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Herriot J.G. — Methods of mathematical analysis and computation
Herriot J.G. — Methods of mathematical analysis and computation

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Название: Methods of mathematical analysis and computation

Автор: Herriot J.G.

Аннотация:

Серия монографий по математическому анализу и вычислениям.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1963

Количество страниц: 210

Добавлена в каталог: 11.12.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\Delta$ operator      2 4
Adams' method      147
Adams' method, modified      148
Adjoint differential equation      130 131
Adjoint matrix      62 63 84
Aitken's $\delta^{2}$-process      100 101 105 106
Aitken, A.C.      95 96 101 103
Augmented matrix      66
Backward difference      8
Bairstow method      44—47
Bi-orthogonal system of vectors      110
Bilinear resolution of matrix      104
Birge — Vieta method      44
Canonical box      90
Cauchy's problem      174
Cayley — Hamilton theorem      83 84
cell      186
Central difference      12
Central-difference interpolation formulas      10—14
Characteristic equation of matrix      81 84
Characteristic function of matrix      80
Characteristic numbers of matrix      80 81
Characteristic numbers of matrix, calculation of      92—111
Characteristic polynomial of matrix      80 84
Characteristic vectors of matrix      80 81
Characteristic vectors of matrix, calculation of      92—111
Characteristics of wave equation      176
Closed formulas      29
Coefficients of double Fourier series, formulas for      168
Coefficients of Fourier series, formulas for      156
Cofactor      56
Column vector      53
Complementary function      121 124 136 163 164
Corrected value      139 145 148 152 153
Corrector formula      138 145 148 152 153
Cramer's rule      65
Crout method of elmination      73—79
Crout method of elmination, check column for      76
Deflation      92 103—107
Descartes' Rule of Signs      48
Determinant, evaluation of      56 76
Determinant, principal minor of      82
Diagonal matrix      62
Difference of factorial polynomial      5
Difference table      2 8 12
Difference, backward      8
Difference, central      12
Difference, forward      2
Difference, repeated      2 3 8 12
Differential equation      112
Differential equation, order      113
Differential equation, ordinary      see "Ordinary differential equation"
Differential equation, partial      see "Partial differential equation"
Dirichlet's problem      173
Dirichlet, theorem of      157
Discriminant of quadratic form      88
Double Fourier series      168—171
Double Fourier series, formulas for coefficients of      168
Double Fourier series, half-range      169
E operator      4
Eigenvalues of matrix      81
Eigenvector of matrix      81
Elimination, Crout method of      73—79
Elliptic partial differential equation      174 175 186—190
Elliptic partial differential equation, finite-difference approximation for      186
Elliptic partial differential equation, stencil for      187
Equality, of matrices      55
Equality, of vectors      53
Error, in numerical differentiation formulas      32 33
Error, in numerical integration formulas      31 32
Error, in polynomial approximation      20 21
Euler's method for ordinary differential equation      118
Even function      157 160
Everett's interpolation formula      14
Exact ordinary differential equation      128 129
Explicit difference method for parabolic partial differential equation      181
Factorial polynomial      5
Factorial polynomial, difference of      5
False position, method of      36—39
Finite discontinuity      157
Finite-difference approximation, for elliptic partial differential equation      186
Finite-difference approximation, for hyperbolic partial differential equation      176
Finite-difference approximation, for parabolic partial differential equation      181 182
Forward difference      2
Fourier cosine series      162
Fourier series      155—172
Fourier series, application to solution of ordinary differential equations      162—165
Fourier series, application to solution of partial differential equations      165—168
Fourier series, double      168—171
Fourier series, formulas for coefficients of      156
Fourier series, half-range      161 162
Fourier sine series      161
Gauss — Jordan method of      71 72
Gauss — Jordan method of elimination      71 72
Gauss — Seidel iteration      79 80
Gauss's interpolation formula, backward      13
