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Rektorys K. (ed.) — Survey of Applicable Mathematics
Rektorys K. (ed.) — Survey of Applicable Mathematics



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Íàçâàíèå: Survey of Applicable Mathematics

Àâòîð: Rektorys K. (ed.)

Àííîòàöèÿ:

This major two-volume handbook is an extensively revised, updated second edition of the highly praised Survey of Applicable Mathematics, first published in English in 1969.
The thirty-seven chapters cover all the important mathematical fields of use in applications: algebra, geometry, differential and integral calculus, infinite series, orthogonal systems of functions, Fourier series, special functions, ordinary differential equations, partial differential equations, integral equations, functions of one and several complex variables, conformal mapping, integral transforms, functional analysis, numerical methods in algebra and in algebra and in differential boundary value problems, probability, statistics, stochastic processes, calculus of variations, and linear programming. All proofs have been omitted. However, theorems are carefully formulated, and where considered useful, are commented with explanatory remarks. Many practical examples are given by way of illustration. Each of the two volumes contains an extensive bibliography and a comprehensive index.
Together these two volumes represent a survey library of mathematics which is applicable in many fields of science, engineering, economics, etc.
For researchers, students and teachers of mathematics and its applications.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1969

Êîëè÷åñòâî ñòðàíèö: 1369

Äîáàâëåíà â êàòàëîã: 06.12.2013

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Parabolic equations      882 907—911
Parabolic segment, area and centroid of      141
Parabolic segment, moments of inertia of      142
Parabolic segment, point      364
Paraboloid of revolution, volume, surface area, centroid, moment of inertia      149
Paraboloid, elliptic and hyperbolic, canonical and transformed equations      255
Paraboloid, elliptic and hyperbolic, theorems      250—251
Parallel, areas theorem      662
Parallel, curves      334—335
Parallel, vectors      265—266
Parallelepiped      142
Parallelism, condition for, of 2 straight lines      213 246
Parallelism, condition for, of a line and a plane      247
Parallelogram, geometrical formulae      135
PARAMETER      218
Parameter in integral      572—579
Parameter of a parabola      160
Parameter, admissible      302
Parametric equations of a circle      219—220
Parametric equations of a curve in a plane      218—220
Parametric equations of a straight line      208—209 243
Parametric function      1303—1304
Parseval equality      699 1006
Partial derivatives      444
Particular integral      731
Pascal's limacon      191
Pedal curve      341
Pencil of lines      211
Pencil of planes      241
Pentkovskij's skeleton nomograms      1206
Periodic solutions of differential equations      774 1095
Permutations and combinations      55—57
Perpendicularity, condition for, of 2 planes      240
Perpendicularity, condition for, of 2 straight lines      214 246
Perpendicularity, condition for, of a line and a plane      246
Perturbation method (weakly nonlinear oscillator)      1095
Pfaffian equation      911—912
Pfaffian equation, geometric interpretation      912
Phase displacement      194
Piecewise smooth curve      298 602
Piecewise smooth function      443
Piecewise smooth surface      343 604
Plane curves, approximate constructions for      203—204
Plane curves, asymptotes of      326—330
Plane curves, asymptotic points on      340
Plane curves, constructions for      150—204
Plane curves, definition of      301 602
Plane curves, envelopes of a one-parameter family of      330—334
Plane curves, explicit and implicit equations of      302
Plane curves, regular (or ordinary) points of      302
Plane curves, singular points      299 302 328—330
Plane curves, subtangent or subnormal      314
Plane figures, applications of integral calculus      650—653
Plane, affine transformation of a      228
Plane, equation of a      238—240
Plane, normal vector to a      238
Plane, projective transformation in a      228—229
Planes, bisection of angles between two intersecting      242
Planes, bundle (star) of      242
Planes, pencil (sheaf) of      241
Plate, deflection of a rectangular, simply supported      1106—1108
Plate, deflection of a square, clamped on boundary      1122—1123
Plemelj formulae      951
Pluecker's conoid      262
Point of accumulation      994
Point of inflexion      322 429
Point of inflexion, ordinary, of first order      322
Point of self-tangency of curves      329
Point, contacts of curves      310
Poisson's differential equation      885
Poisson's distribution      1255—1256
Poisson's integral      894
Polar coordinates      216
Polar coordinates in solid analytic geometry      234
Polar coordinates of plane curves, direction of tangent, curvature, asymptotes      338—341
