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Scarborough J.B. — Numerical Mathematical Analysis
Scarborough J.B. — Numerical Mathematical Analysis

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Название: Numerical Mathematical Analysis

Автор: Scarborough J.B.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1930

Количество страниц: 416

Добавлена в каталог: 17.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute error      3
Accuracy in determination of arguments      24
Accuracy in evaluation of formulas      19
Accuracy of addition      9
Accuracy of averages      10
Accuracy of division      13 17
Accuracy of interpolation formulas      84
Accuracy of linear interpolation      94
Accuracy of logs and antilogs      15 18
Accuracy of multiplication      12 17
Accuracy of powers and roots      14 18
Accuracy of products and quotients      12 13 17
Accuracy of subtraction      11 12
Adams, J.C.      267
Adams, J.C., method of      267
Adams, J.C., method of, remarks on      272
Addition, errors of      9
Adopted values (of physical constants)      20
Alternating series, error in      30
Antilogarithms, accuracy of      16 17
Approximate calculations      1
Approximate numbers      1
Arguments, accuracy in determination of      24
Arguments, exponential functions      26
Arguments, logarithms      24
Arguments, trigonometric functions      25
Asymptotic series      140 298
Average deviation      323
Average deviation, error      320
Averages, accuracy of      10
Averages, method of      357
Ballistic equations      251
Bessel's formula of interpolation      64
Bessel's formula of interpolation for interpolating to halves      64
Bessel's formula of interpolation, power series form of      81
Bessel's formula of interpolation, symmetrical form of      65
Binomial series      30
Binomial series, remainder term of      31
Carvallo      217
Caution in use of empirical formulas      405
Caution in use of quadrature formulas      142
Central-Difference formulas of interpolation      56
Central-Difference formulas, quadrature      124
Central-Difference formulas, quadrature, geometric significance of      128
Central-Difference formulas, quadrature, remainder terms in      165
Charlier, C.L.      169
Check formulas, for 12 ordinates      396 397
Check formulas, for 24 ordinates      401
Chevilliet's formula      161
Complex roots, computation of, by Graeffe's method      205
Complex roots, detection of      206
Convergence of iteration process, for algebraic and transcendental equations      186 193
Convergence of iteration process, for differential equations      256 257
Cubature, formula for      146
Cubature, general statement concerning      148
Cubature, mechanical      117 146
Derivatives and differences, relation between      86
Derivatives, nth      33
Derivatives, partial, of tabulated functions      117
Detection of complex roots      206
Deviation, average      323
Deviation, standard      323
Diagonal difference table      40
Difference of a polynomial      45
Difference, double      103
Differences      40
Differential equations, numerical solution of, accuracy of      264 275
Differential equations, numerical solution of, by Adams's method      267
Differential equations, numerical solution of, by iteration method      218
Differential equations, numerical solution of, by Milne's method      280
Differential equations, numerical solution of, by successive approximations      218
Differential equations, numerical solution of, by the Runge — Kutta method      273
Differential equations, numerical solution of, principle of      218
Differential equations, numerical solution of, starting the solution      222 267
Differentiation, Numerical      114
Differentiation, partial, of tabulated functions      117
Direct measurements      317
Division, accuracy of      13 17
Double differences      103
Double interpolation, by repeated single interpolation      96
Double interpolation, formula for      106
Double interpolation, formula for, remainder term of      111 112
Empirical formulas      351
Empirical formulas, caution in use of      405
Empirical formulas, finding best type of      383
Empirical formulas, finding constants in, by method of averages      357
Empirical formulas, finding constants in, by method of least squares      363
Empirical formulas, finding constants in, by plotting      351
Empirical formulas, finding constants in, when both variables are subject to error      380
Empirical formulas, finding constants in, when residuals are weighted      370
Empirical formulas, general case of non-linear formulas      374
Equal effects, method of      340
Equal effects, principle of      21
