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
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