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| Rektorys K. — Survey of applicable mathematics |
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| Предметный указатель |
Parabola, sub-tangent, sub-normal 162
Parabola, theorems 161-2 223
Parabola, vertex and vertex tangent of 160
Parabolic equations 882 907-11
Parabolic segment, area and centroid of 141
Parabolic segment, moments of inertia of 142
Parabolic segment, point 364
Paraboloid, elliptic and hyperbolic, canonical and transformed equations 255
Paraboloid, elliptic and hyperbolic, theorems 250-1
Paraboloid, of revolution, volume, surface area, centroid, moment of inertia 149
Parallel areas theorem 662
Parallelcurves 334-5
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
Parallelvectors 265-6
PARAMETER 218
Parameter, admissible 302
Parameter, in integral 572-9
Parameter, of a parabola 160
Parametric equations of a circle 219-20
Parametric equations of a curve in a plane 218-20
Parametric equations of a straight line 208-9 243
Parametric function 1303-4
Parseval equality 699 1006
Partial derivatives 444
Partial differential equations see Differential Equations Partial
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 a line and a plane 246
Perturbation method (weakly nonlinear oscillator) 1095
Pfaffian equation 911-2
Pfaffian equation, geometric interpretation 912
Phase displacement 194
Piecewise smooth curve 298 602
Piecewise smooth curve function 443
Piecewise smooth curve surface 343 604
Pl cker's conoid 262
Plane curves, approximate constructions for 203-4
Plane curves, asymptotes of 326-30
Plane curves, asymptotic points on 340
Plane curves, constructions for 150-204
Plane curves, definition of 301 602
Plane curves, envelopes of a 1-parameter family of 330-4
Plane curves, explicit and implicit equations of 302
Plane curves, regular (or ordinary) points of 302
Plane curves, singular points 299 302 328-30
Plane curves, subtangent or subnormal 314
Plane figures, applications of integral calculus 650-3
Plane, affine transformation of a 228
Plane, equation of a 238-40
Plane, normal vector to a 238
Plane, projective transformation in a 228-9
Planes, bisection of angles between 2 intersecting 242
Planes, bundle (star) of 242
Planes, pencil (sheaf) of 241
Plate, deflection of a, rectangular, simply supported 1106-8
Plate, deflection of a, square, clamped on boundary 1122-3
Plemelj formulae 951
Point contacts of curves 310
Point of accumulation 994
Point of inflexion 322 429
Point of inflexion, ordinary, of first order 322
Point of self-tangency of curves 329
Poisson's differential equation 885
Poisson's distribution 1255-6
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 41
Polar coordinates, relations with cartesian coordinates 217-8
Polar coordinates, semi-axis or initial line 216
Polar graph paper 1188
Polar line 326
Polar sub-tangent 175
Pole (polar coordinates) 216
Pole (polar coordinates), (functions of a complex variable) 960
Polhodes, moving and fixed 165
Polygon method of solving differential equations for initial value problems 1073-5
Polygon, area of 207
Polygon, conformal mapping of upper half-plane on 992
Polygon, method for differential equations 1073-5
Polygon, regular, geometrical elements of 136-7
Polynomials 58-61 402
Polynomials, Chebyshev, Hermite, Jacobi, Laguerre 727-9
Polynomials, degree, definition 58
Polynomials, divisor, definition 58
Polynomials, Hermitian forms 100-6
Polynomials, Homer's method 60-61
Polynomials, Jacobi 727-8
Polynomials, Legendre 722-6
Polynomials, linear factor of 59
Polynomials, product and quotient 58
Polynomials, quadratic forms 100-6
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 orientation 212 234
Positive sense of orientation, of a curve with respect to a region 628
Potential equation 1102-3
Potentials of single and double layers 895
Power curves 163-5
Power functions of a complex variable 967
Power series 674-81 955
Power series, absolute convergence 680-1
Power series, applications of 687-90
Power series, arithmetic operations with 676
Power series, convergence 675-8 955
Power series, definition and theorems 674-8 955-6
Power series, differentiation and integration 678-81 956
Power series, expansion of solution to differential equation in a 1069-71
Power series, expansions into 683-6
Power series, in 2 or more variables 680
Power series, inversion 676-7
