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| Riley, Hobson — Mathematical Methods for Physics and Engineering |
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| Предметный указатель |
Probability for union  963 967—970
Probability functions (PF) 981
Probability functions (PF), cumulative (CPF) 981 983
Probability functions (PF), density functions (PDF) 982
Probability generating functions (PGF) 999—1004
Probability generating functions (PGF) and MGF 1005
Probability generating functions (PGF), binomial 1003
Probability generating functions (PGF), definition 1000
Probability generating functions (PGF), geometric 1001
Probability generating functions (PGF), mean and variance 1000—1001
Probability generating functions (PGF), Poisson 1000
Probability generating functions (PGF), sums of RV 1003
Probability generating functions (PGF), trials 1000
Probability generating functions (PGF), variable sums of RV 1003—1004
Probability, axioms 967
Probability, conditional 970—975
Probability, conditional, Bayes' theorem 974—975
Probability, conditional, combining 972
Probability, definition 967
Product rule for differentiation 45—47 49—51
Products of inertia 800
Projection operators for irreps 949 958
Projection tensors 828
Proper rotations 795
Proper subgroups 903
Pseudoscalars 796 799
Pseudotensors 795—799 813
Pseudovectors 795—799
Quadratic equations, complex roots of 86—87
Quadratic equations, properties of roots 10
Quadratic equations, roots of 2
Quadratic forms 293—297
Quadratic forms, positive definite and semi-definite 295
Quadratic forms, quadratic surfaces 297
Quadratic forms, removing cross terms 294
Quadratic forms, stationary properties of eigenvectors 295—296
Quartiles, of RVD 987
Quaternion group 915 955
Quotient law for tensors 788—790
Quotient rule, for differentiation 48
Quotient test for series 130
Radius of convergence 136 717
Radius of curvature of space curves 348
Radius of torsion of space curves 349
random number generation 1177
Random numbers, non-uniform distribution 1194
Random variable distributions see "Probability distributions"
Random variables (RV) 961 981—985
Random variables (RV), continuous 982—985
Random variables (RV), dependent 1038—1047
Random variables (RV), discrete 981—982
Random variables (RV), independent 998 1042
Random variables (RV), sums of 1002—1004
Range, of a matrix 298
Rank of matrices 272
Rank of matrices and determinants 272—273
Rank of matrices and linear dependence 272
Rank of tensors see "Order of tensors"
Rate of change of a function of one real variable 42
Rate of change of a function of several real variables 156—158
Ratio Comparison Test 130
Ratio test (D'Alembert) 129 718
Ratio test (D'Alembert) in convergence of power series 135
Ratio theorem 219
Ratio theorem and centroid of a triangle 220—221
Rayleigh — Ritz method 333—335 859
Real part/term of a complex number 86—87
Real roots, of a polynomial equation 1
Rearrangement methods for algebraic equations 1151—1152
Reciprocal vectors 237—238 372 804 808
Reciprocity relation for partial derivatives 160
Rectangular distribution 1036
Rectangular distribution, Fourier transform of 448
Recurrence relations 502—507
Recurrence relations, characteristic equation 505
Recurrence relations, coefficients 542 543 1163
Recurrence relations, first-order 503
Recurrence relations, functions 562 569—570
Recurrence relations, higher-order 507
Recurrence relations, second-order 505
Reducible representations 926 928
Reduction formulae for integrals 70
Reflections and improper rotations 795
Reflections as symmetry operations 883—884
Reflexivity, and equivalence relations 906
Regular functions see "Analytic functions"
Regular representations 939 952
Regular singular points 540 544—546
Relative velocities 222
Remainder term in Taylor series 141
Repeated roots of auxiliary equation 499
Representations 918
Representations, definition 924
Representations, dimension of 920 924
Representations, equivalent 926—928
Representations, faithful 925 940
Representations, generation of 920—926 954
Representations, irreducible see "Irreps"
Representations, natural 923 952
Representations, product 945—947
Representations, reducible 926 928
Representations, regular 939 952
