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Hayek S.I. — Advanced mathematical methods in science and engineering
Hayek S.I. — Advanced mathematical methods in science and engineering

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Название: Advanced mathematical methods in science and engineering

Автор: Hayek S.I.

Аннотация:

Hayek (Pennsylvania State University) presents methods of applied mathematics that are particularly suited for the application of mathematics to physical problems in science and engineering. The textbook is intended for a three-semester graduate course sequence.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 734

Добавлена в каталог: 03.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel's formula      11
Absolute convergence      216 383
Absorption of particles      296
Acoustic horn, wave equation      124—126
Acoustic medium      306
Acoustic medium, acoustic radiation from infinite cylinder      363
Acoustic medium, scattering from rigid sphere      364
Acoustic medium, speed of sound      125 306
Acoustic medium, wave propagation      303
Acoustic medium, waves, reflection      358
Acoustic medium, waves, refraction      359
Addition theorem, for Bessel      61 409
Adiabatic motion of fluid      306
Adjoint, BC's      455—456
Adjoint, causal auxiliary function      516
Adjoint, differential operators      138 455 467
Adjoint, Green's function      456
Adjoint, self      138 140 142
Airy functions      546 550 573 580
Analytic functions      189 197
Analytic functions, integral representation of a derivative      214
Angular velocity      117
Approximation in the mean      136
Associated Laguerre functions      614
Associated Legendre functions      93
Associated Legendre functions, generating function      94
Associated Legendre functions, integrals of      96
Associated Legendre functions, recurrence formulae      95
Associated Legendre functions, second kind      97
Asymptotic methods      537
Asymptotic series expansion      548
Asymptotic solutions of Airy's function      573 580
Asymptotic solutions of Bessel's equation      564 570 577
Asymptotic solutions of ODE with irregular singular points      563 571
Asymptotic solutions of ODE with large parameter      574 580
Auxiliary function      486 494
Bar, equation of motion      115 297
Bar, vibration of      115 151
Beams      117
Beams, boundary conditions      121
Beams, e.o.m.      120
Beams, forced vibration      159
Beams, vibration      120 121 298
Beams, wave equation      120 298
Bessel coefficient      58
Bessel coefficient, generating function      58
Bessel coefficient, powers      61
Bessel differential equation      58
Bessel function      43 56 61 65
Bessel function, addition theorem      61
Bessel function, asymptotic approximations      65 66
Bessel function, asymptotic solutions      564 570 577
Bessel function, cylindrical      48
Bessel function, generalized equation      56 57 58
Bessel function, integral representation      62—64
Bessel function, integrals      66—67
Bessel function, modified      54—56
Bessel function, of an integer order n      47
Bessel function, of half-orders      51
Bessel function, of higher order      52
Bessel function, of the first kind      44
Bessel function, of the first kind, modified      0
Bessel function, of the order zero      45
Bessel function, of the second kind      44 46 48
Bessel function, plots      651—654
Bessel function, polynomial      67
Bessel function, products      67
Bessel function, recurrence formulae      49—52
Bessel function, spherical functions      52—53
Bessel function, squared      67
Bessel function, wronskian      45 53 55
Bessel function, zeroes      68
beta function      603
Bi-laplacian      300
Bi-laplacian, fundamental solution      476
Bi-laplacian, Green's identity for      469
Bilinear form      138 141 143 155
Bilinear form, S—L system      149 155
boundary conditions      115
Boundary conditions, acoustic medium      307
Boundary conditions, Dirichlet      312
Boundary conditions, elastically supported      115 299
Boundary conditions, fixed      115 299
Boundary conditions, for membranes      299
Boundary conditions, for plate      300
Boundary conditions, free      115 299
Boundary conditions, heat      296
Boundary conditions, homogeneous      142
Boundary conditions, natural      111
Boundary conditions, Neumann      312
Boundary conditions, periodic      150
Boundary conditions, Robin      312
Boundary conditions, simply supported      300
Boundary value problems, Green's function      453
Branch cut      197 198 259 266 267 273
Branch point      197 199
Cartesian coordinates      627
Cauchy integral formula      213
Cauchy integral theorem      210
Cauchy principal value      237 241 242
Cauchy — Riemann conditions      194
Causal fundamental solution      See Fundamental solution causal
Causality condition      480 483
Characteristic equation      4 27 123
Chebyshef      See Tchebyshev
Christoffel's first summation      87
Circular cylindrical coordinates      627
Circular frequency      111
Circular functions, complex      202
Circular functions, derivitive of complex      203
Circular functions, improper real integrals of      239
Circular functions, inverse of complex      206
Circular functions, trigonometric identities of complex      203
Classification of singularities, for complex functions      229
Classification of singularities, for ODE      23
comparison function      143
Complete solution      1 3
Complex Fourier transform, of derivatives      431
Complex Fourier transform, operational calculus      431
Complex Fourier transform, parseval formula for      432
Complex function      190
Complex function, analytic      197
Complex function, branch cut      197 198 259 266 267 273
Complex function, branch point      197 199
Complex function, circular      202
Complex function, continuity      192
Complex function, derivatives      193 194
Complex function, domain      191
Complex function, exponent      205
Complex function, exponential      201
Complex function, hyperbolic      203
Complex function, inverse circular      206
Complex function, inverse hyperbolic      206
Complex function, logarithmic      204
Complex function, multi-valued      197
Complex function, polynomials      201
Complex function, range      191
