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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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Предметный указатель
Schwarz integral 428 Schwarz integral, for half-plane 429 Schwarz — Christoffel theorem 427 Secant, xxxi 24 Second boundary value problem 480 593 Second boundary value problem, for elliptic equations 633 Second boundary value problem, for hyperbolic equations 627 Second boundary value problem, for PDEs 593 Second convergence criterion 338 Second differential 266 Second duality theorem 1018 Second group of derivation formulas 396 Second mean value theorem 295 Second noteworthy limit 241 Second Painleve transcendent 496 Second partial derivatives 266 Second prolongation of operator 720 Second quadratic form of surface 392 Second variation of functional 992 993 Second-order constant coefficient linear ODE 473 1213 Second-order curve 107 Second-order curve invariant 107 Second-order curve, canonical form 107 Second-order curve, center 109 Second-order curve, central 109 Second-order curve, characteristic equation 108 Second-order curve, diameter 108 Second-order curve, elliptic type 108 Second-order curve, general equation 107 Second-order curve, hyperbolic type 108 Second-order curve, normal 111 Second-order curve, on plane 97 Second-order curve, semi-invariant 108 Second-order curve, tangent 111 Second-order curve, vertex 109 Second-order difference equations, linear homogeneous 877 1421 Second-order difference equations, linear nonhomogeneous 879 880 1421 1422 Second-order difference equations, nonlinear 1436 Second-order differential constraint 744 Second-order evolution equation 739 Second-order hypersurface 220 Second-order hypersurface, center 222 Second-order hypersurface, centeral 222 Second-order hypersurface, equation 223 Second-order hypersurface, general equation 220 222 Second-order hypersurface, noncenteral 224 Second-order ordinary differential equations, linear 472—488 1212—1222 Second-order ordinary differential equations, linear, general solution 472 Second-order ordinary differential equations, nonlinear 488—514 1223—1228 Second-order partial differential equations, linear 585—650 1267—1298 Second-order partial differential equations, nonlinear 653 1301—1334 Second-order partial differential equations, quasilinear 654 Second-order partial differential equations, semilinear 653 Second-order variation of functional 993 Secondary diagonal 168 Section, normal 392 Sections, principal normal 393 Sector 58 Sector, circular 58 Sector, spherical 69 Secular terms 502 Segment 58 235 Segment of round cylinder 67 Segment, directed 77 Segment, direction cosine 116 Segment, length 77 Segment, on axis 77 Segment, scale 77 Segment, spherical 69 Segment, value 77 Self-adjoint matrix 168 Self-adjoint operator 206 Self-intersection, point 372 Self-similar solution 669 1442 Self-similar solution, continuous 781 Self-similar solution, exponential 675 Self-similar solution, generalized 677 Self-similar solution, limiting 675 Semi-invariant for probability distribution 1046 Semi-invariant of quadric 148 Semi-invariant of second-order curve 108 Semiaxis 826 842 Semiaxis of ellipsoid 143 Semiaxis of hypersurface 223 Semiaxis, imaginary of hyperbola 102 Semiaxis, imaginary of one-sheeted hyperboloid 144 Semiaxis, imaginary of two-sheeted hyperboloid 144 Semilinear partial differential equations 653 Semimajor axis of ellipse 98 Semiminor axis of ellipse 98 Separable equation 1207 Separable solution 596 Separable solution, additive 596 Separable solution, multiplicative 596 Separated by straight line points 97 Separated equation 456 Separation constant 678 Separation of variables 602 Separation of variables incomplete 597 616 640 Separation of variables, complex 679 Separation of variables, functional 697 Separation of variables, generalized 681 Separation of variables, simple 678 Sequence increasing 238 Sequence infinitely large 239 Sequence, arithmetic 11 Sequence, bounded 237 Sequence, convergent 237 238 Sequence, decreasing 238 Sequence, generic term 237 Sequence, geometric 11 Sequence, limit 237 Sequence, lower limit 240 Sequence, monotone 238 Sequence, numerical 237 Sequence, random 1072 Sequence, upper limit 240 Sequential analysis 1097 Series 337 Series interval 1083 Series interval of convergence 351 Series of order statistics 1082 Series of Poincare type, asymptotic 363 Series solutions for hyperbolic equations 607 Series solutions for ODEs 470 475 492 Series solutions for parabolic equations 605 Series with positive terms, convergence criteria 338 Series with positive terms, divergence criteria 338 Series, Abel convergence criteria 341 Series, Abel theorem 343 Series, Abel transformation 344 Series, absolute convergence 341 Series, arbitrary 341 Series, arithmetic 11 Series, asymptotic 363 Series, Cauchy theorem 343 Series, conditional