Representations, regular, counting irreps 940
Representations, unitary 928
Representative matrices 921
Representative matrices of identity 924
Representative matrices, block-diagonal 928
Representative matrices, eigenvalues 942
Representative matrices, inverse 925
Representative matrices, number needed, and order of group 924
Residue at a pole 750—752
Residue, theorem 752—754
Resolution function 452
Resolvent kernel 873 874
Response matrix, for linear least squares 1115
Rhomboid, volume of 241
Riemann tensor 830
Riemann theorem for conditional convergence 127
Riemann zeta series 131 132
Right hand screw rule 226
Rodrigues' formula for associated Legendre functions 594
Rodrigues' formula for Chebyshev polynomials 597
Rodrigues' formula for Hermite polynomials 596
Rodrigues' formula for Laguerre polynomials 577 596
Rodrigues' formula for Legendre polynomials 559 594
Rolle's theorem 56
Root test (Cauchy) 132 717
Roots of a polynomial equation, properties 9
Roots of unity 100—101
Roots, of a polynomial equation 2
Rope, suspended at its ends 845
Rotation groups (continuous), invariant subspaces 930
Rotation matrices as a group 890
Rotation of a vector see "Curl"
Rotations as symmetry operations 883—884
Rotations, axes and orthogonal matrices 779 780 810
Rotations, improper 795—797
Rotations, invariance under 783
Rotations, product of 780
Rotations, proper 795
Rouche's theorem 755—757
Row matrix 255
Runge — Kutta methods 1186—1188
Rv see "Random variables"
RVD (random variable distributions) see "Probability distributions"
Saddle points 165
Saddle points, sufficient conditions 167 170
Sampling with/without replacement 971
Sampling, correlation 1070
Sampling, covariance 1070
| Sampling, space 961
Sampling, statistics 1065—1072
Scalar fields 353
Scalar fields, derivative along a space curve 355
Scalar fields, gradient 354—358
Scalar fields, line integrals 383—393
Scalar fields, rate of change 355
Scalar product 223—226
Scalar product and inner product 249
Scalar product and metric tensor 807
Scalar product and perpendicular vectors 223 249
Scalar product for vectors with complex components 225
Scalar product in Cartesian coordinates 225
Scalar product, invariance 779 788
Scalar triple product 228—230
Scalar triple product in Cartesian coordinates 229
Scalar triple product in Cartesian coordinates, determinant form 229
Scalar triple product, cyclic permutation of 229
Scalar triple product, interchange of dot and cross 229
Scalars 216—217
Scalars, invariance 779
Scalars, zero-order tensors 782
Scale factors 365 368 370
Scale factors and metric tensor 806 821
Scattering in quantum mechanics 469
Schmidt — Hilbert theory 875—878
Schroedinger equation 612
Schroedinger equation, constant potential 703
Schroedinger equation, hydrogen atom 675
Schroedinger equation, numerical solution 1198
Schroedinger equation, variational approach 854
Schwarz inequality 251 586
Schwarz — Christoffel transformation 733—735
Second differences 1179
Second-order differential equations see "Ordinary differential equations" "Partial
Secular determinant 285
Self-adjoint operators see "Hermitian operators"
Semicircle, angle in 18
Semicircular lamina, centre of mass 200
Separable kernel in integral equations 866—867
Separable variables in ODE 477
Separation constants 648 650
Separation of variables, for PDE 646—681
Separation of variables, for PDE, diffusion equation 649 655—657 671 685
Separation of variables, for PDE, expansion methods 676—678
Separation of variables, for PDE, general method 646—650
Separation of variables, for PDE, Helmholtz equation 671—675
Separation of variables, for PDE, inhomogeneous boundary conditions 655—657
Separation of variables, for PDE, inhomogeneous equations 678—681
Separation of variables, for PDE, Laplace equation 650—655 658—671 676
Separation of variables, for PDE, polar coordinates 658—681
Separation of variables, for PDE, separation constants 648 650
Separation of variables, for PDE, superposition methods 650—657
Separation of variables, for PDE, wave equation 647—649 671 673
Series 118—144
Series solutions of differential equations 537—558 564—568
Series solutions of differential equations about ordinary points 541—544
