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Polyanin A., Manzhirov A.V. — Handbook of Mathematics for Engineers and Scientists
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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 600

Добавлена в каталог: 30.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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