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