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Rektorys K. (ed.) — Survey of Applicable Mathematics
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Íàçâàíèå: Survey of Applicable MathematicsÀâòîð: 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.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1969Êîëè÷åñòâî ñòðàíèö: 1369Äîáàâëåíà â êàòàëîã: 06.12.2013Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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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