convergence 341 Series, convergence domain 348 Series, convergent 337 Series, Dirichlet convergence criteria 341 Series, divergent 337 Series, Fourier 357 358 Series, fractional power 415 Series, functional 348 Series, generic term 337 Series, geometric 11 Series, harmonic 339 Series, hypergeometric 960 1218 Series, Kummer 956 1215 Series, Kummer transformation 344 Series, Laurent 410 412 Series, Leibnitz convergence criterion 341 Series, Maclaurin 353 Series, majorant 349 Series, Mertens theorem 343 Series, Neumann 823 833 Series, numerical 337 Series, power 350 Series, Puiseux power 415 Series, remainder 337 Series, statistical 1083 Series, sum 337 Series, summation methods 344 Series, Taylor 352 410 411 Series, uniformly convergent 349 Serret — Frenet formulas 386 Sesquilinear form in unitary space 213 Sesquilinear form, matrix 214 Set, bounded 263 Set, countable 3 Set, diameter 317 Set, modulus 907 Set, submodulus 907 Set, unbounded 263 Shock wave 790—793 1255 Shooting method 512 Shortest distance 70 Side of polygon 51 Sigma rule 1054 Sign function, xxxi Signature of matrix 182 Signature of quadratic form 218 Similar matrices 181 Similarity method 669 Similarity transformation 181 Simple hypothesis 1094 Simple percentage 7 Simple pole 413 Simple polygon 51 Simple Riemann wave 782 783 Simple separation of variables 678 Simple zero 413 Simplest point process 1076 Simplest problem of calculus of variations 993 Simplex method 1014 Simply connected domain 409 Simpson line 47 Simpson rule 315 808 Simpson rule, for computation of integrals 315 Sine 24 25 Sine integral 941 Sine-Gordon equation 1314 Single-step methods of second-order approximation 471 Single-valued function 236 402 Singular integral 310 311 570 571 Singular integral in sense of Cauchy principal value 430 Singular integral, principal value 311 Singular point 371 391 Singular point of generalized solution 580 Singular point of plane curve 371 Singular point of solutions 494 Singular point of surface 391 Singular solutions 455 Singularity, essential 413 Singularity, isolated 413 Singularity, removable 413 Sinh-Gordon equation 756 1314 Sink 535 538 Sink, spiral 537 Sinusoid, sine curve 25 Sixth Painleve transcendents 499 Size, sample 1082 Size, test 1095 Skew lines 59 Skew self-distributivity equation 1449 Skew-Hermitian matrix 168 Skew-Hermitian operator 206 Skew-symmetric bilinear form 214 Skew-symmetric integral equation 840 Skew-symmetric matrix 168 Skew-symmetric multilinear form 215 Skew-symmetric operator 207 skewness 1045 Slope of straight line 89 Slope of tangent 368 Slope-intercept equation of straight line 89 Small circle of a sphere 71 Small discriminant 108 Smallest value of function 258 Smirnov test 1099 Sokhotskii theorem 431 Solid angle 61 Solid geometry 59 Soliton 1325 Soliton solution 765 Soliton solution of Korteweg — de Vries equation 764 Soliton theory 755 Solution in form of infinite series 597 Solution invariant 669 674 716 724 Solution of eigenvalue problems 604 Solution of system of linear algebraic equations 198 Solution, additive separable 571 596 597 678 Solution, asymptotic for ODEs 477 Solution, asymptotically stable 546 Solution, Boussinesq 1294 Solution, Cardano 158 Solution, Cauchy problem, fundamental 616 617 Solution, classical 594 Solution, D'Alembert for wave equation 600 Solution, Descartes — Euler 160 Solution, discontinuous for quasilinear equations 558 Solution, equilibrium 874 884 Solution, exponential self-similar 675 Solution, feasible 1012 Solution, Ferrari 161 Solution, formal 594 Solution, functional separable 697 Solution, functional separable, special 697 Solution, fundamental 599 615 Solution, fundamental for Cauchy problem 616 617 Solution, fundamental for elliptic equations 642 Solution, fundamental for system of ODEs 539 Solution, general for difference equation 874 884 Solution, general for first-order PDEs 553 Solution, general for ODEs 453 472 488 Solution, generalized 563 Solution, generalized self-similar 677 Solution, generalized separable 681 682 Solution, generalized stable 569 Solution, generalized traveling-wave 698 Solution, generalized viscosity 579 580 Solution, generalized, for first-order PDEs 563 568 Solution, generalized, Hopf formula 565 Solution, Levy 914 Solution, limiting self-similar 675 Solution, multiplicative separable 571 596 678 Solution, N-soliton 764 765 Solution, one-parameter 724 Solution, one-soliton 765 Solution, optimal 1012 Solution, particular 453 472 518 594 599 604 Solution, self-similar 669 1440 Solution, self-similar, continuous 781 Solution, self-similar, exponential 675 Solution, self-similar, generalized 677 Solution, self-similar, limiting 675 Solution, separable 596 Solution, separable, generalized 681 Solution, separable, multiplicative 571 Solution, singular for first-order ODEs 455
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