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Polyanin A., Manzhirov A.V. — Handbook of Mathematics for Engineers and Scientists
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Название: Handbook of Mathematics for Engineers and ScientistsАвторы: Polyanin A., Manzhirov A.V. Аннотация: The Handbook of Mathematics for Engineers and Scientists covers the main fields of mathematics and focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. To accommodate different mathematical backgrounds, the preeminent authors outline the material in a simplified, schematic manner, avoiding special terminology wherever possible.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 600Добавлена в каталог: 30.06.2008Операции: Положить на полку |
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Improper integrals of unbounded functions 309 Improper integrals, sufficient conditions for convergence 302 Improper orthogonal transformations 229 Improper subspace 190 Incenter 47 Incenter point 46 incircle 46 Incircle of triangle 46 47 Incompatible events 1031 Incomplete beta function 947 Incomplete cubic equation 158 Incomplete elliptic integral 970 Incomplete equation of plane 124 Incomplete gamma function, xxxii 946 957 958 Incomplete separation of variables 597 616 640 Incomplete system of eigenfunctions 836 Inconsistent system of linear algebraic equations 197 Increasing function 236 238 Increment of argument 992 Increment of functional 992 Increment, partial 264 Indefinite integrals 273 1129 Indefinite integrals involving exponential functions 1137 Indefinite integrals involving hyperbolic functions 1137 Indefinite integrals involving inverse trigonometric functions 1147 Indefinite integrals involving irrational functions 1134 Indefinite integrals involving logarithmic functions 1140 Indefinite integrals involving rational functions 1129 Indefinite integrals involving trigonometric functions 1142 Indefinite integrals, properties 274 Independent random variables 1060 1067 Independent trials 1037 Independent variable 236 Index of inertia 218 Index of inertia, negative 218 Index of inertia, positive 218 Index of matrix 182 Index of multiplication 12 Index of summation 12 Index, characteristic 1221 Index, Fuchs 749 Inequality, Bunyakovsky 296 Inequality, Cauchy 14 296 343 410 Inequality, Cauchy — Bunyakovski 14 296 343 Inequality, Cauchy — Schwarz 121 193 1043 Inequality, Cauchy — Schwarz — Bunyakovski 14 314 Inequality, Chebyshev 14 297 1070 Inequality, Chebyshev, generalized 15 Inequality, Cramer — Rao 1089 Inequality, Holder 14 297 343 Inequality, Holder — Jensen 15 Inequality, Jensen 245 297 Inequality, Markov 1070 Inequality, Minkowski 14 121 193 296 343 Inequality, Steklov 297 Inequality, Sylvester 178 Inequality, triangle 44 73 193 314 Inequality, triangle, generalized 14 343 Infimum, xxxi Infinite game 1024 Infinite matrix 167 Infinite product 346 348 Infinite product, absolute convergence 346 Infinite product, convergent 346 Infinite product, divergent 346 Infinite products with positive factors 347 Infinite products, convergence criteria 347 Infinite series 1116 Infinite-dimensional linear space 189 Infinitely large function 243 Infinitely large quantity 239 Infinitely large sequence 239 Infinitely small function 242 243 Infinitely small quantity 239 Infinitesimal generator 717 Infinitesimal operator 716 717 730 Inflection point 258 Information theory, basic equation 1438 Information, Fisher 1089 Initial condition, for first-order ODEs 454 Initial condition, for parabolic equations 591 Initial condition, homogeneous 591 Initial conditions, for hyperbolic equations 592 Initial conditions, for ODEs 488 524 Initial conditions, for Riemann problem 785 793 Initial conditions, homogeneous 592 Initial moment of multivariate random variable 1065 Initial moment of two-dimensional random variable 1060 Initial value problem 580 785 Injective linear operator 205 Inner product 192 314 840 Inscribed angle 56 Inscribed polygon in circle 51 Integer number 3 Integer power of complex number 399 Integer power of linear operator 205 Integer power of matrix 172 Integrable combinations 545 Integrable function 286 312 314 Integral equation with degenerate kernel 802 803 811 812 Integral equation with difference kernel 804 813 825 829 841 Integral equation with quadratic nonlinearity 865 Integral equation with weak singularity of second kind 829 Integral equation, Abel 1385 Integral equation, Abel of second kind 1392 Integral equation, Abel of second kind, generalized 1393 Integral equation, Abel, generalized 1386 Integral equation, existence and uniqueness of solution 802 Integral equation, first kind with constant integration limit 824 Integral equation, first kind with variable integration limit 801 Integral equation, Fredholm of first kind 824 825 Integral equation, Fredholm of second kind 829 Integral equation, Gel'fand — Levitan — Marchenko 1328 1333 Integral equation, homogeneous 810 829 Integral equation, kernel 801 825 829 Integral equation, Lalesco — Picard 1403 Integral equation, linear 801 810 824 829 Integral equation, nonhomogeneous 810 829 Integral equation, nonlinear 856 Integral equation, nonlinear with constant integration limits 856 863 Integral equation, nonlinear with degenerate kernel 863 Integral equation, nonlinear with variable integration Integral equation, limit 856 Integral equation, parameter 829 Integral equation, regularization methods 827 Integral equation, right-hand side 810 Integral equation, Schlomilch 1400 Integral equation, second kind with constant integration limits 829 Integral equation, second kind with variable integration limit 810 Integral equation, skew-symmetric 840 Integral equation, symmetric 835 Integral equation, Tricomi 1403 Integral equation, Urysohn with degenerate kernel 863 864 Integral equation, Urysohn, nonlinear 856 Integral equation, Volterra of