P
pair, ordered, 294 parabola, 203 arclength, 204 area, 204 axis, 203 binomial, 69 cubic, 63 diameter, 204 directrix, 203 equation, 203 focus, 203 intersection figure, 221 n-th degree, 64 parameter, 203 quadratic polynomial, 62 radius of curvature, 204 semicubic, 93 semifocal chord, 203 tangent, 204 transformation, 205 vertex, 203 paraboloid, 221 elliptic, 221 hyperbolic, 222 central surface, 224 invariant signs elliptic, 224 hyperbolic, 224 parabolic, 224 of revolution, 222 parallel circle, 244 parallelepiped, 152 rectangular, 152 parallelism lines, 128 parallelism conditions line-plane, 219 lines in space, 219 planes, 216 parallelogram, 134 parallelogram identity, unitary space, 615 parameter, 11, 49 parabola, 203 statistical, 773 parameter space, stochastic, 765 parametric integral, 459 parametric representation, circle, 197 parametrized center of area method, 374 parity, 544 Parseval equation, 422, 516, 579, 618 formula, 729 partial fraction decomposition, 15 special cases, 1029 partial ordering, 297 partial sum, 406 partition, 297 Pascal limacon, 96 Pascal triangle, 13 path, 351 closed, 351 integration, 463 PCNF (principal conjunctive normal form), 345 PDNF (principal disjunctive normal form), 345 pencil of lines, 196 pendulum equation, 841 Foucault, 949 mathematical, 702 period, 703 pentagon, regular, 138 pentagram, 4 pentagram, regular, 138 percentage, 21 calculation, 21 performance score, 372 perimeter circle, 138 ellipse, 200 polygon, 137 period, 50 secant, 76 sine, 75, 82 tangent, 76 period doubling, 836 cascade, 837, 842 period parallelogram, 704 permutability, linear operators, 319 permutation, 745 cyclic, vectors, 207 group, 301 matrix, 892 with repetition, 745 without repetition, 745 perturbation, 535, 941 Pesin formula, 821, 828 phase initial, 82 portrait, dynamical systems. 800 shift, 75, 82 sine, 75, 82 space, dynamical systems, 797 spectrum, 727 physical units, 1012 Picard iteration method integral equation, 567 successive approximation method, 496 Picard-Lindelof theorem, 610 pivot, 891 column, 271, 852 element. 271. 852 row, 271, 852 scheme, 271 pivoting, 271, 274 column pivoting, 892 step, 271 plane equation general, 214 in space, 214 geometry, 128 intersecting, 158 rectifying, 239, 241 space, 150, 214 vector equation, 188 planes orthogonality, conditions, 216 parallel, 150 distance, 217 parallelism, conditions, 216 planimeter, 447 Poincare mapping, 808, 810 Poincare section, 841 point accumulation, 606 asymptotic, curve, 232 boundary, 606 circular, 249 coordinates, 189 corner, 232 cuspidal, curve, 232 discontinuity, 57 double, curve, 232 fixed, conformal mapping, 676 fixed, stable, 836 focal, ordinary differential equation, 495 improper, 192 infinite, 192 interior, 605 isolated, 606 isolated, curve, 232 limit, 237 limiting, 606 multiple, curve, 233 /(.-dimensional space, 117 nearest approach, 237 neighborhood, 605 non-wandering, 815 notion, 128 plane curve, 231 rational, 1 regular, surface, 244 saddle, ordinary differential equation, 495 singular, 225, 232 isolated, 494 ordinary differential equation, 494 surface, 244, 245 spectrum, 622 spiral, ordinary differential equation, 495 surface point circular, 249 elliptic, 248 hyperbolic, 249 parabolic, 249 spherical, 248 umbilical, 249 terminal, curve, 232 transversal homoclinic, 812 umbilical, 249 Poisson differential equation, partial, 538, 667, 670 distribution, 757 formula, 536 integral, 533 polar, 162 angle, 190 axis, 190 coordinates, plane, 190 coordinates, spherical, 209 coordinates, transformation, 191 distance, 244 equation, 542 curve second order, 207 subnormal, 227 subtangent, 227 pole complex function, 673 function, 58 left, 162 multiplicity m, complex function, 693 on the sphere, 162 order m, complex function, 693 origin, 190 right, 162 Polish notation, 355 polyeder, 151 polygon area 2n-gon, 138 n-gon, 137 base angle, 137 central angle, 137 circumcircle radius, 137 circumscribing, 137 exterior angle, 137 inscribed circle radius, 137 interior angle, 137 perimeter, 137 plane, 137 regular, convex, 137, 138 side length, 137 similar, 133 polyhedral angle, 151 polyhedron, 151 convex, 154 regular, 154 polynomial, 62 Bernstein, 935 characteristic, 278 Chebyshev formula, 87 division algorithm, 315 division with remainder, 315 equation, numerical solution, 887 first degree, 62 Hermite, 545, 617 integral rational function, 60 interpolation, 917 irreducible, 315 Laguerre, 513, 617 Legendre, 511, 616 minimal, 316 n-th degree, 63 primitive, 315 product representation, 43 quadratic, 62 ring, 315 second degree, 62 third degree, 63 trigonometric, 927 polynomials. 