V
vagueness, 360 valence in-valence, 348 out-valence, 348 value expected, measurent, 753 system (function of several variables), 117 true, measurement. 790 van der Pol differential equation, 833 variable artificial, 854 basic, 850 Boolean, 344 bound variable, predicate logic, 289 dependent, 47, 271 free, predicate logic, 289 independent, 47, 117, 271 linguistic, 361 non-basic, 850 propositional, 286 random, 751 variance, 753 distribution, 753 sample function, 771 statistics, 773 two-dimensional distribution, 780 variation function, 60 of constants, method, 501 variation of constants differential equation, linear, 507 theorem, 802 variational calculus, 552 auxiliary curve, 554 comparable curve, 554 Euler differential equation, 554 side-condition, 552 variational equation, 804, 821, 914 equilibrium point points, 811 variational problem, 552, 909 brachistochrone problem, 553 Dirichlet, 559 extremal curves, 553 first order, 552 first variation, 561 functional, 553 higher order, 552 higher order derivatives, 556 isoperimetric, general, 553 more general, 560 numerical solution, 560 direct method, 560 finite element method, 561 gradient method, 561 Ritz method, 560 parameter representation, 552 parametric representation, 557 second variation, 561 several unknown functions, 557 side-conditions, 555 simple one variable, 553 several variable, 558 variety, 341 vector absolute value, 180 affhne coordinates, 182 axial, 180 reflection behavior, 268 base, 186 base vector reciprocal, 185 bound,180 Cartesian coordinates, 182 column, 253 components, 648 conjugate, 869 coordinates, 182 Darboux vector, 243 decomposition, 182 diagram, oscillations, 83 differentiation rules, 642 direction in space, 180 direction, vector triple, 180 directional coefficient, 183 expansion coefficient, 183 fields, 642 free, 180 left singular, 285 length, 189 line, 648 magnitude, 180 matrix, 253 metric coefficients, 185 notion, 180 null vector, 181 polar, 180 reflection behavior, 268 pole, origine, 181 position vector, 181 complex-number plane, 34 radius vector, 181 complex-number plane, 34 reciprocal, 186 reciprocal basis vectors, 186 residual, 277 right singular, 285 row, 253 scalar invariant, 657 sliding, 180 space, 597 stochastic, 766 unit, 180 zero vector, 181 vector algebra, 180 geometric application, 189 notions and principles, 180 vector analysis, 642 vector equation line, 188 plane, 188 space curve, 238, 241 vector equations, 187 vector field, 645, 797 Cartesian coordinates, 646 central, 645 circular field, 646 components, 648 contour integral, 662 coordinate definition, 646 vector field (continued) cylindrical, 646 cylindrical coordinates, 647 directional derivative, 650 divergence, 653 point-like source, 668 rotation, 654 sink, 653 source, 653 spherical, 646 spherical coordinates, 647 vector function, 642, 645 derivative, 642 differentiation, 642 hodograph, 642 linear, 267 scalar variable, 642 Taylor expansion, 643 vector gradient, 652 vector iteration, 283, 284 vector lattice, 602 homomorphism, 603 vector potential, 668 vector product, 183 hints, 255 representation in coordinates, 187 vector space, 316, 596 all null sequences, 598 bounded sequences, 598 B(T), 598 (,'([a,b]), 598 e(v([a,b]),rm complex, 597 convergent sequences, 598 Euclidean, 318 finite sequence of numbers, 597 F", 597 T(T), 598 functions, 598 infinite-dimensional, 317, 599 L p, 639 p, 598 n-dimensional, 317 n-dimensional Euclidean, 254 ordered by a cone, 601 partial ordering, 601 real, 316, 597 s of all sequences, 597 sequences, 597 vector subspace stable, 807, 812 unstable, 807, 812 vectors, 180, 253 angle between, 189 collinear, 181 collinearity, 184 commutative law, 255 coplanar, 181 cyclic permutation, 207 double vector product, 184 dyadic product, 255 equality, 180 Lagrange identity, 185 linear combination, 181, 184 mixed product, 184, 187 Cartesian coordinates, 185 orthogonality, 184 products affine coordinates, 185 Cartesian coordinates, 185 products, properties, 183 scalar product, 255 Cartesian coordinates, 185 representation in coordinates, 186 sum, 181 tensor product, 255 triple product, 184 vector product representation in coordinates, 187 Venn diagram, 291 verification, proof, 5 vertex angle, 128 degree, 348 ellipse, 198 graph,348 hyperbola, 200 initial, 348 isolated, 348 level, 354 parabola, 203 plane curve, 232 sink, 358 source, 358 terminal, 348 vertical angle, 143 vertices, distance, 351 vibration, differential equation bar, 526 round membrane, 527 string, 525 Vieta, root theorem, 43 Volterra integral equation, 563, 609 first kind, 585 second kind, 587 volume barrel, 157 block, 152 cone, 156 cube, 152 cylinder, 154 double integral, 474 element, vector components, 660 hollow cylinder, 155 obelisk, 153 parallelepipedon with vectors, 189 polyhedron, 151 prism, 152 pyramid, 152 rectangular parallelepiped, 152 sphere, 156 subset, 635 tetraeder, 213 torus, 157 triple integral, 480 wedge, 154 volume derivative. 651 volume integral, 476 volume scale, 114