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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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Event, frequency 1083 Event, impossible 1031 Event, random 1031 Event, relative frequency 1083 Event, sure 1031 Events incompatible 1031 Events intersection 1031 Events, difference 1031 Events, equivalent 1031 Events, statistically independent 1036 Events, union 1031 Evolute 378 Evolutionary conditions 792 Evolvent 378 379 Exact differential equation 458 Exact solutions of linear PDEs 594 Example Hilbert 997 Example Weierstrass 997 Excenter 47 Excess coefficient 1045 Excess, spherical 72 Excircle of triangle 47 Excircles 46 Existence and uniqueness theorems, for ODEs 454 488 524 543 Existence and uniqueness theorems, for PDEs 557 577 Expansion of polynomial in powers of linear binomial 156 Expansion, asymptotic 363 Expansion, asymptotic two-term 478 Expectation 1042 Expectation of bivariate random variable 1060 Expectation of continuous random variable 1042 Expectation of discrete random variable 1042 Expectation of function of multivariate random variable 1065 Expectation, conditional 1066 Expectation, population 1087 Expected value of random variable 1042 Exponent, Holder 310 Exponential distribution 1052 Exponential form of complex number 405 Exponential function 21 Exponential function, graphs 21 Exponential function, properties 22 Exponential integral 940 958 Exponential self-similar solution 675 Extended complex plane 402 External angle 43 External angle of polygon 51 Extrema, relative 991 Extremal 994 998 Extremal points of function 269 Extremal properties of quadratic form 220 Extremal, admissible 994 998 Extremal, broken 997 999 Extremal, nonsingular 995 Extremal, regular 995 Extremal, regular point 995 Extremum, absolute 991 Extremum, first-order necessary condition 994 Extremum, necessary condition 269 Extremum, point 269 Extremum, sufficient conditions 269 Extrinsic curvature 394 Face of dihedral angle 60 Face of polyhedral angle 60 Face of polyhedron 61 Face of trihedral angle 60 Factor group 227 Factor, reflection 760 Factorial, xxxi 10 Factorial, xxxi, double, xxxi 10 Faithful representation of group 230 False negative rate 1096 False position method 262 False positive rate 1095 Family equation 377 Family of curves 377 Family of planes 151 Favorable event 1031 Feasible region 1012 Feasible solution 1012 Feller theorem 1077 Ferrari solution 161 Feuerbach points 49 Feuerbach theorem 49 Fifth Painleve transcendents 499 Finite differences 884 Finite games 1024 Finite matrix 167 Finite series 12 Finite subgroup 228 Finite sums 1111 Finite-dimensional Euclidean space 193 First boundary value problem, for elliptic equations 633 First boundary value problem, for hyperbolic equations 627 First boundary value problem, for ODEs 480 First boundary value problem, for ODEs, for PDEs 593 First comparison criterion 338 First duality theorem 1018 First group of derivation formulas 396 First integral 542 544 574 First integral, for system of ODEs 544 First mean value theorem 295 First noteworthy limit 241 First Painleve transcendent 496 First quadratic form of surface 390 First variation of functional 992 First-order differential constraint 739 First-order hyperbolic system of quasilinear equations 780 First-order linear difference equations 1407 First-order necessary condition for extremum 994 First-order neighborhood 991 First-order ordinary differential equation, Bernoulli 458 First-order ordinary differential equation, linear 457 First-order ordinary differential equations 453—472 1207—1211 First-order ordinary differential equations integrable by quadrature 453 First-order ordinary differential equations with separated or separable variables 456 First-order ordinary differential equations, Cauchy problem 454 First-order ordinary differential equations, homogeneous 456 First-order ordinary differential equations, homogeneous, generalized 457 First-order ordinary differential equations, not solved for derivative 454 First-order ordinary differential equations, singular solutions 455 First-order ordinary differential equations, solved for derivative 453 First-order ordinary differential equations, uniqueness and existence theorems 454 First-order partial differential equations 553 1247 First-order partial differential equations, Cauchy problem 556 First-order partial differential equations, general solution 553 First-order partial differential equations, linear 1247 First-order partial differential equations, method of separation of variables 571 First-order partial differential equations, nonlinear 1256 First-order partial differential equations, quasilinear 553 1252 Fisher equation 1301 Fisher information 1089 Fisher test 1104 Fisher transformation 1105 Fisher — Snedecor distribution 1086 Fitzhugh — Nagumo equation 1302 Fixed point of function 908 Flat plate, coordinates of center of mass 324 Flat plate, moments of inertia 324 Flux of vector field 333 Focal axis of ellipse 99 Focal axis of hyperbola 