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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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Bilinear functional equations 930 Bilinear series of iterated kernels 838 Bimodal distribution 1045 Binomial algebraic equation 161 Binomial coefficients, xxx 10 937 Binomial distribution 1047 Binomial theorem 10 Binormal 382 Bipolar coordinates 1204 Biquadratic equation 159 Birth — death processes 1077 Bisection method 261 Bisector, perpendicular 46 Bivariate random variable 1060 Bivariate random variable, central moment 1060 Bivariate random variable, expectation 1060 Block matrix 174 Blow-up regime 1303 Bochner transform 449 Body, coordinates of center of mass 327 Body, moments of inertia 327 Bolza functional 1001 Bolza Lagrangian 1001 Bolza problem 1001 Bolza terminal cost function 1001 Bolzano — Cauchy theorem 237 Born — Infeld equation 659 Bound, lower 235 Bound, upper 235 boundary conditions 484 591 592 Boundary conditions, first kind 484 Boundary conditions, homogeneous 481 591 649 Boundary conditions, mixed 486 Boundary conditions, nonhomogeneous 481 649 Boundary conditions, second kind 485 Boundary conditions, third kind 486 Boundary correspondence principle 420 Boundary correspondence theorem 419 Boundary function 419 Boundary point of domain 401 Boundary value problem 427 Boundary value problem with many space variables 634 Boundary value problem, arbitrary cylindrical domain 642 Boundary value problem, difference equations 879 Boundary value problem, elliptic equations 631 Boundary value problem, first 480 593 627 Boundary value problem, Hilbert — Privalov 432 Boundary value problem, hyperbolic equations 623 Boundary value problem, mixed 480 593 627 Boundary value problem, nonhomogeneous 620 624 Boundary value problem, ordinary differential equations 480 Boundary value problem, parabolic equations 645 Boundary value problem, rectangular domains 640 Boundary value problem, second 480 593 627 Boundary value problem, third 480 593 627 Boundary, confidence 1081 Boundary, domain 401 Boundary, positive sense 402 Bounded function 236 Bounded operator 204 Bounded sequence 237 Bounded set 263 Bounded variation 247 313 Boussinesq equation 709 1332 Boussinesq solution 1294 Bracket, Jacobi — Mayer 574 Branch of many-valued function 404 Branch point 414 Branch point infinite order 415 Branch point, function 404 Branch point, logarithmic 415 Branch point, order 414 Brauer theorem 877 Break point 373 Broken extremal 997 999 Bubnov — Galerkin method for integral equations 850 Bubnov — Galerkin method for ODEs 509 Budan — Fourier method 166 Bugaev convergence criterion for series 341 Bunyakovsky inequality 296 Burgers equation 664 666 751 1307 Burgers equation, radial symmetric case 1307 Burman — Lagrange formula 356 Calculus of variations 991 Calculus of variations, simplest problem 993 Canonical basis 217 Canonical coefficients 217 Canonical coordinates, ellipse 98 Canonical coordinates, hyperbola 101 Canonical coordinates, parabola 104 Canonical equation, circle 97 Canonical equation, ellipse 98 Canonical equation, hyperbola 101 Canonical equation, noncentral hypersurface 224 Canonical equation, parabola 104 Canonical equation, straight line in space 132 Canonical equation, straight line passing through given point on plane 90 Canonical equation, straight line passing through two given points on plane 90 Canonical form, Abel differential equation of first kind 463 Canonical form, Abel differential equation of second kind 465 Canonical form, central surfaces 143 Canonical form, elliptic equation 588 Canonical form, gas dynamics systems 786 Canonical form, hyperbolic equation 587 Canonical form, Jordan of matrix 182 Canonical form, linear operators 213 Canonical form, matrix 181 Canonical form, parabolic equation 586 Canonical form, quadric 148 Canonical form, Riccati differential equation 460 Canonical form, second-order curve 107 Canonical representation of quadratic form 217 Canonical second-order curves 107 Canonical substitutions 465 Cantor equation, first 1442 Cantor equation, second 1449 Cap, spherical 69 Cardano solution 158 Carleman equation 1399 Cartesian coordinate system 78 114 Cartesian coordinate system in plane 78 Cartesian coordinate system in space 114 Cartesian coordinate system, oblique 79 Casoratti determinant 901 Casoratti theorem 902 Cauchy convergence criterion for series 339 Cauchy criterion 337 Cauchy distribution 1054 Cauchy equation 1438 Cauchy equation, exponential 1443 Cauchy equation, logarithmic 1439 Cauchy equation, power 1444 Cauchy formula for multiple integration 289 Cauchy formula for ODE 519 Cauchy inequality 14 296 343 Cauchy inequality for functions of complex variables 410 Cauchy integral formula 409 Cauchy principal value for singular integral 311 430 Cauchy problem 591 592 785 1308 Cauchy problem, difference equations 874 889 893 Cauchy problem, existence and uniqueness theorems for ODEs 454 488 524 577 Cauchy problem, first-order ODEs 454 Cauchy problem, first-order PDEs 556 576 