first kind 801 807 Integral equation, Volterra of second kind 807 810 Integral equation, Volterra with quadratic nonlinearity 856 Integral equation, Volterra, nonlinear 856 858—861 Integral equation, Wiener — Hopf of first kind 825 1401 Integral equation, Wiener — Hopf of second kind 829 1406 Integral equations 801—871 1385—1406 Integral equations, first kind with constant limits of integration 824 1396—1400 Integral equations, first kind with variable limit of integration 801 1385—1390 Integral equations, first kind with weak singularity 825 Integral equations, linear 801—855 1385—1406 Integral equations, method of differentiating 866 Integral equations, second kind with constant limits of integration 829 1401—1408 Integral equations, second kind with variable limit of integration 810 1391—1395 Integral formulas of vector calculus 334 Integral indefinite 273 Integral involving power-law functions 1147 Integral of differential binomial 281 Integral of function of complex variable 407 Integral sum 286 317 Integral sum, Stieltjes 312 Integral theorem of de Moivre — Laplace 1038 Integral transform, Bochner 449 Integral transform, Euler, first kind 449 Integral transform, Euler, second kind 450 Integral transform, Fourier 443 449 Integral transform, Fourier cosine 445 449 Integral transform, Fourier inverse 443 Integral transform, Fourier sine 446 449 Integral transform, Fourier, asymmetric form 444 Integral transform, Fourier, n-dimensional 445 Integral transform, Fourier, standard form 443 Integral transform, Gauss 449 Integral transform, Hankel 446 449 Integral transform, Hardy 449 Integral transform, Hartley 449 Integral transform, Hilbert 449 Integral transform, kernel 435 Integral transform, Kontorovich — Lebedev 448 449 Integral transform, Laplace 436 449 Integral transform, Laplace inverse 437 Integral transform, Laplace, two-sided 449 Integral transform, Meijer 447 449 Integral transform, Meler — Fock 449 Integral transform, Mellin 441 449 Integral transform, Mellin inverse 442 Integral transform, Weber 449 Integral transform, Weierstrass 449 Integral transforms 435 1155 Integral transforms inversion formulas 435 Integral transforms, general form 435 Integral transforms, method for linear PDEs 611 Integral with infinite limits 301 Integral, absolutely convergent 303 Integral, Cauchy-type (singular) 310 409 430 Integral, closed path 331 Integral, complete 570 Integral, curvilinear 329 Integral, definite 286 Integral, Dini 1287 Integral, Dirichlet — Mehler 963 Integral, divergent 301 Integral, Duhamel 516 Integral, elliptic of first kind 970 Integral, elliptic of second kind 970 Integral, elliptic of third kind 971 Integral, elliptic, complete of first kind 969 Integral, elliptic, complete of second kind 969 Integral, exponential 958 Integral, fractional 449 Integral, Fresnel 304 Integral, Frullani 307 Integral, general 571 Integral, improper 301 Integral, iterated 319 Integral, Laplace 418 521 963 Integral, Laplace of general form 292 Integral, Laplace, power 294 Integral, Laplace, power, multiple 328 Integral, Laplace, special form 291 Integral, line of first kind 329 Integral, line of second kind 330 331 Integral, logarithmic 958 Integral, multiple Laplace-type 328 Integral, path 329 Integral, Poisson 428 1287 Integral, Poisson, for half-plane 429 Integral, potential-type 291 Integral, Riemann 286 Integral, Schwarz 428 Integral, Schwarz, for half-plane 429 Integral, singular (Cauchy-type) 310 311 430 571 Integral, Stieltjes 312 Integral, surface of first kind 332 Integral, surface of second kind 333 Integrals of motion 766 Integrals, tables 1129 Integrand (function) 273 Integrating factor 459 Integrating factor of Pfaffian equation 773 Integration by parts 275 Integration by parts, repeated 275 Integration of asymptotic series 365 Integration of exponential functions 281 Integration of hyperbolic functions 281 Integration of improper fractions 278 Integration of irrational functions 279 Integration of proper fraction 277 Integration of rational functions 276 Integration of trigonometric functions 282 Intercept equation of plane 125 Intercept-intercept equation of straight line 91 Intergroup sample variance 1108 Interior angle 43 Interior angle of polygon 51 Interpolation nodes 808 Interpolation polynomial 186 Intersection of events 1031 Intersection of four planes 139 Intersection of line and plane 140 Intersection of subspaces 190 Intersection of three planes 139 interval 235 Interval of convergence of power series 351 Interval, closed, xxx 235 Interval, confidence 1093 Interval, estimator 1088 1093 Interval, half-open, xxx 234 Interval, open, xxx 235 Interval, series 1083 Intrinsic equations of curve 388 Intrinsic geometry of surface 391 395 Invariance condition 719 720 732 Invariant 222 731 Invariant condition 731 Invariant of group 731 Invariant of infinitesimal operator 717 Invariant of linear operator 211 Invariant of operator 717 731 Invariant of quadric 148 Invariant of second-order curve 107 Invariant representation 230 Invariant solution 669 674 716 724 Invariant subspace 205 230 Invariant surface condition 732 Invariant, universal 731 Inverse element 225 Inverse Fourier transform 443 614 Inverse function 237 Inverse hyperbolic cosine 40 Inverse hyperbolic cotangent 40 Inverse hyperbolic functions 39 Inverse hyperbolic functions integration formulas 41 Inverse hyperbolic functions, differentiation formulas 41 Inverse hyperbolic functions, expansion in power series 42 Inverse hyperbolic functions, properties 41 Inverse hyperbolic sine 39 Inverse hyperbolic tangent 40 Inverse Laplace transform 437 611 Inverse Laplace transform, tables 1162 Inverse matrix 171 Inverse matrix, left 171 Inverse matrix, right 171 Inverse Mellin transform 442 Inverse Mellin transform, tables 1190 Inverse of mapping 226 Inverse operator 205
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