Equations, algebraic and transcendental      171
Equations, ballistic      251
Equations, differential, numerical solution of, accuracy of      264 275
Equations, differential, numerical solution of, by Adams's method      267
Equations, differential, numerical solution of, by Milne's method      280
Equations, differential, numerical solution of, by successive approximations      218
Equations, differential, numerical solution of, by the Runge — Kutta method      273
Equations, differential, numerical solution of, principle of      218
Equations, differential, numerical solution of, starting the solution      222 267
Equations, locating the roots of      171
Equations, solution of, by iteration      184 191
Equations, solution of, by method of false position      174
Equations, solution of, by Newton — Raphson method      178 187
Equations, solution of, by repeated plotting      177
Error function      288
Error in difference table, effect of      43 44
Error, absolute      3
Error, average      320
Error, inherent, in Euler's formula      169
Error, inherent, in Gauss's formula      167
Error, inherent, in Newton — Raphson method      183
Error, inherent, in Simpson's one-third rule      155 156 163
Error, inherent, in Simpson's three-eighths rule      155
Error, inherent, in Weddle's rule      155
Error, mean square      318
Error, mean, of gun      301
Error, of measurement      308
Error, percentage      3
Error, probable      319
Error, probable, percentage      338
Error, probable, relative      338
Error, relative      3
Errors, accidental      284
Errors, general formula for      7
Errors, of addition      9
Errors, of subtraction      11
Errors, relatively small      8
Errors, systematic      284
Euler      218
Euler's formula of quadrature      139
Euler's formula of summation      140
Euler's formula, compared with Simpson's rule      169
Euler's formula, error in      169
Euler, method of      223
Evaluation of formulas, accuracy in      19
Evaluation of probability integral      296
Exponential series, remainder term in      31 32
Extrapolation      53
False position, method of      174
Function G(v)      252
Function H(y)      251
Function table      96
Functional equation      290
Gauss      113 131
Gauss's quadrature formula      132
Gauss's quadrature formula, expressions for error in      167
Geometric significance of central-difference quadrature formulas      128
Geometric significance of Simpson's rule      120
Geometric significance of Weddle's rule      121
Geometric significance of Weierstrass's theorems      39
Graeffe's root-squaring method      198
Graeffe's root-squaring method, for complex roots      205
Graeffe's root-squaring method, for equal roots      214
Graeffe's root-squaring method, for real roots      201
Graeffe's root-squaring method, principle of      198
Graphical determination of constants in empirical formulas      351
Graphical solution of equations      177
Hermite's formula      112
Horizontal difference table      41
Index of precision      292
Indirect measurements      317 337
Indirect measurements, fundamental problems of      339
Integrating ahead, formula for      227
Integration, numerical      See "Numerical integration"
Interpolation series      84
Interpolation, accuracy of      84
Interpolation, Bessel's formulas for      64 65
Interpolation, definition of      38
Interpolation, double      96 104
Interpolation, inverse      75
Interpolation, Lagrange's formula for      73
Interpolation, Stirling's formula for      60
Interpolation, trigonometric      112
Inverse interpolation      75
Inverse interpolation, by Lagrange's formula      75
Inverse interpolation, by reversion of series      79
Inverse interpolation, by successive approximations      76
Iteration process for algebraic and transcendental equations      184 191
Iteration process for algebraic and transcendental equations, convergence of      186 193
Iteration process for differential equations      218 232
Iteration process for differential equations, convergence of      256 257
Iteration process for differential equations, maximum error due to      266
Lagrange's formula of interpolation      73
Lagrange's formula of interpolation, remainder term in      86 91
Lagrange's formula of interpolation, uses of      74
Law of accidental errors      284
Law of error of a function      296
Least squares, method of      363
Least squares, principle of      304
Linear interpolation, accuracy of      94
Linear interpolation, when permissible      95
Logarithmic series, remainder term in      32
Logarithms, accuracy of      15 16
Maclaurin's series      28
Maclaurin's series, remainder term in      28
Magnitude factor      329
