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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
Transposition      178
Transversality condition      577 1001
Transverse vibration of elastic rods      1294
trapezoid      54
Trapezoid, altitude      54
Trapezoid, base      54
Trapezoid, isosceles      54
Trapezoid, leg      54
Trapezoid, median      54
Trapezoidal rule      315 808 810 824
Trapezoidal rule, computation of integrals      315
Traveling-wave equation      1439
Traveling-wave solution      554 667 775 790 796
Traveling-wave solution, generalized      697
Trefoil      373
Trials independent      1037
triangle      43
Triangle incircle      46 47
Triangle inequality      14 44 73 193 314
Triangle rule      113 176
Triangle, altitude      46
Triangle, area      48
Triangle, center of gravity      45
Triangle, circumcircle      46
Triangle, equilateral      43 51
Triangle, excircle      47
Triangle, isosceles      43 50
Triangle, median      45
Triangle, obtuse      43
Triangle, orthocenter      46
Triangle, plane      43
Triangle, right      43 50
Triangle, right-angled      43
Triangle, scalene      43
Triangle, spherical      71 72
Triangles, Euler      71
Triangles, plane      43
Triangular decomposition      180
Triangular pyramid      63
Triangular representation      201
Triaxial ellipsoid      144
Tricomi equation      1403
Trigonometric circle      24
Trigonometric form of complex number      400
Trigonometric functions      24
Trigonometric functions integration formulas      30
Trigonometric functions of half argument      29
Trigonometric functions of multiple arguments      29
Trigonometric functions, differentiation formulas      29
Trigonometric functions, expansion in power series      30
Trigonometric series      1122—1128
Trigonometric substitutions      280
Trihedral angle      60
Trihedral angle, edge      60
Trihedral angle, face      60
Trihedral angle, vertex      60
Trihedral, moving      382
Trihedral, natural      382
Trihedral, right-handed      121
Triple cross product of vectors      122
Triple integral      324
Triple integral, change of variables      326
Triple integral, estimation theorem      325
Triple integral, geometric applications      327
Triple integral, mean value theorem      325
Triple integral, physical applications      327
Triple integral, properties      324
Triple point      371
Trivial representation of group      230
Trivial solution      197
Truncated cylinder      66
Truncated expansion      749
Truncated prism      62
Tube, cylindrical      67
Two-body problem      1260
Two-dimensional Helmholtz equation      599
Two-dimensional Klein — Gordon equation      618
Two-dimensional Poisson equation      599
Two-dimensional random variable initial moment      1060
Two-dimensional random variable, moment      1060
Two-dimensional random vector, distribution function      1057
Two-dimensional wave equation      618
Two-person game      1024
Two-sheeted hyperboloid, imaginary semiaxis      144
Two-sided Laplace transform      449
Two-term asymptotic expansions      478
Types of linear PDEs      585
Types of matrices      167
Ultrahyperbolic equation      590
Ultraspherical polynomials      987
Umbilical point      393
Unbalanced transportation      1020
Unbiased estimator      1089
Unbounded set      263
Uncomputable integrals      276
Uncorrelated random variables      1061
Underdetermined system of linear algebraic equations      197
Undetermined coefficients method      17 277
Uniform convergence of functions      249
Uniform convergence, Weierstrass criterion      349
Uniform distribution      1051
Uniformly convergent functional series      349
Uniformly convergent series      349
Unimodal distribution      1045
Union of events      1031
Uniqueness and existence theorems for first-order ODEs      454
Uniqueness theorem      171 413
Unit normal vector      389
Unit sphere      220
Unit vector      113
Unit, imaginary      399
Unitarity condition      206
Unitary group      229
Unitary matrix      171
Unitary operator      206
Unitary space      195
Unitary space, isomorphic      196
Unitary space, normed      195
Unitary space, orthogonal elements      195
Unitary transformation      183
Unitary transformation of matrices      183
Universal invariant      731
Unknown quantities      199 201
Unstable focus      536 537
Unstable solution      546
Unstable spiral point      537
Upper bound      235
Upper half-plane      79
Upper limit of sequence      240
Upper price of game      1025
Upper triangular matrix      168
Urysohn equation with degenerate kernel      863 864
Urysohn integral equation      856
Value of segment      77
Value, Cauchy principal, for singular integral      311
Value, characteristic      829 834
