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| Авторизация |
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| Hildebrand F.B. — Methods of Applied Mathematics |
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| Предметный указатель |
Abel’s formula 230
Abel’s integral equation 276 320(74—77)
Absolute length of vector 24
Abstract vector 54
Adjoint kernel 314(47)
Adjoint matrix 14 17
Angle between functions 116(127)
Angle between vectors 24
Augmented matrix 19
Basis 26 33
Basis, standard 27 54
Beam, rotating 175
Beam, vibrating 203(52)
Bending moment 176 181
Bending stiffness 175 179
Bessel's inequality 85
Biharmonic equation 199(32)
Bilinear expansion of kernel 314(49) 324(83)
Brachistochrone 196(15) 203(49)
Calculus of variations 119
Calculus of variations, direct methods of 190
Calculus of variations, semidirect methods of 190
Canonical form 36 44 48 71 169
Canonical matrix 78
Catenary 126
Cauchy principal value 325(84)
Cayley — Hamilton theorem 59 78
Centrifugal force 156
Characteristic equation 31 59
Characteristic equation, reduced 60
Characteristic function 89 248 278
Characteristic function, expansions 91 253
Characteristic function, orthogonality 90 252 314(47)
Characteristic number 30 43 75 89 92 247
Characteristic number, dominant 63
Characteristic number, minimal properties 112(116—125) 194(5) 204(55) 217(93) 328(93—95)
Characteristic number, multiple 32 45 70
Characteristic vector 30 44 69 75
Characteristic-value problem, algebraic equations 30 69 75 122
Characteristic-value problem, algebraic equations, numerical methods 62 65 73 76
Characteristic-value problem, differential equations 89 146 187 189
Characteristic-value problem, integral equations 247 251
Characteristic-value problem, integral equations, numerical methods 278
Coefficient matrix 19
Cofactor 11 22
Cogredient variables 57
Collocation 281 284
Column space 29
Column vector 23 29
Completeness 86 254
Cone, motion on 158
Conformal mapping 305(28—33)
Congruence transformation 42
Conjugate matrices 14
Conjunctive transformation 45
Conservation of energy 208(67)
Conservative force 149 152 165
Constraint 120 139 160 200(35)
Constraint, nonholonomic 162
Contragredient variables 57
convergence, in the mean 87
Convolution 274
Coordinate transformation 54
Coriolis inertia force 157
Cramer’s Rule 11 17
Crout reduction 4 339
Cycloid 196(15)
Defect 3 26
Definite form 47
Delta function 237
Delta, Kronecker 15
Determinant 10
Determinant of product 13
Determinant, cofactor of 11 22
Determinant, Laplace expansion of 11
Determinant, minor of 11
Diagonal matrix 15 37 45
Diagonalization of matrices 37 45 48 71
Differentiation, of integrals 223
Dimension, of vector space 26
Dirac delta function 237
Dirichlet problem 139 177 303(27) 309(36)
Discriminant of matrix 50
Dissipative force 169
Dyad 97(30)
Eigenfunction 89 248
Eigenvalue 30 89 247
Eigenvector 30
Elementary operation 19 41
Equality of matrices 8
Equivalence of matrices 41
Euler equation 125 136 137
Extremal 125
Force potential 149
Fourier constant 83
Fourier series 92
Fourier sine transform 271 318(68)
Fredholm integral equation 222 227 232 246 251 259 269
Fredholm theory of integral equations 269
Function space 81 115(126—131)
Function space, linear dependence in 83
Function space, norm in 82 88
Function space, norm in, Hermitian 88
Function space, orthogonality in 82 88
Function space, scalar product in 82 88
Functional 131
Galerkin, method of 286
Gauss reduction 4
Gauss — Jordan reduction 1
Generalized acceleration 155
Generalized coordinate 151
Generalized force 152
Generalized momentum 155
Generalized velocity 151
Geodesic 195(11—14)
Geometrical vector 54
Gradient, minimization of 138
Gram — Schmidt orthogonalization procedure 35
Gramian 25 99(42)
Green’s formula, for self-adjoint operator 298(16)
Green’s function 228 235 242
Green’s function, construction, by conformal mapping 305(28—33)
Green’s function, generalized 230 300(19—23)
Green’s Theorem 200(34)
Green’s theorem in plane 135
Hamilton's canonical equations 208(67)
Hamilton's principle 148
Hamiltonian function 208(66)
Hermitian angle 24
Hermitian form 43 48
Hermitian kernel 313(46) 314(49)
Hermitian length, of vector 24
Hermitian matrix 31 42 47
Hermitian norm 88
Hermitian orthogonality 24 88
Hermitian scalar product 24 88
Hilbert transform 325(85)
Hilbert — Schmidt theory of integral equations 251
Hilbert’s formula 316(55)
Homogeneous linear equations 13 22
Inertia coefficient 170
Inertia force 156
Inertia force, Coriolis 157
Inertia force, momental 156
Influence function 242
Integral equation 222
Integral equation of first kind 223 257 275
Integral equation of lifting line 331(102)
Integral equation of second kind 223
Integral equation of third kind 223
| Integral equation, approximate solution as limit of set of algebraic equations 281
Integral equation, approximate solution by iterative approximation 259 278