11 Chebyshev, 924 orthogonal, 920 population, 769 two-stage, 754 Posa theorem, 353 position coordinate, reflection, 269 positive definite, 893 postfix notation, 355 postman problem, Chinese, 352 potential complex, 681 equation, 538 field, 662 conservative, 662 rotation, 656 retarded, 537 power complex number, 37 notion, 7 real number, 7 reciprocal, 68 power series, 416 asymptotic, 419, 420 complex terms, 690 expansion, analytic function, 689 inverse, 417 power set, 298 power spectrum, 818 precession angle, 211 predicate, 289 logic, 289 n-ary, 289 predictor, 906 predictor-corrector method, 906 prefixes, metric, 1012 pre-Hilbert space, 615 present value, 25 pressure, 451 prime coprime, 5, 14 decomposition, canonical, 321 element numbers, 320 polynomials, 315 factorization, 321 canonical, 321 Fermat, 321 Mersenne, 321 notation (measurement protocol), 788 number, 320 pair, 321 quadruplet, 321 relatively, 14 triplet, 321 prime formula, predicate logic, 289 principal (a sum of money), 21 principal axis direction, 265 transformation, 264 principal ideal, 313 principal normal section, surface, 248 space curve, 239, 241 principal quantities, 11 principal value integral, improper, 454 inverse hyperbolic function, 700 inverse trigonometric function, 84, 700 logarithm, 698, 700 principle Cauchy, 608 contracting mapping, 608 extensionality, 291 extrapolation principle, 902 Neumann, 307 of bivalence, 286 prism, 151 lines, 151 regular, 151 probability area interpretation, 752 conditional, 750 definition, 749 total, 750 probability integral, 759 probability measure, 816 ergodic, 820 invariant, 816 probability paper, 774 probability theory, 745, 747 probability vector, 767 problem Cauchy, 518 Dirichlet, 528, 670 discrete, 921 inhomogeneous, 537 multidimensional computation of adjustments, 922 Neumann, 670 regularized, 278 scheduling, 861 shortest way, 351 Sturm-Liouville, 515 two-body, 520 process birth process, 769 death process, 769 orthogonalization process, 280 Poisson process, 768 stochastic, 765 product, 7 algebraic, 366 Cartesian fuzzy sets, 369 n-ary, 370 sets,294 cross, 183 derivative, 381 direct group, 301 ft-algebra, 341 dot, 183 drastic, 366 dyadic, 255 dyadic, tensors, 264 inner product, 615 Kronecker, 258 n times direct, 343 product sign, 7 rules of calculation, 7 scalar, 183, 255 vector, 183 programming, 846 computer algebra system, 955 continuous dynamic, 878 discrete dynamic, 878 Bellman functional equation, 879 Bellman functional equation method, 881 Bellman optimality principle, 880 constraint dynamic, 878 constraint static, 878 knapsack problem, 879 problem, 878 purchasing problem, 879 state vector, 878 linear, 846 linear, transportation problem, 857 Maple, 977 Mathematica, 966 problem dual problem, 856 primal problem, 856 programming, discrete continuous dynamical, 878 cost function, 879 decision, 878 decision space, 878 dynamic, 878 functional equation, 880 Bellman, 879 method, 881 knapsack problem, 879, 882 minimum interchangeability, 880 minimum separability, 879 n-stage decision process, 878 optimal policy, 881 optimal purchasing policy, 881 purchasing problem, 879 state costs, 878 state vector, 878 programming, linear constraints, 846 forms, 846 general form, 846 properties, 848 scheduling problem, 861 programming, non-linear see optimization, non-linear, 861 projection sides, 142 projection theorem, orthogonal space, 616 projector, 628 proof by contradiction, 5 constructive, 6 direct, 5 proof (continued) indirect, 288 implication, 5 mathematical induction, 5 step from n to n + 1, 5 proportionality direct, 62 inverse, 64 proportions, 17 proposition, 286 dual, 343 propositional logic, 286 basic theorems, 287 expression, 286 propositional operation, 286 extensional, 286 propositional variable, 286 protocoll, 772 pseudonorm, 624 pseudorandom numbers, 784 pseudoscalar, 270 pseudotensor, 268, 270 pseudovector, 268, 270 Ptolemy's theorem, 136 pulse, rectangular, 697 pyramid, 152 frustum, 152 n-faced, 152 regular, 152 right, 152 truncated, 152 Pythagoras general triangle, 142 right-angled triangle, 141