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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 |
Multivalued functions 197 200 204 205 206 266
N-dimensional sphere 645
Natural boundary condition 111 121
Neumann factor 60
Neumann function 46
Neumann function of order n 48
Neumann integral 92
Neutrons, diffusion of 296
Newton's law of cooling 296
Nonhomogeneous boundary condition 111 121
Nonhomogeneous eigenvalue problem 158
Nonhomogeneous equation 1
Norm of eigenfunctions 159
Norm, of functions 133
Normal asymptotic solutions 635
Normal vector 294
normalization constant 145 461
ODE See Ordinary differential equations
Open end 126 131
Operator in n-dimensional space 472
Ordinary differential equations, asymptotic solution with irregular singular points 563 571
Ordinary differential equations, asymptotic solution with large parameter 574
Ordinary differential equations, asymptotic solutions for large arguments 559
Ordinary differential equations, asymptotic solutions with regular singular points 561
Ordinary differential equations, by Laplace transform 411
Ordinary differential equations, constant coefficients 4
Ordinary differential equations, first-order 2 344
Ordinary differential equations, Frobenius solution 25
Ordinary differential equations, homogeneous 1 4
Ordinary differential equations, Legendre polynomials 71 77
Ordinary differential equations, linear 1
Ordinary differential equations, non-homogeneous 1
Ordinary differential equations, power series solution 25
Ordinary differential equations, second-order 10 350
Ordinary differential equations, self-adjoint 461
Ordinary differential equations, singularities of 23
Orthogonal coordinate systems, generalized 525
Orthogonal eigenfunctions 144 151
Orthogonal functions 133 144 332—333
Orthogonality integral 145 333 351
Orthonormal set 133—134 151
Parseval's formula for transforms, Fourier complex 432
Parseval's formula for transforms, Fourier cosine 423
Parseval's formula for transforms, Fourier sine 428
Parseval's formula for transforms, Hankel 441
Partial differential equations, acoustic wave eq. 307
Partial differential equations, diffusion and absorption of particles 296
Partial differential equations, diffusion of gases 296
Partial differential equations, electrostatic potential 311
Partial differential equations, elliptic 312
Partial differential equations, gravitational potential 309
Partial differential equations, Green's function for 466
Partial differential equations, heat conduction in solids 294
Partial differential equations, Helmholtz eq. 307
Partial differential equations, hyperbolic 312
Partial differential equations, Laplace eq. 308
Partial differential equations, linear 467
Partial differential equations, parabolic 312
Partial differential equations, Poisson eq. 308
Partial differential equations, vibration eq. 297
Partial differential equations, vibration of membranes 298
Partial differential equations, vibration of plates 300
Partial differential equations, water-basin 303
Partial differential equations, wave eq. 302
Particular solution 1 7 9 10 453 456
PDE See Partial differential equations
Periodic boundary conditions 150
Periodic functions 418
Periodic functions, integrals of complex 236
Periodic in time 111
Phase integral method 568
Plane wave front 358
Plane waves, harmonic 301 358
Plates, circular 340
Plates, equation of motion in 300
Plates, fundamental solution for static 477
Plates, fundamental solution for vibration 485
Plates, stiffness 300
Plates, uniqueness 301
Plates, vibration of 299
Polar moment of inertia 132
Pole, of order m 229
Pole, simple 229
Polynomials 201
Positive definite 143 151 460
Positive eigenvalues 157
Potential, electrostatic 311
Potential, gravitational 309 310
Potential, source 306
Potential, velocity 306
Power series 19 216 594
Powers of x in Bessel functions 61
Pressure, external 124 303
Pressure, of fluid 305
Pressure-release plane surface 358—359
Proper S—L system 151
Psi function 600
Raabe's test 589
Radiation, acoustic from infinite cylinder 363
Radius of convergence 19 216 594
Radius of curvature 120
Ratio Test 587
Rayleigh quotient 146
Real integrals, improper 237
Real integrals, improper, by non-circular contours 249
Real integrals, improper, with circular functions 239
Real integrals, improper, with singularities on the real axis 242
Recurrence formula 21 55 59 77—78 95
Recurrence relations, associated Laguerre 614
Recurrence relations, associated Legendre 95
Recurrence relations, Bessel function 51
Recurrence relations, confluent hypergeometric 618
Recurrence relations, exponential integral 609
Recurrence relations, Gamma 599
Recurrence relations, Hermite polynomial 615
Recurrence relations, hypergeometric functions 617
Recurrence relations, incomplete Gamma 602
Recurrence relations, Kelvin 621
Recurrence relations, Laguerre 614
Recurrence relations, Legendre plynomials 78
Recurrence relations, modified Bessel 55
Recurrence relations, Psi 601
Recurrence relations, spherical Bessel 53
Recurrence relations, Tchebyshev 612
Reflection and refraction of plane waves 358
Region, closed 189
Region, multiply connected 190
Region, open 190
Region, semi-closed 190
Region, simply connected 190
Regular point 23 559
Regular singular point 23 25 43 560
Residue theorem 231
Residues and poles 231
Resonance of acoustic horn 126
Riemann sheets 198 200
Riemann sheets, principal 205
Rigid end 126
Rigid sphere, enclosed gas 364
Rodriguez formula 72 81 83 90
Root test 588
Saddle point method 539
Saddle point method, modified 554 558
Sawtooth wave 418
Scattered pressure field 365
Scattering of a plane wave from a rigid sphere 364
Second-order Euler DE 62