Series solutions of differential equations about regular singular points 544—546
Series solutions of differential equations about regular singular points, Frobenius series 545
Series solutions of differential equations, convergence 541
Series solutions of differential equations, indicial equation 545
Series solutions of differential equations, linear independence 546
Series solutions of differential equations, polynomial solutions 544 554—555
Series solutions of differential equations, recurrence relation 542 543
Series solutions of differential equations, second solution 542 549—554
Series solutions of differential equations, second solution, derivative method 551—554
Series solutions of differential equations, second solution, Wronskian method 550 558
Series, convergence of see "Convergence of infinite series"
Series, differentiation of 134
Series, finite and infinite 119
Series, integration of 134
Series, multiplication by a scalar 134
Series, multiplication of (Cauchy product) 134
Series, notation 119
Series, operations 134
Series, particular, arithmetic 120
Series, particular, arithmetico-geometric 121
Series, particular, Fourier see "Fourier series"
Series, particular, geometric 120
Series, particular, Maclaurin 141 143
Series, particular, power see "Power series"
Series, particular, powers of natural numbers 124—125
Series, particular, Riemann zeta 131 132
Series, particular, Taylor see "Taylor series"
Series, summation see "Summation of series"
Shortest path 837
Shortest path and geodesies 825 831
Similarity transformations 288—290 778—779 934
Similarity transformations, properties of matrix under 289—290
Similarity transformations, unitary transformations 290
Simple harmonic oscillator 582 595
Simple harmonic oscillator, energy levels of 604
Simple harmonic oscillator, equation 541
Simple poles 724
Simpson's rule 1167
Simultaneous linear equations 297—312
Simultaneous linear equations and intersection of planes 305—306
Simultaneous linear equations, homogeneous and inhomogeneous 298
Simultaneous linear equations, singular value decomposition 306—312
Simultaneous linear equations, solution using, Cramer's rule 304—305
Simultaneous linear equations, solution using, inverse matrix 300—301
Simultaneous linear equations, solution using, numerical methods see "Numerical methods for simultaneous linear equations"
Sine in terms of exponential functions 105
Sine, Maclaurin series for 143
Sine, orthogonality relations 423
Singular and non-singular integral equations 864
Singular and non-singular linear operators 254
Singular and non-singular matrices 268
Singular integrals see "Improper integrals"
Singular points (singularities) 712 723—725
Singular points (singularities), essential 724 750
Singular points (singularities), removable 725
Singular points of ODE 539
Singular points of ODE, irregular 540
Singular points of ODE, particular equations 541
Singular points of ODE, regular 540
Singular solution of ODE 475 487 488 490
Singular value decomposition and simultaneous linear equations 306—312
Singular value decomposition, singular values 307
sinh, hyperbolic sine 105 720 see
Skew-symmetric matrices 275
Snell's law 847
Soap films 839—840
Solenoidal vectors 358 395
Solid angle as surface integral 401
Solid angle, subtended by rectangle 417
Solid: mass, centre of mass and centroid 196—198
Source density 612
Space curves 346—350
Space curves, arc length 347
Space curves, binormal 348
Space curves, curvature 348
Space curves, Frenet — Serret formulae 349
Space curves, parametric equations 346
Space curves, principal normal 348
Space curves, radius of curvature 348
Space curves, radius of torsion 349
Space curves, tangent vector 348
Space curves, torsion 348
spaces see "Vector spaces"
Span of a set of vectors 247
Sphere, vector equation of 232
Spherical Bessel functions  675
Spherical harmonics  670—671
spherical polar coordinates 367—369
Spherical polar coordinates, area element 368
Spherical polar coordinates, basis vectors 368
Spherical polar coordinates, length element 368
Spherical polar coordinates, vector operators 367—369
Spherical polar coordinates, volume element 208 368
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