T
table with double entry, 119
tacnode, curve, 232
tangent
--- circle, 198
--- formula, 142
--- geometric definition, 130
--- hyperbolic, 87
--- geometric definition. 131
--- law, 142
--- plane, 158 , 395
--- surface, 244 , 246
--- plane curve, 226
--- polygon, 137
--- space curve, 238 , 241
trigonometric, 76
tautology
--- Boolean function, 344
--- predicate logic, 290
--- propositional logic, 288
Taylor
--- expansion, 55 , 389 , 417
--- analytic function, 691
--- one variable, 417
--- several variables, 397
--- vector function, 643
--- formula, 389
--- several variables, 397
two variables, 396
--- series, 389 , 417
--- analytic function, 691
--- one variable, 417
--- several variables, 397
theorem, 389
--- several variables, 396
telegraphic equation, 531
telephone-call distribution, 769
tensor, 262
--- addition, subtraction, 268
--- alternating, 265
--- antisymmetric, 264
--- components, 262
--- contraction, 264 , 268
--- definition, 262
--- dyadic product, 264
--- eigenvalue, 264
--- generalized Kronecker delta, 265
--- inertia, 263
--- invariant, 265
--- multiplication, 268
--- oversliding, 268
--- product, 263
--- vectors, 255
--- rank n, 262
--- rank 0 , 263
--- rank 1 , 263
--- rank 2 , 263
--- rules of calculation, 263 , 264
--- skew-symmetric, 264 , 268
--- spur, 265
--- symmetric, 264 , 268
tension, 263
trace, 265
tensor product approach, 934
tent mapping, 816
term algebra, 341
test problem, linear, 907
test, Kasiski-Friedman, 337
test, statistical, 774
tetraeder, 213
tetragon, 136
tetrahedron, 153
Thales theorem, 139 , 141
theorem
--- Abel, 416
--- Afraimovich-Shilnikov, 842
--- alternating point, 923
--- Andronov-Pontryagin, 814
--- Andronov-Witt, 804 , 805
--- Apollonius, 199
--- Arzeli-Ascoli, 628
--- Baire category, 608
--- Banach
--- continuity, inverse operator, 621
--- fixed-point, 631
--- Banach-Steinhaus, 620
--- Bayes, 750 , 751
--- Berge, 356
--- binomial. 12
--- Birkhoff, 342 , 817
--- Block-Guckenheimer-Misiuriewicz, 829
--- Bolzano
--- one variable, 59
--- several variables, 123
--- boundedness of a function
--- one variable, 60
--- several variables, 123
--- Cauchy integral theorem, 688
--- Cayley, 302 , 355
--- center manifold
--- differential equations, 830
--- mappings, 835
--- Chebyshev, 436
--- Chinese remainder, 328
--- Clebsch-Gordan, 306
--- closed graph, 620
--- constant analytic function, 673
--- convergence, measurable function, 638
--- decomposition, 297
--- Denjoy, 844
--- differentiability, respect to initial conditions, 797
--- Dirac, 353
--- Douady-Oesterle, 826
--- Euclidean
--- algorithm, 324
theorems. 141
--- Euler, 154 , 331
--- Euler-Hierholzer, 352
--- Fatou, 638
--- Fermat, 331 , 388
theorem (continued I)
--- Fermat-Euler, 331
--- fixed point theorem
--- Banach, 608
--- fixed-point
--- Banach, 631
--- Brouwer, 633
--- Schauder, 633
--- Floquet, 803
--- fundamental integral calculus, 458
--- Girard, 164
--- Grobman-Hartman, 811 , 813
--- Hadamard-Perron, 807 , 812
--- Hahn (extension theorem), 625
--- Hellinger-Toeplitz, 620
--- Hilbert-Schmidt, 630
--- Holladay, 932
--- Hurwitz, 503
--- intermediate value
--- one variable, 59
--- several variables, 123
--- KAM (Kolmogorov-Arnold-Moser), 815
--- Krein-Losanovskij, 621
--- Kuratowski, 357
--- Lagrange, 301
--- Lebesgue. majorized convergence, 638
--- Ledrappier, 826
--- Leibniz, 410
--- Lerey-Schauder, 633
--- LeviB., 638
--- limits
--- functions, 405
--- sequences of numbers, 405
--- Liouville, 673 , 801
--- Lyapunov, 803
--- maximum value, analytic function, 673
--- Meusnier, 247
--- nested balls, 608
--- Ore, 353
--- Oseledec, 820
--- Palis-Smale, 815
--- Picard-Lindelof, 610 , 797
--- Poincare-Bendixson, 805
--- Posa, 353
--- Ptolemy's, 136
--- Pythagoras
--- general triangle, 142
--- orthogonal space, 616
--- right-angled triangle, 141
--- Radon-Nikodym, 638
