S
saddle, 804 , 811
saddle form, 249
saddle point
--- differential equation, 495
--- Lagrange function, 862
sample, 754 , 770
--- function, 770
--- random, 770
size, 754
summarizing the sample, 772
--- variable, 770
Sarrus rule, 261
scalar
--- invariant, 263
--- notion, 180
scalar field, 643
--- axial, 644
--- central field, 643
--- coordinate definition, 644
--- directional derivative, 649
--- gradient, 650 , 651
--- plane, 643
scalar matrix, 252
scalar product, 183 , 318
--- Hilbert space, 615
--- representation in coordinates, 186 , 188
--- rotation invariance property, 270
--- two functions, 920
--- vectors, 255
scale
--- cartography, 144
--- equation, 114
--- factor, 114 , 146
--- logarithmic, 114
--- notion, 114
semilogarithmic, 115
scenario, Ruelle-Takens-Newhouse, 842
Schauder fixed-point theorem, 633
scheduling problem, 861
scheme
--- Falk, 254
--- Young, 306
Schmidt, orthogonalization method, 579
Schoenflies symbolism, 307
Schrodinger equation
--- linear, 538
--- non-linear, partial, 547 , 549
--- time-dependent, 539
--- time-independent, 539
Schur's lemma, 306
Schwarz
--- exchange theorem, 395
--- reflection principle, 681
Schwarz-Buniakowski inequality, 615
Schwarz-Christoffel formula, 679
screw
--- left, 242
--- right, 242
search procedure, numerical, 867
secant
--- geometric definition, 130
--- hyperbolic, 87
--- theorem, 138
--- trigonometric, 76
secant-tangent theorem, 138
section, golden, 2 , 4 , 193 , 845
sector formula, 666
sector, spherical, 157
segment
--- normal, 227
--- notion, 128
--- polar normal, 227
--- polar tangent, 227
--- tangent, 227
selection, 870
self-similar, 823
semantically equivalent, 287
--- expressions, 345
semifocal chord
--- ellipse, 198
--- hyperbola, 200
--- parabola, 69 , 203
semigroup. 299
--- free, 299
semimonotone, 613
seminorm, 624
semiorbit, 797
sense class, 133
--- of a figure, 132
sensitive, with respect to the initial values, 829
sentence, 286
sentence-forming functor, 286
sentential operation, 286
separable sets, 625
separation
--- constant, 540
--- theorems (convex sets), 625
--- variables, 489 , 524 , 540
separatrix
--- loop, 808 , 840
surface, 806 , 812
sequence, 404
--- bounded, 598
--- Cauchy sequence, 607
--- convergente, 606
--- finite, 597
--- in metric space, 606
--- infinite, 404
--- numbers, 404
--- bounded, 404 , 598
--- bounded above, 405
--- bounded below, 405
--- convergence, 405
--- converging to zero, 598
--- divergence, 405
--- finite, 597
--- law of formation, 404
--- limit, 405
--- monotone, 404
--- term, 404
series, 18 , 404
--- alternating, 410
--- arithmetic, 18
--- Banach space, 612
--- Clebsch-Gordan, 306
--- comparison criterion, 407
--- constant term, 406
--- convergence, 408
--- absolute , 416
--- non-uniform, 414
--- uniform, 414 , 416
--- convergence theorems, 406
--- convergent, 406
--- D'Alembert's ratio test, 407
--- definite, 18
--- divergence, 409
--- divergent, 406
--- expansion, 417
--- Fourier, 420
--- Laplace transformation, 719
--- Laurent, 692
--- Maclaurin, 418
--- power series. 416
--- Taylor, 389 , 417 , 691
--- finite, 18
--- Fourier, 421
--- complex representation, 421
--- function, 414
--- domain of convergence, 414
--- general term, 406
--- geometric, 19
--- infinite, 19 , 406
--- harmonic, 406
--- hypergeometric, 513
--- infinite, 404 , 406
--- integral test of Cauchy, 408
--- Laurent, 692
--- Maclaurin, 418
--- Neumann, 568
--- Neumann series, 620
--- partial sum, 406
--- power, 416
--- expansion, 417
--- inverse, 417
--- remainder, 406 , 414
--- root test of Cauchy, 408
sum, 406
--- Taylor, 389 , 417
--- analytic function, 691
--- uniformly convergent
--- continuity, 415
--- differentiation, 415
