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