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Hildebrand F.B. — Methods of Applied Mathematics
Hildebrand F.B. — Methods of Applied Mathematics

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Название: Methods of Applied Mathematics

Автор: Hildebrand F.B.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1965

Количество страниц: 362

Добавлена в каталог: 01.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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