D
d'Alembert formula, 536
damping parameter, 897
damping, oscillations, 83
Darboux vector, 243
data type, 340
death process, 769
debt, 23
decay, radioactive, 768
decimal
--- number, 937
--- normalized, 939
--- representation, 937
--- system, 937
decoding, 331
decomposition
--- orthogonal, 616
--- partial fractions, 15
--- vectors, 182
decomposition theorem
differential equation, higher order, 501
Dedekindcut, 297
defect, 909 , 913
--- vector space, 318
definite, positive, 893
defuzzification, 373
degeneracy of states, 541
degree
--- curve, second degree, 205
--- curve, n-th degree, 194
--- homogeneity, 120
--- in-degree, 348
--- matrix, 355
--- measure in degrees, 130
--- out-degree, 348
Delambre equations, 166
--- S distribution, 640
--- S function, 636 , 640
--- application, 717
--- approximation, 717
Dirac, 714
--- S functional, 623
De Morgan
--- law. 293
--- rule, 287
--- Boolean algebra, 343
density function, 752
--- multidimensional, 754
dependence, linear, 272 , 317
deposit
--- in the course of the year, 22
--- regular, 22
--- single, 22
depreciation, 26
--- arithmetically declining, 26
digital, 27
--- geometrically declining, 27
--- straight-line, 26
derivative
--- complex function, 671
--- constant, 380
directional, 649
--- scalar field, 649
--- vector field, 650
distribution, 641
--- exterior, 382
--- fraction, 382
--- Frechet, 632
--- function
--- composite, 382
--- elementary, 380
--- implicit, 383
--- inverse, 383
--- parametric representation, 384
--- several variable, 392
--- generalized, 640
--- higher order, 385 , 395
--- inverse function, 387
--- parametric representation, 387
--- interior, 382
--- left-hand, 380
--- logarithmic, 382
--- mixed, 395
--- one variable, 379
--- partial, 392
--- product, 381
--- quotient, 382
--- right-hand, 380
--- scalar multiple, 380
--- Sobolev sense, 640
--- space, 649
--- sum, 380
--- table, 381
--- vector function, 642
--- volume differentiation, 650
Derive (computer algebra system), 953
Descartes rule, 45
descent, 898
descent method, 868
determinant, 259
differentiation, 261
--- evaluation, 261
--- functional, 121
--- Jacobian, 121
--- multiplication, 260
--- reflection, 260
--- rules of calculation, 260
--- Wronskian, 500 , 802
--- zero value, 260
determination of extrema
--- absolute extremum, 392
--- implicit function, 392
deviation, standard deviation, 753
devil's staircase, 844
diagonal matrix, 252
diagonal method, Maxwell, 684
diagonal strategy, 892
diameter
--- parabola, 204
--- circle, 139
--- conjugate
--- ellipse, 199
--- hyperbola, 202
--- ellipse, 199
--- hyperbola, 202
diffeomorphism, 798
--- Anosov, 829
--- orientation-preserving, 844
difference
--- bounded, 366
--- finite expression. 908
--- sets, 293
--- symmetric, 293
--- significant, 779
--- symmetric
--- sets, 293
--- z-transformation, 735
difference equation, 733
--- boundary value, 740
--- linear, 738
--- partial differential equations, 911
--- second-order, 739 , 740
difference method, 908
--- partial differential equations, 911
difference quotient, 898
difference schema, 18
differentiability
--- complex function, 671
--- function of one variable, 379
--- function of several variables, 394
--- with respect to the initial conditions, 797
differentiable
--- continuously, 632
--- Frechet, 632
differential
--- arc
--- plane, 226
--- surface, 245
--- complete, 394
--- first-order, 380
--- higher order, 394
--- integrability, 468
--- notion, 393
--- partial, 394
--- principal properties, 394
--- quotient (see also derivative), 379
--- second-order. 396
--- total, 394 , 395
--- n-th order, 396
--- second-order, 396
differential calculus, 379
--- fundamental theorem, 388
differential equation, 487
--- boundary value problem, 514
--- eigenfunction, 515
--- eigenvalue, 515
--- eigenvalues, 541
--- flow, 797
--- Fourier transformation, 731
--- Laplace transformation, 721
--- numerical solution, 497
--- operational notation, 502
--- order, 487
--- orthogonality, 515
--- self-adjoint, 514
--- singular solution. 489
--- stiff, 908