--- integration, 415
--- properties, 415
--- Weierstrass criterion, uniform convergence, 415
set, 290
--- absorbing, 799
--- algebra, fundamental laws, 292
--- axioms of closed sets, 606
--- axioms of open sets, 606
--- Borel, 636
set (continued)
--- bounded in metric space. 606
--- cardinality, 298
--- closed, 606
--- closure, 607
--- compact, 628 , 800
--- complex numbers, 34
--- convex, 599
--- dense, 607
--- denumerable infinite, 298
--- disjoint, 292
--- element, 290
--- empty, 291
--- equality, 291
--- equinumerous, 298
--- fundamental 292 , 616
--- fuzzy, 360
--- image, 48
--- infinite, 298
--- integers, 1
--- invariant, 799
--- chaotic, 828
--- fractal, 828
stable, 799
--- irrational numbers, 2
--- linear, 597
--- manyness, 298
--- measurable, 635
--- natural numbers, 1
--- non-denumerable infinite, 298
--- notion of set, 290
--- open, 605
--- operation
--- Cartesian product, 294
--- complement, 292
--- difference, 293
--- intersection, 292
symmetric difference, 293
--- union, 292
--- operations, 291
--- order-bounded, 602
--- original space, 48
--- power, 298
--- power set, 291
--- quotient set, 297
--- rational numbers, 1
--- real numbers, 2
--- relative compact, 628
subset, 291
--- theory, 290
--- universal, 292
--- void, 291
sets, 290
--- coordinates x, y. 294
--- difference, symmetric, 293
sexagesimal degree, 130
shift mapping, 820
shift register, lineare, 316
shooting method, 910
simple, 910
shore-to-ship bearing, 171
SI system, 1012
side or leg of an angle, 128
side-condition, 555
Sierpinski
--- carpet, 824
--- gasket, 824
sieve of Eratosthenes, 320
--- (T-additivity, 635
--- (T-algebra, 635
--- Borelian, 636
sign of a function, 49
signal, 740
--- analysis, 740
synthesis, 740
signature, universal algebra, 340
significance, 779
--- level, 753 , 776
similarity transformation, 280 , 281
simplex
--- method, 850 , 851
--- revised, 855
step, revised, 856
--- tableau, 851
--- revised, 855
Simpson's formula, 900
simulation
--- digital, 783
--- Monte Carlo, 783
sine
--- geometric definition, 130
--- hyperbolic, 87
--- geometric definition, 131
--- trigonometric, 74
sine integral, 460 , 696
sine law, 142 , 164
sine-cosine law, 164
--- polar, 164
sine-Gordon equation, 547 , 549
single-target method, 910
singleton, 363
singular value, 285 , 820
--- decomposition, 285
singular value decomposition, 285
singularity
--- analytic function, 673
--- essential, 673 , 693
--- isolated, 692
--- pole, 693
--- removable, 673
sink, 804 , 811
--- vector field, 653
--- vertex, 358
sinusoidal amount, 82
slack variable, 847
Slater condition, 863
slide rule, 10
--- logarithmic scale, 114
slope
--- plane, 194
--- tangent, 227
small circle, 158 , 175
--- arclength, 175
--- course angle, 176
--- intersection point, 176
--- radius, plane, 175
--- radius, spherical, 17o
smoothing
--- continuous problem, 919
--- parameter. 933
spline, 932
--- cubic, 932
Sobolev space, 613
solenoid, 828
solid angle, 151
soliton
--- antikink, 550
--- antisoliton, 549
--- Boussinesq, 551
--- Burgers, 551
--- differential equation, partial, non-linear, 546
--- Hirota, 551
--- interaction, 547
--- Kadomzev-Pedviashwili, 551
--- kink, 550
--- lattice, 550
--- kink-antikink. 550
--- collision, 550
--- doublet, 550
--- kink-kink
--- collision, 550
--- Korteweg de Vries, 548
--- non-linear, Schrodinger. 549
solution
--- point, 847
--- product form, method separation of variables, 524
SOR method (successive overrelaxation), 896
source, 804 , 811
--- distribution
--- continuous. 669
--- discrete, 669
--- field
--- irrotational, 667
--- pure, 667
--- vector field, 653
--- vertex, 358
space
--- abstract, 48
--- Banach, 612
--- complete, metric, 607 , 608
