ч597
Sturm Ч Liouville equations, boundary conditions      592
Sturm Ч Liouville equations, examples      593Ч597
Sturm Ч Liouville equations, examples, associated Legendre equation      594Ч595
Sturm Ч Liouville equations, examples, Bessel equation      595
Sturm Ч Liouville equations, examples, Chebyshev equation      597
Sturm Ч Liouville equations, examples, Hermite equation      596
Sturm Ч Liouville equations, examples, hypergeometric equation      603
Sturm Ч Liouville equations, examples, Laguerre equation      596Ч597
Sturm Ч Liouville equations, examples, Legendre equation      593Ч594
Sturm Ч Liouville equations, examples, simple harmonic oscillator      595
Sturm Ч Liouville equations, manipulation to self-adjoint form      592Ч593
Sturm Ч Liouville equations, two independent variables      860
Sturm Ч Liouville equations, variational approach      849Ч854
Sturm Ч Liouville equations, weight function      849
Sturm Ч Liouville equations, zeroes of eigenfunctions      603
Subgroups      903Ч905
Subgroups, index      908
Subgroups, normal      905
Subgroups, order      903
Subgroups, order, Lagrange's theorem      907
Subgroups, proper      903
Subgroups, trivial      903
Submatrices      272Ч273
Subscripts and superscripts      111
Subscripts and superscripts, contra- and covariant      805
Subscripts and superscripts, covariant derivative      818
Subscripts and superscripts, dummy      111
Subscripts and superscripts, free      111
Subscripts and superscripts, partial derivative      818
Subscripts and superscripts, summation convention      111 804
Substitution, integration by      66Ч68
Summation convention      111 804
Summation of series      119Ч127
Summation of series, arithmetic      120
Summation of series, arithmetico-geometric      121
Summation of series, contour integration method      764Ч765
Summation of series, difference method      122Ч123
Summation of series, Fourier series method      433
Summation of series, geometric      120
Summation of series, powers of natural numbers      124Ч125
Summation of series, transformation methods      125Ч127
Summation of series, transformation methods, differentiation      125
Summation of series, transformation methods, integration      125
Summation of series, transformation methods, substitution      126
Superposition methods for ODE      581 597Ч601
Superposition methods for PDE      650Ч657
Surface integrals and divergence theorem      407
Surface integrals of scalars, vectors      395Ч402
Surface integrals, Archimedean up thrust      402 416
Surface integrals, physical examples      401
Surfaces      351Ч353
Surfaces of revolution      75Ч76
Surfaces, area of      352
Surfaces, area of, cone      75Ч76
Surfaces, area of, solid, and Pappus' theorem      198Ч200
Surfaces, area of, sphere      352
Surfaces, coordinate curves      352
Surfaces, normal to      352 356
Surfaces, parametric equations      351
Surfaces, quadratic      297
Surfaces, tangent plane      352
Symmetric functions      422
Symmetric functions and Fourier series      425 426
Symmetric functions and Fourier transforms      451
Symmetric matrices      275
Symmetric matrices, general properties      see "Hermitian matrices"
Symmetric tensors      787
Symmetry operations on molecules      883
Symmetry operations, order of application      886
Symmetry, and equivalence relations      906
t substitution      66Ч67
t-test      see "Student's t-test"
Tangent planes to surfaces      352
Tangent vectors to space curves      348
tanh, hyperbolic tangent      see "Hyperbolic functions"
Taylor series      139Ч144
Taylor series and finite differences      1179 1186
Taylor series and Taylor's theorem      139Ч142 747
Taylor series as solution of ODE      1183Ч1184
Taylor series for functions of a complex variable      747Ч748
Taylor series for functions of several real variables      163Ч165
Taylor series, approximation errors      142Ч143
Taylor series, approximation errors, in numerical methods      1156 1166
Taylor series, remainder term      141
Taylor series, required properties      139
Taylor series, standard forms      139
Tensors      see "Cartesian tensors" "Cartesian particular
Test statistic      1120
Tetrahedral group      957
Tetrahedron, mass of      197
Tetrahedron, volume of      195
Thermodynamics, first law of      179
Thermodynamics, Maxwell's relations      179Ч181
Top-hat function      see "Rectangular distribution"
Torque, vector representation of      227
Torsion of space curves      348
Total derivative      157
Total differential      157
Trace of a matrix      263Ч264
Trace of a matrix and second-order tensors      788
Trace of a matrix as sum of eigenvalues      285 292
Trace of a matrix, invariance under similarity transformations      289 934
Trace of a matrix, trace formula      292
Transcendental equations      1150
Transformation matrix      288 294
Transformations, active and passive      797
Transformations, conformal      730Ч738
Transforms, integral      see "Integral transforms" "Fourier "Laplace
Transients in diffusion equation      656
Transients in electric circuits      491
Transitivity, and equivalence relations      906
Transpose of a matrix      255 260Ч261
Transpose of a matrix, product rule      261
Transverse vibrations, membrane      610 673 702
Transverse vibrations, rod      704
Transverse vibrations, string      609
Trapezium rule      1166Ч1167
Trial functions for eigenvalue estimation      852
Trial functions for particular integrals of ODE      500
Trials      961
Triangle inequality      251 586
Triangle, centroid of      220Ч221
Triangular matrices      274
Tridiagonal matrices      1162Ч1164 1190 1193
Trignometric identities      15
Trigonometric identities      10
Triple integrals      see "Multiple integrals"
Uncertainty principle (Heisenberg)      441Ч443
Undetermined coefficients, method of      500
Undetermined multipliers      see "Lagrange undetermined multipliers"
Uniform distribution      1036
Union $\cup$, probability for      see "Probability for union"
Uniqueness theorem, Laplace equation      676
Uniqueness theorem, Poisson equation      638Ч640
