F
face, corner, 151 factor algebra, 340 factor group, 302 factor ring, 314 factor, polynomial, product representation, 43 factorial, 13 generalization of the notion, 462 factoring out, 11 Falk scheme, 254 feasible set, 847 Feigenbaum constant, 837, 839 FEM (finite element method), 913 FFT (fast Fourier transformation), 928 Fibonacci numbers, 325, 845 sequence, 325 field (algebraically), 313 extension, 313 finite, 314 Galois, 314 field axial, 644 central symmetric, 643 circular, 646 conservative, 662 Coulomb, point-like charge, 646, 668 cylinder symmetric. 644 flow, 664 function, 681 gravitational, point mass, 669 Newton, point-like mass, 646 potential, 662 scalar, 643 source, 667 spherical, 643 field theory basic notions, 642 differential equations, partial, 669 fields, superposition, 669 finite difference method, 534 finite element method, 534, 913 fitting problem different versions, 403 linear, 893 non-linear, 107 fixed point conformal mapping, 675, 676 flip bifurcation, 836 fixed-point number, 938 floating-point number, 938 IEEE standard, 939 Maple, 970 Mathematica, 957 semilogarithmic form, 938 Floquet representation, 805 theorem, 803 flow differential equation, 797 edge, 358 scalar field, 664 vector field scalar flow, 664 vector flow, 664 focal line, tractrix, 106 focus, 809 compound, 832 ellipse, 198 hyperbola, 200 parabola, 203 saddle, 804 saddle focus, 809 stable, 804 form quadratic, 893 saddle, 249 formula binomial, 12 Cardano, 41 closed, predicate logic, 289 d'Alembert, 536 Duhamel, 722 Euler, 247, 420 Heron's, 143 integral (series remainder), 418 interpretation, predicate logic, 289 Kirchhoff, 536 Lagrange, 418 Leibniz, 385 Liouville, 501, 802 Maclaurin, 415 manipulation, 953 de Moivre complex number, 37 hyperbolic functions, 90 trigonometric functions, 79 Parseval. 729 Pesin, 821, 828 Plemelj and Sochozki, 593 Poisson, 536 predicate logic, 289 rectangular, 899 Riemann, 530 Simpson, 900 Stirling, 462 tangent, 142 tautology, 290 Taylor one variable, 389 several variables, 397 trapezoidal, 899 formulas Euler, 421, 424 Frenet, 243 predicate logic, 289 four-group, Klein's, 302 Fourier analysis, 420 Fourier coefficient, 420, 927 asymptotic behavior, 422 determination, 403 numerical methods, 424 Fourier expansion, 420 complex functions, 426 forms, 423 symmetries, 422 Fourier integral, 424, 724 complex representation, 724 equivalent representations, 724 Fourier series, 421 best approximation, 617 complex representation, 421 Hilbert space, 617 Bessel inequality, 618 Fourier sum, 421, 927 complex representation, 928 Fourier transformation, 724 addition law, 727 comparing to Laplace transformation, 730 convolution, 729 two-sided, 713 definition, 725 differentiation image space, 728 original space, 728 discrete complex, 928 fast, 928 Fourier cosine transformation, 725 Fourier exonential transformation, 726 Fourier sine transformation, 725 frequency-shift theorem, 728 integration image space, 728 original space, 729 inverse, 725 linearity law, 727 shifting theorem, 728 similarity law, 728 spectral interpretation, 726 survey, 707 tables, 726 transform, 730 fractal, 822 fractile, 752 fraction continued, 3 decimal, 1 improper, 15 proper, 15 fractional part of x, 49 frames, 743 Frechet derivative, 632 differential, 632 Fredholm alternative, 629 alternative theorem, 571 integral equation, 563, 609 first kind, 577 solution method, 569 theorems, 569 Frenet formulas, 243 frequency, 75 angular/radial, 82 distribution, 772 locking, 844 relative, 748 sine, 82 spectrum, 727 continuous, 425 discrete, 425 statistics, 748, 772 cumulative, 773 Fresnel integral, 697 frustum cone, 156 pyramid, 152 function, 47 absolutely integrable, 455, 458 algebraic, 60 amplitude function, elliptic, 703 analytic, 672 area, 91 arrow, 294 autocorrelation, 818 Bessel, 509 modified, 509 beta function, 1056 Boolean, 