I
icosahedron, 154
ideal, 313
--- principal ideal, 313
idempotence law
--- Boolean algebra, 343
--- propositional logic, 287
--- sets, 293
identically valid, 10
identity, 10
--- Boolean function, 344
--- representation of groups, 303
identity matrix, 253
IEEE standard, 939
IF-THEN rule, 372
iff (if andonlyif), 320
image
--- function, 48
--- set, 48
--- space, 48 , 707
--- subspace, 317
imaginary
--- number, 34
--- part, 34
--- unit, 34
implication, 286
--- proof, 5
impulse function, 714
impulse, rectangular, 714
incidence function, 348
incidence matrix, 350
incircle
--- quadrangle, 136
--- triangle, 132 , 143
incommensurability, 4 , 806
increment, 21 , 394
independence
--- linear, 272 , 598
--- path of integration, 468 , 687
--- potential field, 662
induction step, 5
inequality, 28
--- arithmetic and geometric mean, 30
--- arithmetic and quadratic mean, 30
--- Bernoulli, 30
--- Bessel, 618
--- binomial, 31
--- Cauchy-Schwarz, 31
--- Chebyshev, 31 , 754
--- Chebyshev, generalized, 32
--- different means, 30
--- first degree, 33
--- Holder, 32
--- linear, 33
--- first degree, 33
--- solution, 33
--- Minkowski, 32
--- product of scalars, 31
--- pure, 28
--- quadratic, 33
--- solution, 33
--- Schwarz-Buniakowski, 615
--- second degree, 33
--- solution, 28
--- special, 30
--- triangle, 181
--- norm, 611
--- triangle inequality
--- complex numbers, 30
--- real numbers, 30
infimum, 602
infinite
--- denumerable, 298
--- non-denumerable, 298
infinitesimal quantity, 441
infinity, 1
infix form, 298
inflection point, 231 , 390 , 391
initial conditions, 487
--- hid
initial value problem, 487 , 904
inner product, 615
inscribed circle
--- quadrangle, 136
--- triangle, 132
inscribed pentagram. 138
instability, round-off error
--- numerical calculation, 942
insurance mathematics, 21
integer
--- non-negative. 1
--- part of x, 49
--- programming, 847
integrability
--- complete, 521
--- condition, 469
--- conditions, 468 , 662
--- differential, 468
--- quadratic, 579
integral
--- absolutely convergent, 458
--- antiderivative, 427
--- basic
--- notion, 428
--- calculus, 427
--- circuit, 462 , 468
--- complex
--- definite, 685
indefinite, 686
--- complex function
--- measurable function, 637
--- elementary functions, 428
--- error integral, 461
--- Euler, 459 , 461
--- exponential integral, 461
--- Fourier integral, 424 , 724
--- Fresnel, 697
interval of integration, 441
--- Lebesgue integral, 637
--- comparison with Riemann integral, 453
--- limits of integration, 441
--- line integral, 462
--- first type, applications, 464
--- lorarithmic integral, 431
--- lower limit, 441
--- non-elementary, 431 , 460
--- parametric, 459
--- primitive function, 427
--- probability integral, 759
--- Riemann, 441
--- comparison with Stieltjes integral, 453
--- Stieltjes, 628
--- comparison with Riemann integral, 453
--- notion, 453
--- surface integral, 479 , 483 , 485 , 664
--- triple integral, 476
--- upper limit, 441
--- volume integral, 476
integral calculus, 427
--- fundamental theorem, 442 , 458
--- mean value theorem, 444
integral cosine, 460
integral curves, 798
integral equation
--- Abel, 590
--- adjoint, 565 , 592
--- approximation
--- successive, 567
--- characteristic, 592
--- collocation method, 576
--- eigenfunction, 565
--- eigenvalue, 565
--- first kind, 563
--- Fredholm, 563 , 609
--- degenerate kernel, 577
--- first kind, 577
--- second kind, 564
--- general form, 563
--- homogeneous, 563
inhomogeneous, 563
iteration method, 567 , 584
--- kernel, 563
--- degenerate, 564
iterated, 587
--- product, 564
--- kernel approximation, 574
--- tensor product, 574
--- linear, 563
--- Nystrom method, 573
--- orthogonal system, 579 , 582
--- perturbation function, 563
--- quadratically integrable function, 579
--- quadrature formula, 572
--- second kind, 563
--- singular, 590
--- Cauchy kernel, 591
--- transposed, 565
--- Volterra, 563 , 609
--- convolution type, 587
--- first kind, 585
--- second kind, 585
integral equation method, closed curve, 534
integral exponential function, table, 1051
integral formula
--- Cauchy, 689
--- application, 694
--- Gauss, 666
--- series remainder, 418
integral logarithm, table, 1053
integral norm, 639
integral surface, 518
integral test of Cauchy, 408
integral theorem, 665
--- Cauchy, 688
--- Gauss, 665
--- Green, 666
--- Stokes, 666
integral transformation, 707
--- application, 709
--- Carson, 707
--- definition, 707
--- Fourier, 707
--- Gabor. 743
--- Hankel, 707
