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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 Scientists
Авторы: 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.
Organized in ascending order of complexity, the material is divided into two parts. The first part is a coherent survey of the most important definitions, formulas, equations, methods, and theorems. It covers arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, special functions, calculus of variations, and probability theory. Numerous specific examples clarify the methods for solving problems and equations. The second part provides many in-depth mathematical tables, including those ofexact solutions of various types of equations.
This concise, comprehensive compendium of mathematical definitions, formulas, and theorems provides the foundation for exploring scientific and technological phenomena.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 2006
Количество страниц: 600
Добавлена в каталог: 30.06.2008
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Предметный указатель
System, hyperbolic 781 790
System, linear algebraic equations 197
System, linear algebraic equations inconsistent 197
System, linear algebraic equations, consistent 197
System, linear algebraic equations, determined 197
System, linear algebraic equations, homogeneous 197
System, linear algebraic equations, nonhomogeneous 197
System, linear algebraic equations, square 197
System, linear algebraic equations, underdetermined 197
System, linear constant-coefficient ODE 528
System, linear constant-coefficient ODE, first-order 1239
System, linear equations, elementary transformation 199
System, ODEs, autonomous 545
System, ODEs, characteristic equation 529
System, ODEs, first integral 544
System, ODEs, fundamental solutions 539
System, ODEs, Liouville formula 540
System, ODEs, Wronskian determinant 539
System, random variables 1057
System, second-order ODEs 1232
System, solved for derivative (for ODEs) 542
System, strictly hyperbolic 781 790
System, two algebraic equations in two unknowns 198
System, two constant-coefficient first-order linear ODEs 1229
System, two constant-coefficient second-order linear ODEs 1232
Systems, linear ODEs 1229—1237
Systems, linear PDEs 1341 1342
Systems, nonlinear first-order PDEs 1336—1341
Systems, nonlinear ODEs 1239—1246
Systems, nonlinear PDEs of general form 1374—1382
Systems, nonlinear second-order PDEs 1343—1373
t-distribution 1056
Tangency, point 56
Tangent line 251
Tangent line, to surface 388
Tangent plane 268 381 389
Tangent plane, to quadric 152
Tangent plane, to surface 152
Tangent to second-order curve 111
Tangent, positive sense 369
Tangent, slope 368
Tangent, xxxi 24 26 56 368 380
Tangential curvature vector 392
Taylor formula 257 266
Taylor formula, remainder 257
Taylor power series 352 410 411
Telegraph equation 1282
Terminal cost function, Bolza 1001
Terminal value problem 580 583 584
Termination point 373
Terms, secular 502
test 1095
Test power 1096
Test size 1095
Test specificity 1095
Test, Bartlett 1103
Test, Cauchy 303
Test, Cochran 1104
Test, Fisher 1104
Test, Kolmogorov 1099
Test, likelihood ratio 1097
Test, Pearson 1100
Test, Romanovskii 1101
Test, Smirnov 1099
Test, statistical 1095
Test, Wald 1097
Theorem integral of de Moivre — Laplace 1038
Theorem of arrangement of two lines in space 136
Theorem of boundary correspondence 419
Theorem of projections 44
Theorem, Abel 343 411
Theorem, Abel — Ruffini 162
Theorem, Abel, on convergence of power series 351
Theorem, absolute value 296
Theorem, absolute value, for double integral 318
Theorem, absolute value, for triple integral 325
Theorem, addition 1055
Theorem, algebra, fundamental 162
Theorem, Bernoulli 1070
Theorem, binomial 10
Theorem, Bolzano — Cauchy 237
Theorem, boundary correspondence 419
Theorem, Brauer 877
Theorem, Casoratti 902
Theorem, Cauchy 254
Theorem, Cauchy, multiply connected domain 409
Theorem, Cauchy, residue 416
Theorem, Cauchy, series 343
Theorem, Cauchy, simply connected domain 409
Theorem, Cayley — Hamilton 186 212
Theorem, central limit 1071
Theorem, Ceva 48
Theorem, Chebyshev 1070
Theorem, Chetaev of instability 550
Theorem, continuity, for characteristic functions 1067
Theorem, convergence of collocation method 524
Theorem, convolution, for Fourier transform 444
Theorem, convolution, for Laplace transform 437
Theorem, curl 334
Theorem, de Moivre — Laplace integral 1038
Theorem, de Moivre — Laplace, limit 1048
Theorem, de Moivre — Laplace, local 1038
Theorem, decomposition 208 1055
Theorem, density multiplication 1062
Theorem, Descartes 165
Theorem, Dirichlet 295 358
Theorem, Dirichlet, representation of function by Fourier series 357
Theorem, divergence 334
Theorem, double integral, mean value 318
Theorem, duality, second 1018
Theorem, estimation for double integral 318
Theorem, estimation for triple integral 325
Theorem, Euler 61 393
Theorem, Euler — Lagrange 1009
Theorem, existence and uniqueness, Cauchy problem for ODEs 488 524
Theorem, existence and uniqueness, for first-order ODEs 454
Theorem, existence and uniqueness, for first-order PDEs 557 577
Theorem, existence and uniqueness, for systems of ODEs 543
Theorem, Feller 1077
Theorem, Feuerbach 49
Theorem, first duality 1018
Theorem, first mean value for integration 295
Theorem, Fredholm 834
Theorem, fundamental of algebra 162
Theorem, Gakhov first 432
Theorem, Gakhov second 433
Theorem, Gauss 335
Theorem, Green 335
Theorem, half-side 73