Unit step function      see "Heaviside function"
Unit vectors      223
Unitary, matrices      276
Unitary, matrices, eigenvalues and eigenvectors      283
Unitary, representations      928
Unitary, transformations      290
Upper triangular matrices      274
Variable end-points      see "End-points for variations variable"
Variable, dummy      62
Variance $\sigm^{2a$, from MGF      1005
Variance $\sigm^{2}a$      988
Variance $\sigm^{2}a$ from PGF      1001
Variance $\sigm^{2}a$ of dependent RV      1044
Variance $\sigm^{2}a$ of sample      1067
Variation of parameters      514Ч516
Variation, constrained      844Ч846
Variational principles, physical      846Ч849
Variational principles, physical, Fermat      846
Variational principles, physical, Hamilton      847
Variations, calculus of      see "Calculus of variations"
Vector operators      353Ч375
Vector operators, acting on sums and products      360Ч361
Vector operators, combinations of      361Ч363
Vector operators, curl      359 374
Vector operators, del $\nabla$      354
Vector operators, del squared $\nabla^{2}$      358
Vector operators, divergence (div)      358
Vector operators, geometrical definitions      404 406
Vector operators, gradient operator (grad)      354Ч358 373
Vector operators, identities      362 827
Vector operators, Laplacian      358 374
Vector operators, non-Cartesian      363Ч375
Vector operators, tensor forms      820Ч824
Vector operators, tensor forms, curl      823
Vector operators, tensor forms, divergence      821Ч822
Vector operators, tensor forms, gradient      821
Vector operators, tensor forms, Laplacian      822
Vector product      226Ч228
Vector product in Cartesian coordinates      228
Vector product, anticommutativity      226
Vector product, definition      226
Vector product, determinant form      228
Vector product, non-associativity      226
Vector spaces      247Ч252 955
Vector spaces of infinite dimensionality      583Ч586
Vector spaces of infinite dimensionality, associativity of addition      583
Vector spaces of infinite dimensionality, basis functions      583Ч584
Vector spaces of infinite dimensionality, commutativity of addition      583
Vector spaces of infinite dimensionality, defining properties      583
Vector spaces of infinite dimensionality, Hilbert spaces      584Ч586
Vector spaces of infinite dimensionality, inequalities: Bessel, Schwarz, triangle      586
Vector spaces, action of group on      930
Vector spaces, associativity of addition      247
Vector spaces, basis vectors      248Ч249
Vector spaces, commutativity of addition      247
Vector spaces, complex      247
Vector spaces, defining properties      247
Vector spaces, dimensionality      248
Vector spaces, inequalities: Bessel, Schwarz, triangle      251Ч252
Vector spaces, invariant      930 955
Vector spaces, matrices as an example      257
Vector spaces, parallelogram equality      252
Vector spaces, real      247
Vector spaces, span of a set of vectors in      247
Vector triple product      230
Vector triple product, identities      230
Vector triple product, non-associativity      230
Vectors as first-order tensors      781
Vectors as geometrical objects      246
Vectors, algebra of      216Ч238
Vectors, algebra of, addition and subtraction      217Ч218
Vectors, algebra of, addition and subtraction, in component form      222
Vectors, algebra of, angle between      225
Vectors, algebra of, associativity of addition and subtraction      217
Vectors, algebra of, commutativity of addition and subtraction      217
Vectors, algebra of, multiplication by a complex scalar      226
Vectors, algebra of, multiplication by a scalar      218
Vectors, algebra of, multiplication of      see "Scalar product" "Vector
Vectors, algebra of, outer product      785
Vectors, applications, centroid of a triangle      220Ч221
Vectors, applications, equation of a line      230Ч231
Vectors, applications, equation of a plane      231Ч232
Vectors, applications, equation of a sphere      232
Vectors, applications, finding distance from a line to a line      235Ч236
Vectors, applications, finding distance from a line to a plane      236Ч237
Vectors, applications, finding distance from a point to a line      233Ч234
Vectors, applications, finding distance from a point to a plane      234Ч235
Vectors, applications, intersection of two planes      232
Vectors, base      342
Vectors, calculus of      340Ч375
Vectors, calculus of, differentiation      340Ч345 350
Vectors, calculus of, integration      345Ч346
Vectors, calculus of, line integrals      383Ч395
Vectors, calculus of, surface integrals      395Ч402
Vectors, calculus of, volume integrals      402 403
Vectors, column      255
Vectors, compared with scalars      216Ч217
Vectors, component form      221Ч222
Vectors, derived quantities, curl      359
Vectors, derived quantities, derivative      340
Vectors, derived quantities, differential      344 350
Vectors, derived quantities, divergence (div)      358
Vectors, derived quantities, reciprocal      237Ч238 372 804 808
Vectors, derived quantities, vector fields      353
Vectors, derived quantities, vector fields, curl      412
Vectors, derived quantities, vector fields, divergence      358
Vectors, derived quantities, vector fields, flux      401
Vectors, derived quantities, vector fields, rate of change      356
Vectors, examples of      216
Vectors, graphical representation of      216Ч217
Vectors, irrotational      359
Vectors, magnitude of      222Ч223
Vectors, non-Cartesian      342 364 368
Vectors, notation      216
Vectors, physical, acceleration      341
Vectors, physical, angular momentum      241
Vectors, physical, angular velocity      227 241 359
Vectors, physical, area      399Ч401 414
Vectors, physical, area of parallelogram      227 228
Vectors, physical, force      216 217 224
Vectors, physical, moment/torque of a force      227
Vectors, physical, velocity      341
Vectors, polar and axial      798
Vectors, solenoidal      358 395
Vectors, span of      247
Velocity vectors      341
Venn diagrams      961Ч966
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