C
calculation complex numbers, 36 determinants, 260 numerical accuracy, 941 basic operations, 940 tensors, 263 calculus differentiation, 379 errors, 787 integral, 427 observations, measurement error, 787 propositional, 286 variations, 552 canonical form, circle-mapping, 843, 844 canonical system, 519 Cantor function, 844 Cantor set, 822, 823, 827 cap, spherical, 157 capacity, edge, 358 Caratheodory condition, 631 Cardano formula, 41 cardinal number, 291, 298 cardinality, set, 298 cardioid, 98 carrier function, 575 Carson transformation, 707 Cartesian coordinates plane, 189 space, 208 folium, 94 cartography scale, 144 cascade, period doubling, 839, 842 Cassinian curve, 98 category, second Baire category, 814 catenary curve, 88, 105, 555 catenoid, 88 Cauchy integral, 592 integral formula, 689 integral formulas, application, 694 method, differential equations of higher order, 502 principal value improper integral, 457 principal value, improper integral, 454 principle, 608 problem, 518 sequence, 607 theorem, 390 Cauchy-Riemann differential equations, partial. 672 Cayley table, 300 theorem, 302, 355 center circle, 197 curvature, 230 spherical, 175 center manifold theorem differential equations, 830 mappings, 835 center of area method, 374 center of gravity, 213 arbitrary planar figure. 453 arc segment, 452 closed curve, 452 double integral, 474 line integral, first type, 464 method, 373 generalized, 374 parametrized. 374 trapezoid, 453 triangle, 132 triple integral, 480 center of mass, 191, 213 central angle, 130 curves, 205 field, 643 limit theorem, Lindeberg—Levy, 765 surface, 220 centroid, points having masses, 191 chain, 297, 351 directed, elementary, 357 graph,357 elementary, 357 Markov, 766 stationary, 766 time-homogeneous, 766 rule, 643 composite function, 382 stochastic, 765, 766 chaos, 797, 841 attractor, strange, 828 from torus to chaos, 841 one-dimensional mapping, 829 routes to chaos, 829 through intermittence, 843 transition to chaos, 839 character group element, 304 representation of groups, 305 characteristic, 10 characteristic equation, 494, 503, 505 characteristic strip, 519 Chebyshev approximation, 923 continuous, 923 discrete, 926 formula, 87 inequality, 31 polynomials, 924 theorem, 436 Chinese remainder theorem, 328 X2 distribution, 762 X2 test, 775, 776 Cholesky decomposition, 893 method, 278, 893 chord, 140 theorem, 138 circle Apollonius, 682 area, 138 center, 197 chord, 138 circumference, 138 convergence, 690 curvature, 230 plane curve, 228 dangerous, 149 definition, 138, 197 equation Cartesian coordinates, 197 polar coordinates, 197 great circle, 158, 173 intersection, 158 mapping, 843, 844 parametric representation, 197 periphery, 138 plane, 138, 197 radius, 138, 197 small circle, 158, 175 tangent, 138, 198 circuit directed, graph, 357 Euler, 352 Hamilton, 353 circuit integral, 468 being zero, 470 circular field, 646 point, 249 sector, 140 segment, 140 circumcircle quadrangle, 136 triangle, 132, 142 circumscribing quadrangle, 136 triangle, 132 cissoid, 95 Clairaut differential equation, ordinary, 493 differential equation, partial, 520 class defined by identities, 341 equivalence class, 297 midpoint, 773 statistics, 772 Clebsch-Gordan coefficient, 306 series, 306 theorem, 306 closure closed linear, 616 linear, 597 set, 607 transitive, 295 clothoid, 105 code, 331 ASCII (American Standard Code for Information Interchange), 936 public key, 331 RSA (Rivest, Shamir, Adleman), 331 codimension, 829 coding, 331, 335 coefficient, 11 Clebsch-Gordan, 306 coefficient (continued) comparison. 16 Fourier, 420 leading, 38 matrix, extended, 892 metric, 185, 186 vector decomposition, 182 collinearity, vectors, 184 collocation boundary, 913 domain. 913 method, 576, 909, 913 points, 909, 913 column pivoting, 892 column sum criterion, 895 combination, 745 with repetition, 745 without repetition, 745 combinatorics, 745 commensurability, 4 commutative law Boolean algebra, 342 matrices, 254 propositional logic, 287 sets, 293 vectors, 255 commutativity, scalar product, 183 commutator, 319 comparable function, 558 complement, 292 algebraic, 259 fuzzy, 368 fuzzy set, 365 orthogonal, 616, 624 sets, 292 Sugeno complement, 368 Yager complement, 368 complementary angles formulas, 78 completeness relation, 618 completion, metric space, 610 complex analysis, 671 complex function, 47 pole, 673 complex number, 34 plane, 34 complex mapping, 684 