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
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