--- topological equivalent, 810
--- Weber, 545
differential equation, higher order, 497
--- constant coefficients, 500
decomposition theorem, 501
--- Euler, n-th order, 504
--- fundamental system, 500
--- n-th order, 500
--- lowering the order, 499 , 501
--- normal form, 505
--- quadrature, 501
--- superposition principle, 501
--- system, 497
--- system of linear, 505
--- system of solutions, 498
--- variation of constants, 501
differential equation, linear
--- autonomous, on the torus, 803
--- first-order, 801
--- fundamental theorem, 801
--- homogeneous, 801
--- homogeneous systems, 506
--- inhomogeneous, 801
--- inhomogeneous systems, 506
--- matrix-differential equation, 801
--- non-autonomous, on the torus, 844
--- periodic coefficients, 803
--- second order, 507
--- Bessel, 509
defining equation, 508
--- Hermite, 514
--- hypergeometric, 513
--- Laguerre, 513
--- Legendre, 511
--- method of unknown coefficients, 507
differential equation, ordinary, 487
--- approximate integration, 904
--- autonomous, 800
--- Bernoulli, 491
--- boundary value conditions, 487
--- boundary value problem, 487
--- center, 495
--- central point, 495
--- Clairaut, 493
direction field, 488
--- element, singular, 493
--- exact, 489
--- existence theorem, 488
--- explicit, 487
--- first-order, 488
--- approximation methods, 496
--- important solution methods, 489
--- flow, 797
--- fraction of linear functions, 494
--- general solution, 487
--- general, n-th order, 487
differential equation, ordinary (continued)
--- graphical solution, 497
--- homogeneous, 489
--- implicit, 487 , 492
--- initial value conditions, 487
--- initial value problem, 487
--- integral, 487
--- integral curve, 488
--- integral, singular, 493
--- integrating factor, 490
--- Lagrange, 492
--- linear, 731
--- constant coefficients, 721
--- first-order, 490
--- variable coefficient, 722
--- linear, planar, 797 , 811
--- multiplier, 490
--- non-autonomous, 800
--- notion, 487
--- particular solution, 487
--- point, singular, 493
--- radicals, 493
--- ratio of arbitrary functions, 496
--- Riccati, 491
--- separation of variables, 489
--- series expansion, 496
--- singular point, 494
--- solution, 487
--- successive approximation, 496
--- van der Pol, 833
differential equation, partial, 517
--- approximate integration, 911
--- Cauchy-Riemann, 530 , 672
--- characteristic system, 518
--- Clairaut, 520
--- completely integrable, 521
--- eigenfunction, 541
--- electric circuit, 531
--- elliptic type, 522
--- constant coefficients, 524
--- Euler, calculus of variations, 554
--- field theory, 669
--- first-order, 517
--- canonical system, 519
--- characteristic strip, 519
--- characteristic system, 517
--- linear, 517
--- non-linear, 519
--- non-linear, complete integral, 519
--- total differentials, 521
--- two variables, 520
--- Fourier transformation, 732
--- Hamilton, 801 , 841
--- heat conduction equation
--- one dimensional, 531
--- one-dimensional, 529
--- three-dimensional, 537
--- Helmholtz, 540
--- hyperbolic type, 522 , 524
--- integral surface, 518
--- Laplace, 669
--- Laplace transformation, 723
--- linear, 517
differential equation, partial (continued)
--- non-linear, 546
--- Schrodinger, 549
--- normal system, 519
--- notion, 487
--- parabolic type, 522
--- constant coefficients, 524
--- Poisson, 538 , 667 , 670
--- quasilinear, 517
--- reduced, 830
--- reduced, normal form, 830
--- second-order, 522
--- constant coefficients, 524
--- separation of variables, 540
--- ultrahyperbolic type, constant coefficients, 524
differential operation
--- review, 658
--- vector components, 659
differential operator
divergence, 653 , 658
--- gradient, 650 , 651 , 658
--- Laplace, 657 , 658
--- nabla, 656 , 658
--- non-linear, 632
--- relations, 658
--- rotation, 654 , 658
--- rules of calculations, 658
--- space, 649 , 656
--- vector gradient, 652
differential transformation, affine, 674
differentiation, 379
--- complex function, 671
--- composite function, 397
--- function
--- elementary, 380