Power series, substitution into another power series 678
Power series, with centre at the origin 675
Powers of natural numbers 54-5
Powers of trigonometric functions 114
Powers with integral exponents 49-50
Precision, modulus of 1316
Preservation of the region, theorem on 457
Prime ends, Carath odory's theory of 985
Primitive function 486-7
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, addition rule for 1245 1247
Probability, Bernoulli experiment 1246
Probability, classical definition of 1245
Probability, conditional 1248
Probability, density 1249
Probability, distributions 1249 1255
Probability, expectation 1279
Probability, graph paper 1188
| Probability, law of large numbers 1261-2
Probability, multiplication rule for 1246
Probability, normal approximation 1256-7
Probability, normal distribution, general 1253
Probability, normal distribution, importance as approximation to other distributions 1254
Probability, normal distribution, standard 1252
Probability, of complement to an event 1245
Probability, of events 1245-8
Probability, probabilities see also Random variables
Probability, random sampling without replacement 1247
Probability, random variables 1248
Probability, theory 1245-63
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 266-8
Projective transformations of a plane 228-9
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 to 111
Quadrants, signs of trigonometric functions in 111
Quadratic and Herrnitian forms 100-6
Quadratic and Herrnitian forms, congruent 106
Quadratic and Herrnitian forms, functional, theorem on minimum of 1046
Quadratic and Herrnitian forms, matrix notation 102
Quadratic equations 77-79
Quadratic tensor 285
Quadratic tensor, discriminant of 77
Quadrics 247-57
Quadrics, canonical equations 254-6
Quadrics, cone 252
Quadrics, cylinders 252-3
Quadrics, degenerate 256
Quadrics, general equations 253-5
Quadrics, transformed equations 253-5
Quadrilateral geometrical formulae 134-5
Quality control of manufactured products 1279-84
Quartic equations see Biquadratic
Raabe test for convergence of a series 385-6
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,  -quantile 1251
Random variables, coefficient of variation 1251
Random variables, discrete and continuous 1248-9
Random variables, discrete and continuous, variance of 1250-1
Random variables, distribution(s), basic-integral valued 1255-7
Random variables, distribution(s), law 1248
Random variables, distribution(s), normal 1253-4
Random variables, distribution(s), Poisson's, of rare events 1256
Random variables, expectation of a sum, product, ratio 1259-60
Random variables, expectation of a sum, product, ratio, addition theorem 1259
Random variables, families of 1257-9
Random variables, functions of 1320-1
Random variables, integral-valued 1255-7
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, standard deviation 1251
Random variables, standard normal distribution 1252-4
Random variables, variance of a sum of 1260-1
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 592-3
Rectangular simply supported plate, deflection of 1106-8
Rectification of circle, Kochinski's 151-2
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) 995-6
Region(s), closed, of type A 603 605
Region(s), closed, with boundary included 996
Region(s), connected,  -tuply connected, simply connected 996
Region(s), of Carathodory's type (C-region) 988
Region(s), of type. A 603 605
Region(s), regular 900
Region(s), solid (or three-dimensional) of type A 605
Region(s), theorem on preservation of 457
Regression coefficient 1266
Regression functions, linear 1288-91
Regression functions, linear, with several independent variables 1297-9
Regression functions, nonlinear 1299-1301
Regula falsi method 1179 1237
Regular conic sections 227
Regular functions 941
Regular hypersurfaces 1035-6
Regular mapping 455-8
Regular nets (and irregular) 1112-3
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 136-7
Relative accuracy of a scale 1187
Relative complement of sets 83
Relative maximum and minimum 430 476
Relaxation method in solving linear algebraic equations 1157-8
Removable singular point on a curve or surface 299 347
Removable singularity theorem 890-1
Repeated integrals 611
Residual sum of squares 1307
Residue theorem 962-5
Resolvent (Green's) 815
Resonance curve 196 200
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