image space, 707
inverse, 707
integral transformation (continued)
--- kernel, 707
--- Laplace, 707
--- linearity, 707
--- Mellin, 707
--- multiple, 709
--- one variable, 707
--- original space, 707
--- several variables, 709
--- special, 707
--- Stieltjes, 707
--- Walsh, 744
--- wavelet, 740 , 741
--- fast, 743
integral, definite, 440
--- differentiation, 443
--- notion, 427
--- particular integral, 442
--- table, 1056
--- algebraic functions, 1059
--- exponential function, 1057
--- logarithmic function, 1058
--- trigonometric functions, 1056
integral, elliptic, 437
--- first kind, 431 , 437 , 703
--- second kind, 437
--- series expansion, 462
--- table, 1061
--- third kind, 437
integral, improper, 440
--- Cauchy's principal value, 454 , 457
--- convergent, 454 , 456
--- divergent, 454 , 456
infinite integration limits, 453
--- notion, 453
--- principal value, 454
--- unbounded integrand, 453
integral, indefinite, 427
--- basic integral, 428
--- cosine function, table, 1043
--- cotangent function, table, 1049
--- elementary functions, 428
--- elementary functions, table, 1023
--- exponential function, table, 1051
--- hyperbolic functions, table, 1050
inverse hyperbolic functions, table, 1055
inverse trigonometric function, table, 1054
irrational functions, table, 1030
--- logarithmic functions, table, 1053
--- notion, 428
--- other transcendental functions, table, 1050
--- sine and cosine function, table, 1045
--- sine function, table, 1041
--- table, 1023
--- tangent function, table, 1049
--- trigonometric functions, table, 1041
integral, logarithmic, 431
integral, surface
--- first type, 479
--- general form, 485
--- second type, 483
integrand, 428 , 441
integrating factor, 490
integration
--- approximate
--- ordinary differential equation, 904
--- partial differential equation, 911
--- complex plane, 685
--- constant, 428
--- function, non-elementary, 460
--- graphic, 432
--- graphical, 446
in complex, 694
interval, 441
--- limit
--- depending on parameter, 459
--- lower, 441
--- upper, 441
--- logarithmic, 430
--- numerical, 898
--- multiple integrals, 903
--- partial, 431
--- power, 430
--- rational functions, 432
--- rules
--- by series expansion, 431
--- by substitution, 431
--- constant multiple rule, 429
--- definite integrals, 443
--- general rule, 429
indefinite integrals, 430
interchange rule, 444
interval rule, 443
--- series expansion, 446 , 460
--- sum rule, 429
--- under the integration sign, 459
--- variable, 441
--- variable, notion, 428
--- vector field, 660
--- volume, 450
integrator, 447
intensity, source, 668
interaction, soliton, 547
intercept theorem, 134
interest, 22
--- calculation, 21
--- compound, 22
intermediate value theorem
--- one variable, 59
--- several variables, 123
intermediate variable, 382
intermittence, 839 , 843
Internationale Standard Book Number ISBN, 332
interpolation
--- Aitken-Neville, 918
--- condition, 917
--- formula
--- Lagrange, 918
--- Newton, 917
--- fuzzy system, 377 , 378
--- knowledge-based, 377
--- node, 898
--- equidistant, 904
--- points, 917
--- quadrature, 899
--- spline, 917 , 931
--- bicubic, 933
--- cubic, 931
--- trigonometric, 917 , 927
interpretation
--- formula, predicate logic, 289
--- variable, 287
intersection, 292
--- angle, 159
--- by two oriented lines, 147
--- fuzzy set, 365
--- on the sphere, 171
--- point
--- four planes, 216
--- lines, 195
--- plane and line, 218
--- three planes, 216
--- two lines, space, 219
--- set, fuzzy set, 366
--- sets, 292
--- without visibility, 147
interval
--- convergence, 416
--- numbers, 2
--- order (O)-interval, 602
--- rule, 443
--- statistics, 772
invariance
--- rotation invariance, 265
--- transformation invariance, 265
--- translation invariance, 265
invariant, 706
--- quadratic curve, 206
--- scalar, 212
--- scalar invariant, 184
--- surface second order, 224
inverse, 601
inverse function, 51
--- hyperbolic, 91
--- trigonometric, 84
inverse transformation, 707
inversion
--- Cartesian coordinate system, 269
--- conformal mapping, 676
--- space, 269
involute, 237
irrational
--- algebraic, 2
--- quadratic, 2
isometry, space, 611
isomorphic
--- vector spaces, 601
isomorphism, 302 , 341
--- Boolean algebra, 343
--- graph, 349
--- groups, 302
--- surjective norm, 626
iteration, 884
inverse, 283
--- method, 283 , 884 , 895
--- ordinary, 884 , 896
--- sequential steps, 896
--- simultaneous steps, 896
--- vector, 284
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