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