--- directions, 210
--- finite-dimensional, 628
--- higher-dimensional, 117
--- Hilbert, 615
--- infinite-dimensional, 599
--- isometric, 611
--- Kantorovich, 603 , 628
--- linear, 596
--- p space, 639
--- metric, 604
--- completion, 610
--- convergence of sequence, 606
--- normable, 612
separable, 607
--- non-reflexive, 626
--- normed
--- axiom, 611
--- properties, 612
--- ordered normed, 613
--- orthogonal, 616
--- reflexive, 626
--- Riesz, 602
second adjoint, 626
separable, 607
Sobolev, 613
--- unitary, 615
--- vector, 596
space curve, 238
--- binormal, 239 , 241
--- coordinate equation, 241
--- curvature, 240
--- direction, 238
--- equation, 214 , 238
--- moving trihedral, 239
--- normal plane, 238 , 241
--- osculating plane, 238 , 241
--- principal normal, 239 , 241
--- radius of curvature, 240
--- radius of torsion, 242
--- tangent, 238 , 241
--- torsion, 242
--- vector equation, 238 , 241
space inversion, 269
--- mixed product, 270
scalar product, 270
spectral radius, 620
spectral theory, 622
spectrum, 727
--- amplitude, 727
--- continuous, 623
--- frequency, 727
--- linear operator, 622
--- phase, 727
sphere, 156
--- ellipsoid, 220
--- equation, three forms, 243
spherical
--- biangle, 161
--- coordinates, 209
--- diagon, 161
--- distance, 158
--- field, 643
--- helix, 177
--- lune, 161
spiral, 103
--- Archimedean, 103
--- hyperbolic, 104
--- logarithmic, 104 , 233
spline
--- basis spline, 933
--- bicubic, 933
--- approximation, 935
--- interpolation, 933
--- cubic, 931
--- interpolation, 931
smoothing, 932
--- interpolation, 917 , 931
--- natural, 931
--- normalized Z?-spline, 933
--- periodic, 931
smoothing, 932
--- matrix, 252
--- tensor, 265
square, 135
stability
--- absolutely stable, 907
--- first approximation, 804
--- integration of differential equation, 907
--- Lyapunov stability, 803
--- orbital, 803
--- periodic orbit, 804
--- perturbation of initial values, 907
--- round-off error, numerical calculation, 942
structural, 813 , 814
standard
--- deviation, 753 , 791 , 793
--- error, 790
--- normal distribution, 759
state
--- degenerate, 541
--- particle, 538
space, stochastic, 765
stationary, 539
statistics, 745
--- descriptive, 772
--- estimate, 771
--- mathematical, 745 , 769
sample function, 770
steady state, 797
Steffensen method, 886
step
--- from n to n + 1 , 5
--- function, 697 , 714 , 734 , 744
--- interval parameter, 897
size, 904
--- change, 905
steradian, 151
stereometry, 150
Stieltjes
--- integral, 628
--- comparison with Riemann integral, 453
--- notion, 453
--- transformation, 707
Stirling formula, 462
stochastic
--- basic notions, 765
--- chains, 766
--- process, 765
--- processes, 765
stochastics, 745
Stokes, integral theorem, 666
strangling, 264
Strategie
--- mutations-selektion-, 871
stream function, 681
strip, characteristic, 519
strophoide, 95
structure
--- algebraic, 286
--- classical algebraic, 298
Sturm
--- chain, 44
--- function, 44
sequence, 889
--- theorem, 44
Sturm-Liouville problem, 515
sub determinant, 259
subdomain, 933
subgraph, 349
--- induced, 349
subgroup, 300
--- criterion, 300
--- cyclic, 300
--- invariant, 301
--- normal, 301
--- trivial, 300
subinterval, 441
subnormal, 227
subring, 313
--- trivial, 313
subset, 291 , 597
--- affne, 597
--- linear, 597
--- open, 605
subspace, 317
--- affne, 597
--- criterion, 317
--- invariant, representation of groups, 305
subtangent, 227
subtraction
--- complex numbers, 36
--- computer calculation, 940
--- polynomials, 11
--- rational numbers, 1
subtractive cancellation, 940
sum, 6
--- algebraic, 366
--- drastic, 366
--- of the digits
--- alternating, first order, 322
--- alternating, second order, 322