Second-order linear DE, adjoint 139
Self-adjoint differential operator 138 457 460 473
Self-adjoint eigenvalue problem 143
| Separation of variables 319
Separation of variables, cartesian coordinates 319 338 351
Separation of variables, cylindrical coordinates 322 326 328 334 340 346 347 353 362
Separation of variables, spherical coordinates 324 331 341 364
Series, convergence of 19
Series, infinite 74
Series, power 19 216 594
Shear forces 299
Shift theorem 403 407 635
Simple pole 229 554
Simply supported beam 159
Sine, in terms of Legendre polynomial 88
Sine, integral 610
Sine, of a complex variable 202
Singular point, solutions 23 25 43
Singularities, classification 23 229
Singularities, essential 229
Singularities, isolated 197 229
Singularities, poles 229
Singularities, principal part 229
Singularities, removable 229
Small arguments 65
Small circle integral 248
Small circle theorem 247
Snell's law 361
Source, heat See Heat source
Source, potential 306
Specific heat, ratio 306
Speed See Wave speed
Spherical Bessel functions 52
Spherical Bessel functions, recurrence formula 53
Spherical Bessel functions, wronskian 53
Spherical coordinates 629
Spherical harmonic waves 364
Stability 127
standing waves 308
Static deflection 418
Stationary phase, method 552
Stationary phase, path 552
Stationary phase, point 552
Steady-state temperature distribution 309
Steady-state temperature distribution, in a circular sheet 496
Steady-state temperature distribution, in annular sheet 322 334
Steady-state temperature distribution, in rectangular sheet 319
Steady-state temperature distribution, in semi-infinite bar 518
Steady-state temperature distribution, in semi-infinite sheet 491
Steady-state temperature distribution, in solid cylinder 326
Steady-state temperature distribution, in solid sphere 324
Steepest descent method 539 553
Steepest descent paths 540
Steepest descent saddle point 539
Step function See Heaviside function
Stirling formula 544
Stretched strings 102
Stretched strings, equation of motion 111
Stretched strings, fixed 112
Stretched strings, Green's function for 460 465
Stretched strings, vibration of 109 112 152
Stretched strings, wave propagation 109
Sturm — Liouville equation, asymptotic behavior of 148 155
Sturm — Liouville equation, boundary conditions 150 155
Sturm — Liouville equation, fourth order equation 155
Sturm — Liouville equation, periodic boundary conditions 150
Sturm — Liouville equation, second order 148 459
Subnormal asymptotic solution 565
Sum of a series method 519
Superposition, principle of 321
Surface of n-dimensional sphere 645
S—L problem See Sturm — Liouville systems
Taylor series, complex 218
Taylor's expansion series 217
Tchebychev polynomials 612
Telegraph equations 130
Temperature distribution, steady state See Steady state temperature distribution
torque 132
Torsional vibrations 132 153
Torsional vibrations, boundary conditions 133
Torsional vibrations, circular bars 132 153
Torsional vibrations, wave equation 132
Transient motion of a square plate 351
Transmission line equation 130
Transverse elastic spring 121
Trigonometric series See Fourier series
Undetermined coefficients 7
Uniform convergence 402 592
Uniqueness theorem 137 141 312
Uniqueness theorem, BC's 313 315
Uniqueness theorem, differential equations 13
Uniqueness theorem, diffusion eq. 315
Uniqueness theorem, Helmholtz 314
Uniqueness theorem, initial conditions 13 315 316
Uniqueness theorem, Laplace 312
Uniqueness theorem, Poisson 312
Uniqueness theorem, wave equation 316
Variable, cross-section 126 153
Variable, density 152
Variation of parameters 9
Velocity field, potential 306
Velocity of a wave See Wave speed
Velocity potential 306
Velocity, vector particle 303 305
Vibration equation 297 349
Vibration equation, bounded medium 307
Vibration equation, forced 159 307
Vibration equation, forced, of a membrane 298 338 353
Vibration equation, free 341
Vibration equation, free, of a circular plate 340
Vibration equation, Green's function for 460 462 465 512 514
Vibration equation, longitudinal 113 115 151
Vibration equation, non-homogenous Dirichlet, Neumann or Robin 349
Vibration equation, of a bar 115 151
Vibration equation, of a beam 117 298
Vibration equation, of a string 109 112 152 356 413 429 433 512
Vibration equation, one dimensional continua 297
Vibration equation, torsional 132
Vibration equation, transient vibration 349
Vibration equation, uniqueness 297
Volume of n-dimensional sphere 645
Watson's lemma 538 543
Wave equation 111 115 120 132 302 306 355
Wave equation, acoustic horn 125—126
Wave equation, acoustic medium 303
Wave equation, axisymmetric spherical 365
Wave equation, beam 120
Wave equation, cylindrical harmonic 362
Wave equation, harmonic plane waves 302
Wave equation, spherical harmonic 364
Wave equation, time dependent source 349 uniqueness of 316
wave number 111 120 302
Wave operator, Green's identity for 471 510
Wave propagation, in infinite plates 436
Wave propagation, in infinite, 1-D medium 355
Wave propagation, in semi-infinite string 420
Wave propagation, in simple string 109 113 117
Wave propagation, spherically symmetric 357
Wave propagation, surface of water basin 303
Wave propagation, transient, in string 356
Wave speed, characteristic 297
Wave speed, in acoustic medium 125 306
Wave speed, in membrane 298
Wave speed, longitudinal in a bar 115
Wave speed, shear 133
Wave speed, stretched string 111
Wavelength 302
Weber 45
Weierstrass test for uniform convergence 593
Weighting function 134
Whirling of string 109 117 122
WKBJ method, for irregular singular points 568
WKBJ method, for ODE with large parameters 580
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