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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
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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