Cauchy problem, fundamental solution 616 617 Cauchy problem, generalized 627 Cauchy problem, Hamilton — Jacobi equation 577 Cauchy problem, hyperbolic equations 617 Cauchy problem, parabolic equations 615 Cauchy problem, second-order ODEs 488 Cauchy problem, system of PDEs 785 Cauchy series multiplication formula 343 Cauchy tests 303 Cauchy theorem 254 343 Cauchy theorem, multiply connected domain 409 Cauchy theorem, residue 416 Cauchy theorem, simply connected domain 409 Cauchy — Bunyakovski inequality 14 296 343 Cauchy — Hadamard formula 411 Cauchy — Riemann conditions 402 Cauchy — Riemann sum 286 Cauchy — Schwarz inequality 121 193 1043 Cauchy — Schwarz — Bunyakovski inequality 14 314 Cauchy-type singular integral 310 409 430 Cayley — Hamilton theorem 186 212 Center of mass of body 327 Center of mass of flat plate 324 Center, curvature 375 Center, ellipse 99 Center, equilibrium point, for ODEs 537 Center, gravity of triangle 45 Center, hyperbola 102 Center, pencil 92 Center, regular polygon 55 Center, second-order curve 109 Center, second-order hypersurface 222 Center, surface 143 151 Centered rarefaction wave 558 Central angle 55 56 Central cross-correlation function 1073 Central cylinder 225 Central hypersurface 222 Central limit theorem 1071 Central moment 1043 Central moment, bivariate random variable 1060 Central moment, n-dimensional random variable 1065 Central second-order curve 109 Central surface 143 Centroid 45 Ceva theorem 48 Character of group element 231 Characteristic 654 Characteristic equation 514 654 1046 1066 Characteristic equation, difference equation 881 Characteristic equation, linear operator 211 Characteristic equation, linear PDEs 585 Characteristic equation, matrix 185 Characteristic equation, quadratic form 150 Characteristic equation, second-order curves 108 Characteristic equation, system of ODEs 529 Characteristic function 1046 1066 Characteristic function, Continuity Theorem 1067 Characteristic index 1221 Characteristic matrix 183 Characteristic point 377 Characteristic polynomial, linear operator 211 Characteristic polynomial, matrix 185 Characteristic quadratic form 150 Characteristic quadratic form of quadric 150 Characteristic system for first-order PDEs 553 555 573 576 Characteristic value integral equation 829 834—836 840 Characteristic value, linear operator 209 Characteristic velocity 790 Chebyshev formula 808 Chebyshev functions of second kind 985 Chebyshev inequalities 14 297 1070 Chebyshev inequalities, generalized 15 Chebyshev nodes 523 Chebyshev polynomials, first kind 983 Chebyshev polynomials, second kind 984 Chebyshev theorem 1070 Chetaev theorem of instability 550 Chi-square distribution 1054 Chord 56 143 Christoffel symbols, first kind 396 Christoffel symbols, second kind 396 circle 56 97 Circle, canonical equation 97 Circle, curvature 375 Circle, diameter 56 Circle, great of a sphere 68 70 Circle, nine-point 49 Circle, osculating 375 Circle, parametric equations 98 Circle, small of a sphere 71 Circular point 393 Circular sector 58 Circulation 331 Circumcenter 46 circumcircle 46 Circumcircle of triangle 46 Circumscribed about circle, polygon 51 Cissoid of Diocles 372 Clairaut equation 467 572 1262 Clairaut system 1240 Clarkson — Kruskal direct method 708—710 Classical definition of probability 1033 Classical integral functional 993 Classical method of symmetry reductions 716 Classical solution 594 Classification, central second-order hypersurfaces 223 Classification, noncentral second-order hypersurfaces 224 Classification, points on surface 394 Classification, quadrics 148 Classification, second-order linear PDEs 585 Closed domain 402 Closed model of transportation problem 1020 Closed path integral 331 Coalition game 1024 Cochran statistic 1104 Cochran test 1104 Coefficient, asymmetry 1045 Coefficient, asymmetry, sample 1088 Coefficient, correlation, multiple 1066 Coefficient, excess 1045 Coefficient, excess, sample 1088 Coefficient, Pearson first skewness 1045 Coefficient, reflection 760 Coefficient, regression 1063 Coefficient, variation 1045 Coefficients, binomial, xxx 10 28 Coefficients, canonical for quadratic form 217 Coefficients, Fourier 358 Coefficients, Lame 1196 Coefficients, system of linear equations 197 Coefficients, undetermined 847 Cofactor of matrix entry 176 Cofactor of minor 177 Cole — Hopf transformation 751 Cole — Kevorkian scheme (method) 504 Collinear vectors 113 Collocation method 509 523 847 848 860 Collocation method integral equations 847 860 Collocation method, convergence theorem 524 Collocation points 848 Column expansion of determinant 176 Column vector 167 Column vectors, linear combination 171 Column vectors, linearly dependent 171 Column vectors, linearly independent 171 Column, pivot 1016 Columns, basic 178 Combinations 1033 Combinations integrable 545 Combinations integrable with repetitions 1034 Common difference 11 Common logarithm 9 Common ratio 11 Commutative composition law 225 Commutative group 226 Commutator of operators 755
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