Gauss's interpolation formula, forward      11 12
Gauss's method of      67—71 183
Gauss's method of elimination      67—71 183
Givens' method, for general complex matrix      111
Givens' method, for real symmetric matrix      110
Green's function      135
Half-range double Fourier series      169
Half-range Fourier series      161 162
Hamilton — Cayley theorem      83 84
Hamming, R.W.      146
Heat conduction problem, in one dimension      174
Heat conduction problem, in two dimensions      171
Heat conduction problem, steady-state      172
Heat equation, Fourier series solution of      165—168
Hermitian form      89
Hermitian matrix      89
Higher-order ordinary differential equation      151—154
Hyperbolic partial differential equation      174 175—180
Hyperbolic partial differential equation, fininte-difference approximation for      176
Hyperbolic partial differential equation, stencil for      177
Identity matrix      62
Implicit difference method for parabolic partial differential equation      182
Indicial function      133
Initial-value problem      174
Inner product of vectors, complex components      86
Inner product of vectors, real components      54
Integrating factor for ordinary differential equation      128 130
Interpolating function      1
Interpolating polynomial      1
Interpolation      1—21
Interval of dependence      176
Inverse interpolation      19
Inverse matrix      62
Inverse matrix, calculation of      69 72 78
Iterative procedure for square root      41
Iterative process, order of      39 40
Jacobi method, for characteristic numbers      108
Jacobi method, variations of      109
Jordan canonical form of matrix      90
Jump discontinuity      131 157
Kronecker delta      15 57
Lagrange three-point interpolation, coefficients for      17
Lagrange's interpolation formula      15
Lagrangian coefficient function      15 17
Lanczos' method for reduction of matrix to tri-diagonal form      110
Laplace's differential equation      172 173
Latent roots of matrix      81
Latent vector of matrix      81
Lattice points      186
Left-hand limit      157
Length of vector      54
Lineal element      116
Linear differential equation      120—137
Linear differential equation, constant coefficients      120—125
Linear differential equation, first order      127
Linear differential equation, second order      129
Linear equations      52—111
Linear transformation      57
Linearly dependent vectors      55
Linearly independent solutions of ordinary differential equations      121
Linearly independent vectors      55
Link of net      186
Lipschitz condition      119
Lower triangular matrix      68
Matrices, equality of      55
Matrices, similar      89
Matrices, sum of      55
Matrix      55
Matrix multiplication      57—61
Matrix polynomial      84
Matrix, bilinear resolution of      104
Matrix, characteristic equation of      81 84
Matrix, characteristic function of      80
Matrix, characteristic numbers of      80 81
Matrix, characteristic numbers of, calculation of      92—111
Matrix, characteristic polynomial of      80 84
Matrix, characteristic vectors of      80 81
Matrix, characteristic vectors of, calculation of      92—111
Matrix, diagonal      62
Matrix, eigenvalues of      81
Matrix, eigenvector of      81
Matrix, hermitian      89
Matrix, identity      62
Matrix, inverse of      62
Matrix, inverse of, calculation of      69 72 78
Matrix, Jordan canonical form      90
Matrix, latent roots of      81
Matrix, latent vector of      81
Matrix, lower triangular      68
Matrix, minimum polynomial of      85
Matrix, nonsingular      62
Matrix, orthogonal      64
Matrix, power of      83
Matrix, principal diagonal of      62
Matrix, proper numbers of      81
Matrix, proper values of      81
Matrix, proper vector of      81
Matrix, rank of      66
Matrix, reduction to tri-diagonal form      110
Matrix, secular equation of      81
Matrix, singular      62
Matrix, spectrum of      81
Matrix, square      55
Matrix, symmetric      61
Matrix, trace of      82
Matrix, transpose      61 86
Matrix, tri-diagonal      110 111 183
Matrix, unit      62
Matrix, upper triangular      68
Mesh of net      186
Milne and Reynolds      146
Milne's method      145—147
Milne's method for second-order differential equation      152—154
Milne's method for systems of differential equations      151 152
Minimum polynomial of matrix      85
Minor      56
Modified Adams' method      148
Multiplication of matrix, by matrix      57—61
Multiplication of matrix, by scalar      56