101 Focal distance of ellipse 98 Focal distance of hyperbola 102 Focal distance of parabola 105 Focal parameter of ellipse 98 Focal parameter of hyperbola 102 Focal properties of hyperbola 102 Focal properties of parabola 105 Focal property of ellipse 99 Focal radius of parabola 105 Focal radius right 99 102 Focus of hyperbola 102 Focus of parabola 105 Focus, stable, for ODEs 537 Focus, unstable, for ODEs 537 Focus-directrix property of ellipse 100 Focus-directrix property of hyperbola 103 Focus-directrix property of parabola 105 Folium of Descartes 374 Form, bilinear 214 992 Form, bilinear degenerate 215 Form, bilinear nondegenerate 215 Form, bilinear skew-symmetric 214 Form, bilinear symmetric 214 Form, canonical 462 473 Form, canonical for central surfaces 143 Form, canonical of gas dynamics systems 786 Form, canonical of matrix 181 Form, canonical of quadric 148 Form, canonical of second-order curve 107 Form, linear 213 Form, multilinear 215 Form, multilinear, skew-symmetric 215 Form, multilinear, symmetric 215 Form, normal 473 Form, quadratic 216 218 840 Form, quadratic, degenerate 216 Form, quadratic, negative definite 216 Form, quadratic, nondegenerate 216 Form, quadratic, nonnegative 216 Form, quadratic, nonpositive 216 Form, quadratic, positive definite 216 Form, quadratic, second of surface 392 Form, sesquilinear 213 Formal solution 594 Formula of finite increments 254 Formula of integration by parts 275 409 Formula of repeated integration by parts 275 Formula, Bayes 1036 Formula, Bernoulli 1037 Formula, Bessel 950 Formula, Burman — Lagrange 356 Formula, Cauchy for ODE 519 Formula, Cauchy integral 409 Formula, Cauchy multiple integration 289 Formula, Cauchy series multiplication 343 Formula, Cauchy — Hadamard 411 Formula, Chebyshev 808 Formula, D'Alembert 1278 Formula, de Moivre 400 Formula, Dini 429 Formula, Dirichlet 295 Formula, Euler 405 944 Formula, for calculation of volume of domain 327 Formula, Fourier cosine inversion 445 Formula, Fourier inversion 444 Formula, Frenet 377 Formula, Gauss 396 808 Formula, Green 428 Formula, Heron 48 Formula, Hopf 565 Formula, Kontorovich — Lebedev inversion 448 Formula, Leibnitz 256 Formula, Liouville 473 518 Formula, Liouville for system of ODEs 540 Formula, Maclaurin 257 Formula, Meijer inversion 447 Formula, Newton — Leibniz 288 Formula, Newton — Leibniz for function of complex variable 408 Formula, Peterson — Codazzi 396 Formula, Poisson 949 1038 Formula, Post — Widder 441 Formula, quadrature 808 Formula, Serret — Frenet 386 Formula, Stirling 944 Formula, Sturges 1083 Formula, total probability 1036 Formula, Watson 292 Formula, Willier 74 Formulas, Bayes 1063 Formulas, D'Alembert (Gauss) 73 Formulas, Euler — Fourier 358 Formulas, Frenet 377 Formulas, Frobenius 174 Formulas, Mollweide 44 Formulas, Peterson — Codazzi 397 Formulas, Serret — Frenet 386 Formulas, Weingarten 396 Forward Kolmogorov equation 1076 Fourier coefficients 358 Fourier cosine inversion formula 445 Fourier cosine transform 445 449 Fourier cosine transform, asymmetric 445 Fourier cosine transform, tables 1177 Fourier expansion of even functions 360 Fourier expansion of odd functions 360 Fourier inversion formula 444 Fourier method 602 Fourier series 357 358 Fourier series in complex form 360 Fourier series integration 359 Fourier series of square-integrable functions 361 Fourier series, criteria of uniform convergence 361 Fourier series, differentiation 359 Fourier series, Dirichlet — Jordan convergence criteria 358 Fourier series, Lipschitz convergence criteria 358 Fourier series, Riemann localization principle 358 Fourier sine transform 445 446 449 Fourier sine transform, asymmetric 446 Fourier sine transform, tables 1182 Fourier transform 443 449 614 843 Fourier transform inverse 443 Fourier transform, alternative 444 Fourier transform, asymmetric 444 Fourier transform, asymmetric form 444 Fourier transform, n-dimensional 445 Fourier transform, solving linear problems of mathematical physics 615 Fourier transform, standard form 443 Fourth Painleve transcendent 498 Fourth — degree algebraic equation 159 Fourth-order linear PDEs 1294 Fourth-order nonlinear PDEs 1332 FRACTION 6 Fractional integral 449 Fractional power series 415 Fredholm alternative 834 Fredholm alternative, for symmetric integral equations 839 Fredholm integral equation, first kind 824 825 Fredholm integral equation, second kind 829 852 Fredholm integral equation, second kind with degenerate kernel 830 Fredholm integral equation, second kind with symmetric kernel 835 Fredholm kernel 825 829 Fredholm theorems 834 Free oscillations 1213 Free terms of linear system of equations 197 Frenet formulas 377 Frequency histogram 1086 Frequency of event 1083 Frequency of variate value 1083 Frequency polygon 1085 Frequency, cumulative 1084 Fresnel integrals 304 942 Frobenius formulas 174 Frullani integral 307 Frustum of cone 67 68 Frustum of pyramid 64 Fuchs index 749 Function incomplete beta 947 Function incomplete gamma, xxxii 946
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