Complex function, uniqueness of limit      192
Complex hyperbolic functions      203
complex numbers      185
Complex numbers, absolute value      186 187
Complex numbers, addition      185
Complex numbers, argand diagram      186
Complex numbers, argument      187
Complex numbers, associative law      186
Complex numbers, commutative law      186
Complex numbers, complex conjugate      186
Complex numbers, distributive law      186
Complex numbers, division      185
Complex numbers, equality      185
Complex numbers, imaginary part      185
Complex numbers, multiplication      185
Complex numbers, polar coordinates      186
Complex numbers, powers      188
Complex numbers, real part      185
Complex numbers, roots      188
Complex numbers, subtraction      185
Complex numbers, triangular inequality      188
Compressed columns      127
Compressible fluid      305
Condensation      306
Conductivity, material      295
Conductivity, thermal      295
Confluent hypergeometric function      618
Conservation of mass      303 305
Constitutive equation      119
Continuity equation      125
Contour evaluation of real improper integrals      249
Convergence, absolute      216 383 586
Convergence, conditional      586
Convergence, of a series      19
Convergence, radius      19 216
Convergence, region      216
Convergence, tests      586
Convergence, uniform      137 586
Convolution theorem, complex exponential transform      431
Convolution theorem, cosine transform      423
Convolution theorem, Laplace transform      403
Convolution theorem, multiple-complex exponential transform      436
Convolution theorem, sine transform      426
Coordinate system, cartesian      627
Coordinate system, circular cylindrical      628
Coordinate system, elliptic-cylindrical      628
Coordinate system, general orthogonal      625
Coordinate system, oblate spheroidal      632
Coordinate system, prolate spheroidal      630
Coordinate system, spherical      629
Cosine, complex      202
Cosine, expansion in Legendre      89
Cosine, Fourier series      163
Cosine, Fourier transform      384
Cosine, improper integrals with      239
Cosine, integral function      610
Critical angle      361
Critical load      128
Critical speed      124
Curl, cartesian      627
Curl, circular cylindrical      628
Curl, elliptic cylindrical      629
Curl, generalized orthogonal      625
Curl, oblate spheroidal      632
Curl, prolate spheroidal      631
Curl, spherical      630
Curvature      120
Cylindrical Bessel function      48
Cylindrical coordinates      628
D'Alembert      587
Debeye's first order approximation      543
Delta function      See Dirac delta function
Density, fluid      306
Derivative, of a complex function      193 194
dielectric constant      311
Differential equation      4 10 56—58 91
Differential equation, first order      2
Differential equation, linear      1 2 4
Differential equation, n-th order      4 20
Differential equation, non-homogeneous      1
Differential equation, ordinary      See Ordinary differential equations
Differential equation, partial      See Partial differential equations
Differential equation, second order      10 25
Differential equation, singularities      23
Differential equation, Sturm — Loiuville      148 155
Differential equation, with constant coefficients      4
Differential operation      1 453
Diffusion of electrons      296
Diffusion of gasses      296
Diffusion of particles      196
Diffusion operator      470
Diffusion, coefficient      297
Diffusion, constant      296
Diffusion, equation      293 342
Diffusion, fundamental solution for      480
Diffusion, Green's function for      515
Diffusion, Green's identity for      470
Diffusion, steady state      343
Diffusion, transient      343
Diffusion, uniqueness      315
Diffusion, uniqueness of      315
Dipole source      459
Dirac delta function      161 453 635
Dirac delta function, integral representation      635 637 643
Dirac delta function, Laplace transformation of      406
Dirac delta function, linear transformation of      644
Dirac delta function, n-dimensional space      643
Dirac delta function, n-th order      459 641 646—647
Dirac delta function, scaling property      636 643
Dirac delta function, sifting property      636 643
Dirac delta function, spherically symmetric      645
Dirac delta function, transformation property      639
Distributed functions      642
Divergence, cartesian      627
Divergence, circular cylindrical      628
Divergence, elliptic cylindrical      629
Divergence, generalized orthogonal      625
Divergence, oblate spheroidal      632
Divergence, prolate spheroidal      631
Divergence, spherical      630
Eigenfunction      108 144 151 159 308 336
Eigenfunction, expansions with Green's functions      492 497
Eigenfunction, norm      159
Eigenfunction, orthogonal      332 336 337 343
Eigenfunction, orthogonality      133 144
Eigenfunction, properties      144
Eigenvalue      108 142 157 308
Eigenvalue problem      108 142
Eigenvalue problem, Green's function      459 461
Eigenvalue problem, homogeneous      158
Eigenvalue problem, non-homogeneous      158
Elastically supported boundary      121 133 299
Electrons, diffusion      296
Electrostatic potential      311
Electrostatic potential, field within a sphere      331
Entire function      197
Equation of motion, bars      113
Equation of motion, beams      117
Equation of motion, plates      299
Equation of motion, stretched membranes      298
Equation of motion, stretched string      111
Equation of motion, torsional bars      132
Error function      604
Error function, complementary      604
Euler's equation      4 125
Expansion, Bessel functions      60
Expansion, Fourier series      88
Expansion, Legendre polynomial      85 87
Exponential function, complex      201
Exponential function, periodicity of      202
Exponential integral function      608
Exponents, complex      205
Exponents, derivative      206
Exterior region      493
Factorial function      See Gamma function
Ferrer's function      93
Fixed boundary      115 121 133 299
Fixed shaft, vibration of      122
Fluid density      306
Fluid flow, around an infinite cylinder      328
Fluid flow, incompressible      309
Forced vibration, of a beam      159
Forced vibration, of a membrane      338
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