--- Riemann, 409
--- Riesz, 624
--- Riesz-Fischer, 618
--- Rolle, 388
--- Schauder, 629
--- Schwarz, exchange, 395
--- Sharkovsky, 829
--- Shilnikov, 840
--- Shinai, 829
--- Shoshitaishvili, 830
--- Smale, 840
--- stability in the first approximation, 804
--- Sturm, 44
theorem (continued II)
--- superposition law, 669
--- Sylvester, of inertia, 282
Taylor, 389
--- one variable, 417
--- several variables. 396
Thales, 139 , 141
total probability, 750
Tutte, 356
--- variation of constants, 802
--- Weierstrass, 414 , 607
--- one variable, 60
--- several variables. 123
--- Wilson, 331
--- Wintner-Conti, 800
--- Young, 824 , 825
theory
--- distribution, 714
--- elementary number, 320
--- field, 669
--- function, 671
--- graph, algorithms, 348
--- probability, 745
--- risk, 21
--- set, 290
--- spectral, 622
--- vector fields, 642
theta function, 705
time frequency analysis, 743
tolerance, 364
topological
--- conjugate, 810
--- equivalent, 810
torsion, space curve, 242
torus, 157 , 828 , 829
--- differential equation, linear, autonomous, 803
--- dissolving, 841
--- formation, 837 , 842
--- invariant set, 806
--- losing smoothness, 842
--- resonance torus, 842
total curvature, 243
trace
--- matrix, 252
tensor, 265
tractrix, 106
trail, 351
--- Euler, 352
--- open, 352
trajectory, 797
transform, 707
transformation
--- Cartesian into polar coordinates, 400
--- covering, 299
--- determinant, 211
--- element of area, 474
--- element of curved surface, 482
--- geometrical, 141
--- Hopf-Cole, 551
--- identical, 11
--- invariance, 265
--- linear, 262 , 319 , 600
--- method, 283
transformation (continued)
--- orthogonal coordinates, 210
--- principal axes, 264 , 281
--- quadratic form, 281
--- similarity, 280 , 281
--- wavelet transformation, 740
transition
--- matrix, 766 , 767
--- probability, stochastic, 766
transitivity, 29
translation
--- invariance, 265
--- primitive, 310
transport, network, 358
transportation problem. 857
transposition law, 288
trapezoid, 135
--- Hermite's trapezoidal formula, 900
trapezoidal
--- formula, 899
--- sum, 899
traversing, 147
tree, 354
--- hight, 354
--- ordered binary, 354
--- regular binary, 354
--- rooted, 354
--- spanning, 354 , 355
--- minimum, 355
triangle
--- altitude, 132
--- area, 193
--- bisector, 132
--- center of gravity, 132
--- circumcircle, 132
--- congruent, 133
--- coordinates, 917
--- equilateral, 132
--- Euler, 162
--- incircle, 132
--- inequality, 181
--- axioms of norm, 258
--- complex numbers, 30
--- metric space, 604
--- norm, 611
--- real numbers, 30
--- unitary space, 615
--- isosceles, 132
--- median, 132
--- orthocenter, 132
--- Pascal, 13
--- plane. 131
--- area, 141 , 143
--- basic problems, 143
--- Euclidean theorems, 141
--- general, 141
--- incircle, 143
--- radius of circumcircle, 142
--- right-angled, 132 , 141
tangent formula, 142
--- polar, 162
--- similar, 133
--- spherical, 161
--- basic problems, 167
--- calculation, 167
--- Euler, 162
--- oblique, 169
--- right-angled, 168
triangular
--- decomposition, 891
--- matrix, 253
--- lower, 253
--- upper, 253
triangularization, FEM (finite element method), 914
triangulation, geodesy
--- first fundamental problem, 147
--- second fundamental problem, 148
trigonometry
--- plane, 141
--- spherical, 158
trihedral
--- angle, 151 , 163
--- moving, 238 , 239
triple (ordered 3 -tuple), 294
triple integral, 476
--- application, 480
trochoid, 100
truncation, measurement error, 787
truth
--- function, 286 , 287
--- conjunction, 286
--- disjunction, 286
--- equivalence, 286
--- implication, 286
--- NAND function, 288
--- negation, 286
--- NOR function, 288
table, 286
--- value, 286
turbulence, 798 , 841
Tutte theorem, 356
two lines, transformation, 205
two-body problem, 520
type, universal algebra, 340
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