complex-valued function, 47 complexification, 601 composition, 371 max-average, 371 max-(/-norm), 371 compound interest, 22 calculation, 22 computation of adjustment, 917 computer basic operations, 940 error of the method, 942 error types, 939, 941 internal number representation, 938 internal symbol representation, 936 numerical accuracy, 941 numerical problems in calculation, 939 use of computers, 936 computer algebra systems applications, 979 basic structure elements, 955 differential and integral calculus, 992 elements of linear algebra, 988 equations and systems of equations, 984 functions, 956 graphics, 998 infix form, 956 list, 956 manipulation of algebraic expressions, 979 numbers, 955 object, 955 operator, 956 prefix form, 956 programming, 955 purpose, 953 set, 956 suffix form, 956 terms, 956 type, 955 variable, 956 concave, curve, 228 conchoid Nicomedes, 96 general, 96 of the circle, 96 of the line, 96 conclusion, 372 concurrent expressions, 345 condition boundary value, ordinary differential equation, 487 Caratheodory, 631 Cauchy (convergence), 122 Dirichlet (convergence), 422 initial value, ordinary differential equation, 487 Kuhn-Tucker, 862 Lipschitz, higher-order differential equation, 498 Lipschitz, ordinary differential equation, 488 number, 894 regularity condition, 876 Slater, 863 cone, 156, 221, 613 central surface, 224 circular, 156 generating, 602 imaginary, 224 normal, 613 regular, 613 solid, 613 truncated, 156 vector space, 599 confidence interval, 781 regression coefficient, 781 variance, 778 limit for the mean, 777 prescription, 792 probability, 776 region, 781 congruence algebraic, 327 corners, 151 linear, 328 method, 783 plane figures, 133 polynomial congruence. 330 quadratic, 329 relation, 340 kernel, 341 simultaneous linear, 328 system simultaneous linear, 328 theorems, 133 congruent directly, 132 indirectly, 133 mapping, 132, 133 conic section, 156, 205, 207 singular, 207 conjugate complex number, 36 conjunction, 286 elementary, 345 consistency integration of differential equation, 907 order p, 907 constant Euler, 460 in polynomial, 60 propositional calculus, 286 term, 272 constants mathematical, frequently used, 1010 natural, 1010 continuation, analytic, 691 continued fractions, 3 continuity composite functions, 59 elementary function, 58 from below, 635 function one variable, 57 several variables, 122 Holder, 591 continuous, absolutely, 638 continuum, 298 contour integral vector field, 662 contracting principle, 608 contraction, 264 tensor, 268 contradiction, Boolean function, 344 control digit, 332 convergence absolute, 409, 416 complex terms, 690 alternating series test of Leibniz, 410 Banach space, 612 circle of convergence, 690 condition of Cauchy, 52 conditional, 409 complex terms, 690 in mean, 422 infinite series, complex terms, 690 integration of differential equation, 907 non-uniform, 414 order p, 907 sequence of numbers, 405 complex terms, 689 series, 406, 408 complex terms, 689 uniform, 414-416 uniformly, function sequences, 606 weak,629 Weierstrass criterion, 415 convergence criterion comparison criterion, 407 D'Alembert's ratio test, 407 integral test of Cauchy, 408 root test of Cauchy, 408 convergence theorem, 406 measurable function, 638 conversion, number systems, 937 convex, curve, 228 convolution Fourier transformation, 729 Laplace transformation, 713 one-sided, 729 two-sided, 729 z-transformation, 736 coordinate inversion, 269 coordinate line, 209, 266 coordinate surface, 209, 266 coordinate system double logarithmic, 115 Gauss-Krueger, 143 left-hand, 207 orientation, 207 orthogonal, 180 orthonormal, 180 plane, 189 right-hand, 207 semilogarithmic. 115 Soldner, 143 spatial, 207 transformation, 262 coordinate transformation, 210, 267, 647 equation central curves second order, 205 quadratic curve (parabolic), 206 coordinates affine, 185 axis, 189 barycentric, 917 Cartesian, 186 plane, 189 space, 208 Cartesian, transformation, 191 contravariant, 187, 268 covariant, 187, 268 curvilinear, 190, 244, 266 three dimensional, 209 cylindrical, 209 vector field, 647 Descartes, 189 equation, space curve, 241 Gauss, 244 Gauss-Kruger, 160 geodetic, 143 ccordinates (continued) geographical, 160 mixed, 267 point, 189 polar, plane, 190 polar, spherical, 209 representation with scalar product, 187 Soldner, 160 spherical, 209 vector field, 647 transformation, 190 triangle coordinates, 917 vector, 182 coprime, 5 corner convex, 151 figure, 150 northwest corner rule, 858 symmetric, 151 trihedral, 151 correction form, 896 corrector, 906 correlation, 779 analysis, 779 coefficient, 780 empirical, 780 cosecant geometric definition, 130 hyperbolic, 87 trigonometric, 76 coset left, 301 right, 301 cosine geometric definition, 130 hyperbolic, 87 geometric definition. 