Polar coordinates, relations with cartesian coordinates      217—218
Polar coordinates, semi-axis or initial line      216
Polar graph paper      1188
Polar line      326
Polar sub-tangent      175
Pole (functions of a complex variable)      960
Pole (polar coordinates)      216
Polhodes, moving and fixed      165
Polygon method of solving differential equations for initial value problems      1073—1075
Polygon, area of      207
Polygon, conformal mapping of upper half-plane on      992
Polygon, method for differential equations      1073—1075
Polygon, regular, geometrical elements of      136—137
Polynomials      58—61 402
Polynomials, Chebyshev, Hermite, Jacobi, Laguerre      727—729
Polynomials, degree, definition      58
Polynomials, divisor, definition      58
Polynomials, Hermitian forms      100—106
Polynomials, Horner's method      60—61
Polynomials, Jacobi      727—728
Polynomials, Legendre      722—726
Polynomials, linear factor of      59
Polynomials, product and quotient      58
Polynomials, quadratic forms      100—106
Polynomials, real coefficients with      60
Polynomials, sum and difference      58
Polynomials, Taylor's formula      61
Polynomials, zero      58
Population characteristics      1277
Position ratio of a point      227
Position vector      264
Positive half line      212
Positive numbers      41
Positive sense of a curve with respect to a region      628
Positive sense of orientation      212 234
Potential equation      1102—1103
Potentials of single and double layers      895
Power curves      163—165
Power series      674—681 955
Power series in 2 or more variables      680
Power series with centre at the origin      675
Power series, absolute convergence      680—681
Power series, applications of      687—690
Power series, arithmetic operations with      676
Power series, convergence      675—678 955
Power series, definition and theorems      674—678 955—956
Power series, differentiation and integration      678—681 956
Power series, expansion of solution to differential equation in a      1069—1071
Power series, expansions into      683—636
Power series, inversion      676—677
Power series, substitution into another power series      678
Power(s) of natural numbers      54—55
Power(s) of trigonometric functions      114
Power(s) with integral exponents      49—50
Power(s), functions of a complex variable      967
Precision, modulus of      1316
Preservation of the region, theorem on      457
Prime ends, Caratheodory's theory of      985
Primitive function      486—487
Primitive period of a sine curve      193
Principal, normal (unit vector) of a curve      306
Principal, vectors      265
Prism, centroid of      142
Prism, truncated triangular      142
Prism, volume and surface areas of      142
Probability, probabilities      see also "Random variables"
Probability, probabilities, addition rule for      1245 1247
Probability, probabilities, Bernoulli experiment      1246
Probability, probabilities, classical definition of      1245
Probability, probabilities, conditional      1248
Probability, probabilities, density      1249
Probability, probabilities, distributions      1249 1255
Probability, probabilities, expectation      1279
Probability, probabilities, graph paper      1188
Probability, probabilities, law of large numbers      1261—1262
Probability, probabilities, multiplication rule for      1246
Probability, probabilities, normal approximation      1256—1257
Probability, probabilities, normal distribution, general      1253
Probability, probabilities, normal distribution, importance as approximation to other distributions      1254
Probability, probabilities, normal distribution, standard      1252
Probability, probabilities, of complement to an event      1245
Probability, probabilities, of events      1245—1248
Probability, probabilities, random sampling without replacement      12
Probability, probabilities, random variables      1248
Probability, probabilities, theory      1245—1263
Probit scale      1272
Producer's risk      1280
Product method      1098—1108
Product of matrices      87
Product of sets      83
Product of tensors      293
Product of vectors      266—268
Projective transformations of a plane      228—229
Projective transformations of a regular conic section      229
Prolate circular involute      173
Prolate cycloid      167
Prolate epicycloid      169
Prolate spheroid      148 248
Proper value of eigenvalue problem      804 915 1015
Pure point spectrum      1016
Pyramid, centroid, position of      143
Pyramid, frustum, volume of      144
Pyramid, regular frustum, lateral area of      144
Pyramid, triangular, volume of      143
Quadrants, definition      206
Quadrants, first, reduction of trigonometric functions      111
Quadrants, signs of trigonometric functions in      111
Quadratic and Hermitian forms      100—106
Quadratic and Hermitian forms, congruent      106
Quadratic and Hermitian forms, matrix notation      102
Quadratic equations      77—79