Integral equation, approximate solution by kernel approximation 292 335(117 118)
Integral equation, approximate solution by methods of undetermined coefficients 283
Integral equation, approximate solution by methods of undetermined coefficients, collocation 284
Integral equation, approximate solution by methods of undetermined coefficients, least squares 286
Integral equation, approximate solution by methods of undetermined coefficients, weighting functions 286
Integral equation, Fredholm 222 227 232 246 251 259 269
Integral equation, singular 271
Integral equation, Volterra 222 226 263 275
Integral operator 261 263
Integral operator, positive 330(96)
Integral operator, positive definite 330(96)
Integro-differential equation 331(102)
Invariant of matrix 50
Inverse matrix 16
Inverse matrix, left 97(27)
Inverse matrix, right 97(27)
iterated kernel 266
Jordan canonical matrix 77
Kernel 222
Kernel, adjoint 314(47)
Kernel, auxiliary 323(82)
Kernel, bilinear expansion of 314(49) 324(83)
kernel, hermitian 313(46)
Kernel, iterated 266
Kernel, reciprocal 267 317(61)
kernel, resolvent 267 317(61)
Kernel, self-adjoint 314(47)
Kernel, separable 246
kernel, skew-symmetric 330(97)
kernel, symmetric 228 251
kinetic energy 149 150 166
Kinetic potential 150
Kronecker delta 15
Lagrange multiplier 120 140 160
Lagrange’s equations 151
Lagrange’s equations for electrical network 213(82)
Lagrangian function 150
Laplace expansion of determinant 11
Laplace transform 272 274 321(75)
Laplace's equation 138 177 219(100) 303(27—33)
latent root 30
Law of cosines, in function space 116 (128)
Least-squares approximation 84 286
Left inverse of matrix 97(27)
Length of vector 23 70
Lifting-line equation 332(102)
Limit in the mean 87
Linear algebraic equations, coefficient matrix of 19
Linear algebraic equations, Cramer’s rule 11 17
Linear algebraic equations, Crout reduction 4 339
Linear algebraic equations, defect of 3
Linear algebraic equations, Gauss reduction 4
Linear algebraic equations, Gauss — Jordan reduction 1
Linear algebraic equations, homogeneous 13 22
Linear algebraic equations, homogeneous, transposed 29
Linear algebraic equations, nullity of 26
Linear algebraic equations, solvability of 21 30 34 44
Linear algebraic equations, system of 1
Linear algebraic equations, system of, augmented matrix of 19
Linear algebraic equations, system of, characteristic-value problem 30 69 75
Linear algebraic equations, system of, characteristic-value problem, numerical methods 62 65 73 76
Linear algebraic equations, tridiagonal 344
Linear algebraic equations, trivial solution of 13 22
Linear dependence 25 83
Linear transformation 4
Matrix 4 166 285
Matrix, addition 8
Matrix, adjoint 14 17
Matrix, augmented 19
Matrix, canonical 77
Matrix, coefficient 19
Matrix, conformability 8
Matrix, conjugate 14
Matrix, diagonal 15 37 45 71
Matrix, differentiation 107(87)
Matrix, discriminant of 50
Matrix, elementary operation on 19 41
Matrix, equality 8
Matrix, equivalence 41
Matrix, function of 57
Matrix, hermitian 31 42 47
Matrix, invariant of 50
Matrix, inverse 16 97(27)
Matrix, latent root of 30
Matrix, modal 38 45 71
Matrix, modal, orthonormal 38 45 71
Matrix, multiplication 5 7 8
Matrix, nonsingular 13
Matrix, normal 103(67) 104(68 71)
Matrix, orthogonal 39
Matrix, partitioning 9
Matrix, positive definite 48 70
Matrix, rank of 18
Matrix, scalar 15
Matrix, singular 13
Matrix, symmetric 30
Matrix, trace of 51
Matrix, transpose of 13
Matrix, triangular 41
Matrix, unit 14
Matrix, unitary 45
Matrix, zero 15
Maxima and minima 119 193(1)
Membrane, deflection of 176 190
Membrane, vibration of 176 189
Mercer’s theorem 314(49)
Minimal properties of characteristic numbers 112(116—125) 194(5) 204(55) 328(93—95)
Minimal surface 126 137
Minor 11
Minor, principal 51
Modal column 30
Modal matrix 38 45 71 168
Modal matrix, orthonormal 38 45 71
Momental inertia force 156
Momentum 155
Multiple characteristic number 45
Natural boundary condition 128 173 176 177 180
Natural coordinates 168
Natural transition condition 129
Natural vibration mode 79 168
Negative definite matrix 105(76)
Neumann problem 178 310(38)
Neumann series 266
Nonconservative force 153
Nonsingular matrix 13
Norm 82 88
Norm, Hermitian 88
Normal coordinates 165
Normal matrix 103(67) 104(68 71)
Nullity 26
Numerical vector 23 54
Orthogonal matrix 39
Orthogonal transformation 42 56
Orthogonality of functions 82 88 252
Orthogonality of vectors 24 70
Orthogonalization 34
Orthonormal basis 36
Orthonormal modal matrix 38 45 71 168
Orthonormal set of functions 83
Orthonormal set of vectors 33
Parallelogram law 99(45)
Parametrization in calculus of variations 143
Parseval’s equality 86
Partitioning of matrix 9
Pendulum, compound 153 170
Pendulum, simple 152
Plate, deflection of 179
Poisson’s equation 177 240 303(27)
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