287, 344 bounded, 50 circular, geometric definition, 130 comparable, 558 complement, 368 complex, 47, 671 algebraic, 698 bounded, 673 linear, 675 linear fractional, 676 quadratic, 677 square root, 677 complex variable, 671 complex-valued, 47 composite, 62 derivative, 382 intermediate variable, 382 continuity in interval, 57 one-sided, 57 piecewise, 57 continuous, complex, 671 cosecant, 76 cosine, 75 cotangent, 76 cyclometric, 84 cylindrical, 509 density, 752 dependent, 121 discontinuity, 57 removable, 58 discrete, 734 distribution, 751 double periodic, 704 elementary, 60 elementary, transcendental. 698 elliptic, 437, 693, 704 entire rational, 60 error function, 461 Euler, 331 even, 50 exponential, 61, 71 exponential, complex, 679 exponential, natural, 698 function series, 414 gamma, 461 generalized, 639, 640, 717 function (continued I) Green, 532 Hamilton, 520, 801 harmonic. 669, 672 Heaviside, 641 Hermite, 616 holomorphic, 672 homogeneous, 120 homographic, 61, 65 hyperbolic, 87, 699 geometric definition, 130, 131 impulse, 714 increment, 907 independent, 121 integrable, 441 integral rational, 60 first degree, 62 n-th degree, 63 second degree, 62 third degree, 63 inverse, 51 complex, hyperbolic, 699 complex, trigonometric, 699 derivative, 383 derivative of higher order, 387 existence, 60 hyperbolic, 91 trigonometric, 61, 84 irrational, 61, 69 Jacobian, 703 Lagrangian, 862 Laguerre, 616 Laplace, 669 limit, 51 at infinity, 53 infinity, 52 iterated, 122 left-hand, 52 right-hand, 52 Taylor expansion, 55 limit theorems, 53 linear, 60, 62 linear fractional, 61, 65 local summable, 639 logarithm, complex, 678 logarithmic, 61, 71 loop function, 1007 MacDonald, 509 matrix exponential, 802 mean value, 444 measurable, 636 meromorphic, 693, 704, 719 monotone decreasing, 49 increasing, 49 non-elementary, 60 notion, 47 odd, 50 of angle, 74 one variable, 47 order of magnitude, 55 parametric representation derivative of higher order, 387 function (continued II) periodic, 50, 716 piecewise continuous, 57 point of discontinuity, 57 finite jump, 58 tending to infinity, 57 positive homogeneous, 558 power, 70 primitive, 427 quadratic, 60 random variable, 751 rational, 61, 64 real, 47 regular, 672 Riemann, 530 sample function, 770 secant, 76 several variables, 47, 117 sign of, 49 sine, 74 special fractional linear fractional, 64 step, 734 stream, 681 strictly monotone, 49 sum of linear and fractional linear functions, 678 summable, 637 switch, 346 tangent, 76 theory, 671 theta, 705 transcendental, 61 trigonometric, 61, 74, 699 geometric definition, 130 truth, 286, 287 Weber, 509 Weierstrass, 705 function system orthogonal, 920 orthonormal, 920 function theory, 671 functional, 553, 619 definition, 47 linear, 319, 600, 601 linear continuous, 623 L space, 624 functional determinant, 121, 266, 474 fundamental form first quadratic, of a surface, 245 second quadratic, of a surface, 248 fundamental formulas spherical trigonometry, 164 fundamental laws, set algebra, 292 fundamental matrix, 802-804 fundamental problem first, triangulation, 147 second, triangulation, 148 fundamental system differential equation, higher order, 500 fundamental theorem Abelian groups, 302 algebra, 43 elementary number theory, 321 integral calculus, 442 future value, 25 fuzzy control, 374 inference, 372 linguistics, 361 logic, 360 logical inferences, 372 product relation, 371 relation, 369 relation matrix, 370 system, 377 systems, applications, 374 valuation, 369 fuzzy set aggregation, 365 aggregation operator, 370 complement, 365 composition, 371 cut (representation theorem), 364 degree, 364 empty, 363 intersection, 365 intersection set, 366 level set, 364 normal, 364 peak, 363 similarity, 364 subnormal, 364 subset, 363 support, 360 tolerance interval, 363 union, 365 universal, 363 fuzzy sets cut, 364 intersection, 366 union, 366