Value, characteristic of operator      209
Value, game      1025
Van der Pol — Krylov — Bogolyubov scheme (method)      503
Vandermonde determinant      179
Vandermonde matrix      179
Variable density      327
Variable incomplete separation      597
Variable parameter      87
Variable, artificial      1016
Variable, basic      1015
Variable, nonbasic      1015
Variable, phase      546 1010
Variable, random      1039
Variable, symmetric random      1041
Variables independent      236
variables, dependent      236
Variables, random independent      1060 1067
Variance      1044
Variance of empirical distribution      1088
Variance of random variable      1044
Variance, multifactor analysis      1108
Variance, population      1087
Variance, residual      1066 1108
Variance, sample      1088
Variate value, frequency      1083
Variation of argument      992
Variation of functional      992
Variation, coefficient      1045
Variation, second of functional      993
Variation, total of function      247
Vector      113 167 187
Vector field, flux      333
Vector field, potential      331
Vector opposite to vector      113
Vector space      187
Vector stochastic process      1072
Vector, associated      213
Vector, curvature      383
Vector, Darboux      386
Vector, geodesic curvature      392
Vector, issuing from point A with endpoint B      189
Vector, length      113
Vector, normal      124
Vector, normal curvature      392
Vector, normal unit      389
Vector, position      115
Vector, tangential curvature      392
Vector, two-dimensional random      1057
Vector, unit      113
Vector, zero      113
Vectors in space      113
Vectors, collinear      113
Vectors, coordinate      388
Vectors, coplanar      113
Vectors, cross product      121
Vectors, difference      113 188
Vectors, linear combination      188
Vectors, parallel      113
Vectors, scalar product      120
Vectors, scalar triple product      123
Vectors, sum      113
Vectors, triple cross product      122
Velocity, characteristic      790
Versatile trigonometric substitution      282
Vertex      43
Vertex of ellipse      99
Vertex of hyperbola      102
Vertex of parabola      105
Vertex of polygon      51
Vertex of polyhedral angle      60
Vertex of polyhedron      61
Vertex of second-order curve      109
Vertex of trihedral angle      60
Vertical asymptote      242
Vertices of spherical triangle      71
Vibration equation with axial symmetry      1282
Vibration of string      1276
Viete theorem      158 159 163
Viscosity solution      564
Volterra integral equation with quadratic nonlinearity      856
Volterra integral equation, first kind      801 807
Volterra integral equation, nonlinear      856
Volterra integral equation, second kind      807 810 858
von Mises transformation      667
Von Neumann minimax theorem      1026
Wald test      1097
Watson formula      292
Wave equation, linear      585 1278
Wave equation, linear, three-dimensional      618
Wave equation, linear, two-dimensional      618
Wave equation, nonlinear      723 1312—1317
Wave, breaking      559
Wave, centered rarefaction      558
Wave, rarefaction      559 785 1255
Wave, Riemann      782 783
Wave, shock      561 790—793 1255
Wave, “overturn”      559
Weak convergence      1069
Weak law of large numbers      1069
Weak local maximum      993 1001 1002 1006
Weak maximum of functional      991
Weak neighborhood      991
Weak singularity      801
Weak singularity of second kind      829
Weak solution      563
Weber parabolic cylinder function      967
Weber transform      449
wedge      63 65
Weierstrass condition      998
Weierstrass criterion of uniform convergence      349
Weierstrass example      997
Weierstrass function      998 1000
Weierstrass function, elliptic      976
Weierstrass transform      449
Weierstrass — Erdmann conditions      997 999
Weierstrass — Erdmann conditions in multidimensional case      999
Weight of variate value      1083
Weingarten formulas      396
Whitham rule of “equal areas”      562
Whittaker equation      960
Whittaker functions      960
Wiener process      1086
Wiener — Hopf equation, first kind      825 1401
Wiener — Hopf equation, second kind      829 1406
Willier formula      74
wronskian      473 482 518
Wronskian determinant      see “Wronskian”
Wronskian of degenerate hypergeometric functions      958
Wronskian of Legendre functions      967
Wronskian, for system of ODEs      539
Y-transform      448 449
Zero asymptotic      364
Zero matrix      167
Zero of function      413
Zero operator      204
Zero simple      413
Zero vector      113
Zero-order neighborhood      991
Zeros of Bessel functions      951
Zhukovskii function      404 424
Zone, spherical      69
“Games with nature”      1024
“Hoof”      67
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