Theorem, Hilbert — Schmidt 837
Theorem, Jacobi 180
Theorem, Kolmogorov 1070
Theorem, Kronecker — Capelli 198
Theorem, Lagrange 254
Theorem, Laplace 177
Theorem, Laplace transform, convolution 437
Theorem, Laplace transform, limit 440
Theorem, Legendre 72
Theorem, limit, for Bernoulli process 1038
Theorem, limit, for Laplace transform 440
Theorem, Lindeberg central limit 1071
Theorem, Liouville 403 414
Theorem, local of de Moivre — Laplace 1038
Theorem, Lyapunov of asymptotic stability 549
Theorem, Lyapunov of stability 549
Theorem, Lyapunov, central limit 1071
Theorem, mean value 295
Theorem, mean value for double integral 318
Theorem, mean value for triple integral 325
Theorem, Menelaus 49
Theorem, Mertens, series 343
Theorem, Meusnier 392
Theorem, minimax, for antagonistic two-person zero-sum games 1026
Theorem, minimax, von Neumann 1026
Theorem, Morera 410
Theorem, Morley 49
Theorem, Neyman — Fisher 1090
Theorem, on basic minor 178
Theorem, Ostrogradsky — Gauss 334
Theorem, Peano existence for system of ODEs 543
Theorem, Poisson 428 1070
Theorem, polynomial remainder 156
Theorem, probability multiplication 1035
Theorem, projections 44
Theorem, Ptolemy 52
Theorem, Pythagorean 50 193
Theorem, Riemann 419
Theorem, Riemann — Schwarz 426
Theorem, Rolle 254
Theorem, Rouche 413
Theorem, Schwarz — Christoffel 427
Theorem, second duality 1018
Theorem, second mean value for integration 295
Theorem, Sokhotskii 431
Theorem, Stewart 48
Theorem, Stokes 334
Theorem, Sturm comparison 487
Theorem, Sylvester 186 187
Theorem, triple integral, mean value 325
Theorem, uniqueness 413
Theorem, Viete 158 159 163
Theorem, von Neumann minimax 1026
Theorems of differentiable functions 254
Theorems of instability 549
Theorems of stability 549
Theorems, Fredholm 834
Theoretical distribution function 1082
Theory, game 1024
Theory, stability 546
Theta functions 978
Third boundary value problem, for elliptic equations 634
Third boundary value problem, for hyperbolic equations 627
Third boundary value problem, for ODEs 481
Third boundary value problem, for PDEs 593
Third Painleve transcendent 497
Third-order nonlinear PDEs 1327
Three-dimensional Helmholtz equation 600
Three-dimensional Laplace equation 643 644
Three-dimensional Poisson equation 599
Three-dimensional wave equation 618
Throat ellipse 145
Tikhonov regularization method 828
Titov — Galaktionov method 693
Toroidal coordinates 1205
Torsion 385
Torsion of space curves 385
Torsion radius 385
Torus 68 70
Total derivative 265
Total increments of function 264
Total probability formula 1036
Total variation of function 247
Trace of linear operator 209
Trace of matrix 171
Trajectory, orthogonal 379
Transcendent, Painleve 495
Transcendental branch point 415
transform 435
Transform integral 435
Transform inverse 435
Transform, Bochner 449
Transform, Euler of first kind 449
Transform, Euler of second kind 450
Transform, Fourier 443 449 614 843
Transform, Fourier cosine 445 449
Transform, Fourier inverse 443 614
Transform, Fourier sine 445 446 449
Transform, Fourier, asymmetric form 444
Transform, Fourier, n-dimensional 445
Transform, Fourier, standard form 443
Transform, Gauss 449
Transform, Hankel 446 449 1398
Transform, Hardy 449
Transform, Hartley 449
Transform, Hilbert 449 1396 1398
Transform, Kontorovich — Lebedev 448 449
Transform, Laplace 436 449 611 804 813 843 856
Transform, Laplace inverse 437
Transform, Laplace, two-sided 449
Transform, Meijer (K-transform) 447 449
Transform, Mellin 441 449 826 842 844
Transform, Mellin inverse 442
Transform, Weber 449
Transform, Weierstrass 449
Transformation group 228
Transformation in plane 717
Transformation invertible 267
Transformation of equation of quadric to canonical form 152
Transformation of matrices, orthogonal 182
Transformation, Abel 345
Transformation, Appell 1266
Transformation, auto-Backlund 663
Transformation, Backlund 497 663—665
Transformation, Cole — Hopf 751
Transformation, congruence 182
Transformation, Congruent 182
Transformation, conjunctive 183
Transformation, contact 660
Transformation, equivalence 180
Transformation, Euler 661
Transformation, Fisher 1105
Transformation, Galileo 718
Transformation, Gauss 974
Transformation, graphs of functions 259
Transformation, hodograph 455 657 658
Transformation, Hopf — Cole 666 1308
Transformation, Kummer 345 957
Transformation, Kummer — Liouville 475
Transformation, Landen 974 975
Transformation, Landen, ascending 975
Transformation, Landen, descending 974
Transformation, Legendre 469 660 663
Transformation, linear 656
Transformation, Lorentz 718 1278
Transformation, one-parameter 716
Transformation, orthogonal 182
Transformation, orthogonal, improper 229
Transformation, point 655
Transformation, proper orthogonal 229
Transformation, scaling 656 676 923
Transformation, similarity 181
Transformation, simplifying boundary conditions 649
Transformation, simplifying initial conditions 649
Transformation, translation 656 668
Transformation, unitary 183
Transformation, von Mises 667
Transforming matrix 181
Transition point 477
Transition probability 1075
Translation, parallel 220
Translation, transformation 656 668
Transportation problem 1019 1020
Transportation problem, closed model 1020
Transportation problem, mathematical model 1019
Transportation problem, open model 1020
Transportation, unbalanced 1020
TRANSPOSE 170
Transpose of matrix 170
Transpose of operator 207
Transposed equation 825 829 834
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