--- implicit, 383
--- inverse, 383
--- one variable, 379
--- parametric representation, 384
--- several variables, 392
--- graphical, 384
--- higher order
--- inverse function, 387
--- parametric representation, 387
--- implicit function, 398
--- logarithmic, 382
--- several variables, 397
--- under the integration sign, 459
--- volume, 650
differentiation rules
--- basic rules, 380
derivative of higher order, 385
--- function
--- one variable, 380
--- several variables. 380 , 395
--- table, 386
--- vector function, 642
--- vectors, 642
diffusion coefficient, 538
diffusion equation, 551
--- three-dimensional, 537
digon, spherical, 161
dihedral angle, 150
dihedral group, 299
dimension, 822
--- capacity, 823
--- correlation, 825
defined by invariant measures, 824
Douady-Oesterle, 826
--- formula, 317
--- generalized. 825
--- Hausdorff, 822
--- information, 824
--- lower pointwise, 824
--- Lyapunov, 825
--- measure, 824
--- metric, 822
--- Renyi, 825
--- upper pointwise, 824
--- vector space, 317 , 599
Dirac
distribution, 640
--- measure, 636 , 816
--- theorem, 353
directing curve, 154
direction
--- cosine, space, 210
--- plane curve, 225
--- space, 210
--- space curve, 238
directional
--- angle, 145
derivative, 651
directrix
--- ellipse, 198
--- hyperbola, 201
--- parabola, 203
Dirichlet
--- condition, 422
--- problem, 528 , 670
discontinuity, 57
--- function, 57
--- removable, 58
discount, 21
discretization error
--- global, 907
--- local, 907
discretization step interval, 898
discriminant, 522
disjoint, 292
disjunction, 286
--- elementary, 345
dispersion, 753
dissolving torus, 841
distance, 451
--- Hamming distance, 604
--- line-point, 195
--- metric space, 604
--- planes, 217
--- parallel, 217
--- point-line, space, 218
--- point-plane, space, 215
--- spherical, 158
--- two lines, space, 218
--- two points, 191
--- space, 212
distribution, 639 , 640 , 717
--- binomial, 755
--- X2, 762
--- continuous, 758
derivative, 640
Dirac, 640
discrete, 754
--- exponential, 760
--- Fisher, 763
--- frequency, 772
--- function, 751
--- function, continuous, 752
--- hypergeometric, 755 , 756
--- logarithmic normal, 759
--- lognormal distribution, 759
--- measurement error density, 788
--- normal, 758
--- Poisson, 757
--- regular, 640
--- standard normal, 759
--- Student, 763
--- t distribution, 763
--- theory. 714
--- Weibull, 761
distribution problem, 860
distributive law
--- Boolean algebra, 342
--- matrices, 254
--- propositional logic, 287
--- ring, field, 313
--- sets, 293
--- tensors, 264
distributivity, product of vectors, 184
divergence, 667
--- central field, 654
definition, 653
different coordinates, 653
--- improper, 405
--- proper, 405
--- remark, 650
--- sequence of numbers, 405
--- series, 409
--- theorem, 665
--- vector components, 659
--- vector field, 653
divisibility, 320
--- criteria, 322 , 323
division
--- complex numbers, 37
--- computer calculation, 940
--- external, 192
--- golden section, 193
--- harmonic, 192
--- in extreme and mean ratio, 193
--- internal, 192
--- line segment, plane, 192
--- polynomial, 14
--- rational numbers, 1
--- segment, space, 212
divisor, 320
--- greatest common (g.c.d.)
--- integer numbers, 323
--- linear combination, 324
divisor (continued)
--- polynomials, 14
--- positive, 322
dodecahedron, 154
domain, 118
--- closed, 118
--- convergence, function series, 414
doubly-connected, 118
--- function, 47
--- image, set, 48
--- multiply-connected, 118
--- non-connected, 118
--- of attraction, 800
--- of individuals, predicate calculus, 289
--- open, 118
--- operator, 600
--- set, 48
--- simply-connected, 118 , 687
--- three or multidimensional, 118
--- two-dimensional, 118
--- values, set, 48
dot product, 183
double integral, 471
--- application, 474
--- notion, 471
double line, 205
dual, 343
duality
--- linear programming, 856
--- non-linear optimization, 863
--- theorem, strong, 864
duality principle, Boolean algebra, 343
dualizing, 343
Duhamel formula, 722
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