--- alternating, third order, 322
--- first order, 322
second order, 322
--- third order, 322
--- residual squares, 921
--- Riemann, 441
--- rules of calculation, 6
summation sign, 6
--- transverse, 322
--- vectors, 181
summation convention, Einstein's, 262
superposition
--- fields, 669
--- law, fields, 669
--- non-linear, 549
--- oscillations, 82
--- principle, 683
--- differential equation, linear, 507
--- differential equations, higher order, 501
supplementary angle formulas, 79
support
--- compact, 742
--- measure, 816
--- membership function, 360
supporting functional, 625
supremum, 602
surface, 243
--- area, double integral, 474
--- B-B representation, 935
--- barrel, 157
--- block, 152
--- cone, 156
--- conical, 156 , 214
--- constant curvature, 249
--- cube, 152
--- curvature of a curve, 247 , 249
--- cylinder, 154
--- developable, 250
--- element, 247
--- element, vector components, 660
--- equation, 223
--- in normal form, 220
space, 213
--- equation, space, 243
--- first quadratic fundamental form, 245
--- Gauss curvature, 249
--- geodesic line, 250
--- harmonic, 544
--- integral, 479 , 663 , 664
--- first type, 479
--- general form, 485
second type, 483 , 484
--- line element, 245
--- line of curvature, 248
--- metric, 247
--- minimal, 249
--- normal, 244 , 246
--- normal vector, 244
--- oriented, 483
--- patch, area, 247
--- polyhedron, 151
--- principal normal section, 248
--- pyramid, 152
--- quadratic, 223
--- radius of principal curvature, 247
--- rectangular parallelepiped, 152
--- rectilinear generator, 222
--- representation with splines, 931
--- rotation symmetric, 213
--- ruled, 250
second order, 220 , 223
--- central surfaces, 224
--- invariant signs, 224
--- types, 223
second quadratic fundamental form, 248
sphere, 156
--- tangent plane, 244 , 246
--- torus, 157
--- transversal, 806
surplus variable, linear programming, 850
switch
--- algebra, 342 , 346
--- function, 346
--- value, 346
Sylvester, theorem of inertia, 282
symbol
--- internal representation (computer), 936
--- Kronecker, 265
--- Legendre, 329
symmetry
--- axial, 133
--- central, 132
--- element, 307
--- Fourier expansion, 422
--- group, 308
--- applications in physics, 312
--- crystallography, 310
--- molecules, 308
--- quantum mechanics, 312
--- operation, 307
--- crystal lattice structure, 310
--- improper orthogonal mapping, 307
--- reflection, 307
--- rotation, 307
--- without fixed point, 307
--- with respect to a line, 133
system
--- chaotic according to Devaney, 829
--- cognitive, 375
--- complete, 618
--- differential equation, higher order, 497
--- linear, 505
--- differential equations, partial
--- canonical system, 519
--- normal system, 519
--- dynamical, 797
--- chaotic, 829
--- conservative, 798
--- continuous, 797
--- C"'-smooth, 797
--- discrete, 798
--- dissipative, 798
--- ergodic, 817
--- invertible, 797
--- mixing, 817
--- motion, 797
--- time continuous, 797
--- time discrete, 797
--- time dynamical, 798
--- volume decreasing, 798
--- volume preserving, 798
--- volume shrinking, 798
--- equation
--- numerical solution, 890
--- four points, 213
--- generators, 300
--- knowledge based interpolation, 377
--- linear equations, 271 , 272
--- compatible, 273
--- consistent, 273
--- fundamental system, 273
--- homogeneous, 272
--- inconsistent, 273
--- inhomogeneous, 272
--- overdetermined, 277
--- pivoting, 274
--- row echelon form, 276
solvable, 273
--- trivial solution, 273
--- mixing, 829
--- Morse-Smale, 815
system (continued)
--- normal equations, 277
--- orthogonal, 616
--- orthonormal, 617
--- term-substitutions, 340
--- trigonometric, 616
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