Newton — Raphson method      39—44
Newton's backward-difference formula      7—10
Newton's forward-difference formula      4—7 10
Newton's three-eighths rule      28 32 146
Node of net      186
Nonsingular matrix      62
Numerical differentiation      22—25 32 33
Numerical integration      22 25—32
Numerical solution of ordinary differential equations      117 137—154
Numerical solution of partial differential equations      173—190
Odd function      157
Open formulas      29
Operator $\Delta$      2 4
Operator E      4
Ordinary differential equation      112—154
Ordinary differential equation, Adams' method      147
Ordinary differential equation, Adams' method, modified      148
Ordinary differential equation, adjoint equation      130 131
Ordinary differential equation, application of Fourier series to solution of      162—165
Ordinary differential equation, auxiliary equation      121
Ordinary differential equation, complete      120
Ordinary differential equation, direction field      116
Ordinary differential equation, Euler's method      118
Ordinary differential equation, exact      128 129
Ordinary differential equation, existence theorem      119
Ordinary differential equation, first-order      137
Ordinary differential equation, general solution of      114
Ordinary differential equation, graphical solution of      116
Ordinary differential equation, higher-order      151—154
Ordinary differential equation, homogeneous      120
Ordinary differential equation, integral curve of      116
Ordinary differential equation, integrating factor      128 130
Ordinary differential equation, isocline      116
Ordinary differential equation, linear      120—137
Ordinary differential equation, linear, constant coefficients      120—125
Ordinary differential equation, linear, first-order      127
Ordinary differential equation, linear, second-order      129
Ordinary differential equation, linearly independent solutions of      121
Ordinary differential equation, Milne's method      145—147 151—154
Ordinary differential equation, modified Adams' method      148
Ordinary differential equation, nonhomogeneous      120
Ordinary differential equation, numerical solution of      117 137—154
Ordinary differential equation, particular solution of      114
Ordinary differential equation, reduced      120
Ordinary differential equation, Runge — Kutta method      149—151
Ordinary differential equation, solution of      114
Ordinary differential equation, solution of, by graphical procedure      116
Ordinary differential equation, stability problem      146
Ordinary differential equation, starting solution of      140—145
Ordinary differential equation, variation of parameters, method of      125—127
Ordinary differential equations, system of      113 151 152
Orthogonal matrix      64
Orthogonal vectors      54
Overrelaxation      188
Parabolic partial differential equation      174 175 180—186
Parabolic partial differential equation, explicit method for      181
Parabolic partial differential equation, finite-difference approximation for      181 182
Parabolic partial differential equation, implicit method for      182
Parabolic partial differential equation, stability of numerical solution      181 182
Parabolic partial differential equation, stencil for explicit method      181
Parabolic partial differential equation, stencil for implicit method      182
Partial differential equation      112 165—172 173—190
Partial differential equation, application of Fourier series to solution of      165—172
Partial differential equation, elliptic      174 175 186—190
Partial differential equation, hyperbolic      174 175—180
Partial differential equation, numerical solution of      173—190
Partial differential equation, parabolic      174 175 180—186
Partial differential equations, classification of      1^4
Periodic function      155
Piecewise continuous function      131
Polynomial equations, solution of      42—51
Positive definite quadratic form      88
Power method      92 93—103
Power method, acceleration of convergence      100 102
Power of matrix      83
Predicted value      139 145 148 151 152
Predictor formula      138 145 148 151 152
Predictor-corrector method      139 140 145 148 151—154
Principal diagonal      62
Principal minor of determinant      82
Proper numbers of matrix      81
Proper values of matrix      81
Proper vector of matrix      81
Quadratic form      88
Quadratic form, discriminant of      88
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