Maxima and minima of tabulated functions      116
Mean error of gun      301
Mean square error      318
Measures of precision      318
Measures of precision, computation of, from residuals      324
Measures of precision, geometric significance of      322
Measures of precision, relations between      321
Merriman, Mansfield      380
Method of averages      357
Method of equal effects      340
Method of false position      174
Method of iteration      see "Iteration"
Method of successive approximations      218
Milne's method      280
Milne, W.E.      280
Modulus of complex roots, theorem relating to      212
Moors, B.P.      134 135
Moulton, F.R.      218 252
Multiplication, accuracy of      12 17
Negligible effects, criterion for      341
Newton — Raphson method      179
Newton — Raphson method, geometric significance of      181
Newton — Raphson method, inherent error in      183
Newton's formula for backward interpolation      50 51
Newton's formula for forward interpolation      48 49
Newton's formula, as a power series      80
Normal equations      364 372
Normal equations, rule for writing down      364 372
Numerical differentiation      114
Numerical integration      117
Numerical integration, by central-difference quadrature formulas      124
Numerical integration, by Euler's formula      139
Numerical integration, by Gauss's formula      131
Numerical integration, by Simpson's rule      119
Numerical integration, by Weddle's rule      121
Numerical solution of differential equations, accuracy of      266 275
Numerical solution of differential equations, advantages and disadvantages of      282
Numerical solution of differential equations, by Adams's method      267
Numerical solution of differential equations, by Milne's method      280
Numerical solution of differential equations, by Runge — Kutta method      273
Numerical solution of differential equations, by successive approximations      218 232
Numerical solution of differential equations, starting the      222 267
Partial derivatives of tabulated functions      117
Pearson, Karl      112
Percentage error      3
Percentage error, probable error      338
Picard, E.      218
Polynomial, differences of a      45
Polynomial, formula when nth differences are constant      385
Polynomials, use of approximating      225
Powers and roots, accuracy of      14 15 18
Precision and accuracy, difference between      317
Precision measures      318
Precision measures, computation of, from residuals      324
Precision measures, geometric significance of      322
Precision measures, relations between      321
Principle of equal effects      21
Principle of Graeffe's method      198
Principle of iteration process      218
Principle of least squares      304 305 307
Probability equation      292
Probability integral and its evaluation      296
Probability of errors lying between given limits      286
Probability of hitting a target      299
Probable error and weight, relation between      323
Probable error in indirect measurements      338
Probable error of a function      338
Probable error of a gun      301
Probable error of arithmetic and weighted means      324
Probable error, computation of, from residuals      324
Probable error, definition of      319
Probable error, formulas for      324 327 338
Probable error, meaning of      337
Product, accuracy of      12 17
Product, relative error of      12
Propagation of errors      338
Quadrature formulas in equidistant ordinates      117
Quadrature formulas, caution in use of      142
Quadrature formulas, central-difference      124
Quadrature formulas, Euler's      139
Quadrature formulas, Gauss's      131
Quadrature, mechanical      117
Quotient, accuracy of      13 17
Quotient, relative error of      13
Reciprocals of roots, relations between coefficients and      208
Regula falsi method      174
Rejection of observations and measurements, rule for      346
Relation between derivatives and differences      86
Relation between probable error and weight      323
Relation between roots and coefficients      201 208
Relative accuracy of Simpson's rules      155
Relative error and significant figures      3
Relative error and significant figures, theorems concerning      3 6
Relative error of a product      12
Relative error of a quotient      13
Relative error probable      338
Remainder term, in Bessel's formulas      89 90
Remainder term, in central-difference quadrature formulas      166
Remainder term, in Euler's formula      169
Remainder term, in formula for double interpolation      111 112
Remainder term, in formula for interpolating to halves      90 91
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