131 law, 142 law for sides, 164 rule, spherical triangle, 164 trigonometric, 75 cotangent geometric definition, 130 hyperbolic, 87 trigonometric, 76 Coulomb field, point-like charge, 646, 668 counterpoint, 158 course angle, 159 covariance, two-dimensional distribution, 780 covering transformation, 299 covering, open, 800 Cramer rule, 275 credit, 22 criterion convergence sequence of numbers, 405 series, 406 series with positive terms, 407 uniform, Weierstrass, 415 divisibility, 323 subspace, 317 cross product, 183 cryptanalysis, classical, methods, 337 Kasiski-Friedman test, 337 statistical analysis, 337 cryptography, conventional methods, 335 linear substitution ciphers, 336 substitution, 335 monoalphabetic, 335 monographic, 335 polyalphabetic, 335 polygraphic 335 transposition, 335 cryptology, 334 AES algorithm, 339 classical Hill cypher method, 336 matrix substitution method, 336 Vigenere cypher method, 336 cryptosystem, 334 Diffie-Hellman key exchange, 338 encryption context free, 334 context sensitive, 334 IDEA algorithm, 340 mathematical foundation, 334 one-time pad, 338 one-way function, 339 public key methods, 338 RSA method, 339 security of cryptosystems, 335 subject, 334 crystal class, 311 crystal system, 311 crystallography lattice, 310 symmetry group, 310 cube, 152 curl, 668 density. 669 field pure, 668 zero-divergence field, 668 line, 655 curvature center, 230 circle, 230 curves on a surface, 247 Gauss surface, 249 mean, surface, 249 minimal total curvature, 932 plane curve, 228 radius, 230 curve on a surface, 247 principal, 247 space curve, 240 surface, 247, 249 constant curvature, 249 total, 243 curve algebraic, 93, 194 n-th order, 234 arc cosine, 84 arc cotangent, 84 arc sine, 84 curve (continued I) arc tangent, 84 Archimedean spiral, 103 area cosine, 91 area cotangent, 92 area sine, 91 area tangent, 92 astroid, 102 asymptote, 231, 234 asymptotic point. 232 B-B representation, 935 cardioid, 98 Cartesian folium, 94 Cassinian, 98 catenary, 105 cissoid, 95 clothoid, 105 concave, 228 conchoid of Nicomedes, 96 convex, 228 corner point, 232 cosecant, 76 cosine, 75 cotangent, 76 curvature, 228 cuspidal point, 232 cycloid, 100 damped oscillation, 83 directing, 154 double point, 232 empirical, 106 envelope, 236 epicycloid, 101 epitrochoid, 102 equation complex form, 701 plane, 194, 225 second degree, 205 second order, 205 space, 214 error curve, 72 evolute, 236 evolvent, 236, 237 of the circle, 104 exponential, 71 fourth order, 96 Gauss error curve, 759 general discussion, 235 hyperbolic cosine, 88 hyperbolic cotangent, 89 hyperbolic sine, d>^ hyperbolic tangent, 88 hyperbolic type, 68, 70 hyperbolice spiral, 104 hypocycloid, 102 hypotrochoid, 102 imaginary, 194 inflection point, 231 involute, 237 isolated point, 232 Koch curve, 823 lemniscate, 99 length, line integral, first type, 464 curve (continued II) logarithmic, 71 logarithmic spiral, 104 loops, 1007 Lorentz curve, 94 multiple point, 233 normal, plane, 226 7j.-th degree, 63, 194 7i.-th order, 63, 194 parabolic type, 63 Pascal limacon, 96 plane, 225 angle, 228 direction, 225 vertex, 232 quadratic, 205 radius of curvature, 228, 229 representation with splines, 931 secant, 76 second degree, 205 second order, 205 semicubic parabola, 93 sine, 75 space, 238 spherical, 158, 172, 643 spiral, 103 strophoide, 95 tacnode, 232 tangent, 76 plane, 226 terminal point, 232 third degree, 65 third order, 93 tractrix, 106 transcendent, 194 trochoid, 100 witch of Agnesi, 94 curves family of, envelope, 237 second order central curves, 205 parabolic curves, 206 polar equation, 207 spherical, intersection point, 178 cut, 292 Dedekind's, 297 fuzzy sets, 364 set, 292 cutting plane method, 877 cycle, 351 chain, 357 limit, 833 cycloid, 100 basis, 100 common, 100 congruent, 100 curtate, 100 prolate, 100 cylinder, 154, 223 circular, 155 elliptic, 223 hollow, 155 hyperbolic, 223 cylinder (continued) invariant signs elliptic, 224 hyperbolic, 224 parabolic, 224 parabolic. 223 cylindrical coordinates, 209 cylindrical function, 509 cylindrical surface, 154, 213