Quadratic functional, theorem on minimum of      1046
Quadratic tensor      285
Quadratic tensor, discriminant of      77
Quadrics      247—257
Quadrics, canonical equations      254—256
Quadrics, cone      252
Quadrics, cylinders      252—253
Quadrics, degenerate      256
Quadrics, general equations      253—255
Quadrics, transformed equations      253—255
Quadrilateral, geometrical formulae      134—135
Quality control of manufactured products      1279—1284
Quartic equations      see "Biquadratic"
R-integrability      see "Riemann"
Raabe test for convergence of a series      385—386
Radius of circle, circumscribed on triangle      118
Radius of circle, inscribed in triangle      118
Radius of convergence of a power series      675 955
Radius of curvature      315 324 366
Radius of torsion      316
Radius vector of centre of mass of a system of particles      238
Random errors      1316
Random variables      1248
Random variables, coefficient of variation      1251
Random variables, discrete and continuous      1248—1249
Random variables, discrete and continuous, variance of      1250—1251
Random variables, distribution(s), basic-integral valued      1255—1257
Random variables, distribution(s), law      1248
Random variables, distribution(s), normal      1253—1254
Random variables, distribution(s), Poisson's, of rare events      1256
Random variables, expectation of a sum, product, ratio      1259—1260
Random variables, expectation of a sum, product, ratio, addition theorem      1259
Random variables, families of      1257—1259
Random variables, functions of      1320—1321
Random variables, integral-valued      1255—1257
Random variables, median      1251
Random variables, mode of      1251
Random variables, multinomial      1258
Random variables, normal distribution of      1252
Random variables, normal distribution of, for a pair      1259
Random variables, normal distribution of, probabilities of events determined by      1253
Random variables, P-quantile      1251
Random variables, standard deviation      1251
Random variables, standard normal distribution      1252—1254
Random variables, variance of a sum of      1260—1261
Rank of a matrix      64
Rank of a quadratic form      101
Rank of a system of vectors      63
Rational curve      301
Rational functions, integration of      495—500
Rational integral function      58
Rational numbers      41
Rational numbers, field of      86
Rayleigh's quotient      808 1048 1090
Real cone, canonical and transformed equations      254
Real function      397
Real numbers      42—44
Real numbers, absolute value      46
Real numbers, algebraic and transcendental      43
Real numbers, bounds (greatest lower, least upper) of      43
Real numbers, general powers of      51—52
Real numbers, inequalities between      44—46
Real numbers, roots of      50—51
Real space      998
Rearrangement of a series      384
Reciprocal equations      81—82
Reciprocal spiral      176
Rectangle of given perimeter having greatest area      433
Rectangular coordinates      205 233
Rectangular graph paper      1188
Rectangular rule for definite integrals      592—593
Rectangular simply supported plate, deflection of      1106—1108
Rectification of circle, Kochinski's      151—152
Rectification of circle, Sobotka's      152
Rectifying plane      309
Reduced equations of a straight line      243
Refinement of nets      1113
Reflection, cartesian coordinate system      236
Reflection, Riemann — Schwarz principle      983
Region(s)      995—996
Region(s) of Caratheodory's type (C-region)      988
Region(s) of type A      603 605
Region(s), closed, of type A      603 605
Region(s), closed, with boundary included      996
Region(s), connected, k-tuply connected, simply connected      996
Region(s), regular      900
Region(s), solid (or 3-dimensional) of type A      605
Region(s), theorem on preservation of      457
Regression coefficient      1266
Regression functions, linear      1288—1291
Regression functions, linear, with several independent variables      1297—1299
Regression functions, nonlinear      1299—1301
Regula falsi method      1179 1237
Regular conic sections      227
Regular functions      941
Regular hypersurfaces      1035—1036
Regular mapping      455—458
Regular nets (and irregular)      1112—1113
Regular point of a curve      299
Regular point of a curve, of a function of a complex variable      957
Regular point of a curve, of a surface      347
Regular polygon, geometrical elements of      136—137
Relative accuracy of a scale      1187
Relative complement of sets      83
Relative maximum and minimum      430 476
Relaxation method in solving linear algebraic equations      1157—1158
Removable singular point on a curve or surface      299 347
Removable singularity theorem      890—891
Repeated integrals      611
Residual sum of squares      1307
Residue theorem      962—965
Resolvent (Green's)      815
Resonance curve      196 200
Revolution, surfaces of      257—259
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