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| Авторизация |
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| Поиск по указателям |
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| Hildebrand F.B. — Advanced Calculus for Applications |
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| Предметный указатель |
Fourier series, complex form 253 (43)
Fourier series, double 442
Fourier sine integral 238
Fourier sine series 217
Fourier sine series, double 442
Fourier transforms 240
Fourier — Bessel integral 242
Fourier — Bessel series 226
Fourier — Bessel transforms 242
Free end condition 190 195
Free vibration, of beam 244 (10)
Free vibration, of membrane 446
Free vibration, of string 244 (7)
Frenet formulas 274
Frequency, natural 69 244 10)
Fresnel integrals 598 (77)
Frobenius, method of 129
Frobenius, method of, exceptional cases 135
Functional dependence 344
Functions, analytic 521
Functions, beta 91 (43)
Functions, circular 512
Functions, confluent hypergeometric 141 169 174
Functions, Conjugate 523
Functions, cosine-integral 32
Functions, digamma 90 (42)
Functions, doublet 65
Functions, elementary 511
Functions, error 464
Functions, even 218
Functions, exponential 512 518
Functions, exponential-integral 32
Functions, gamma 73
Functions, homogeneous 35
Functions, hyperbolic 43 (15) 513
Functions, Laguerre 82 (6) 142 176
Functions, Legendre 161
Functions, logarithmic 514
Functions, multivalued 536
Functions, odd 218
Functions, potential 284
Functions, sine-integral 32
Functions, single-valued 283
Functions, singularity 63
Functions, square-wave 83 (9)
Functions, stream 307
Functions, triangular-wave 83 (10)
Functions, unit impulse 64
Fundamental set, of solutions 48 (39)
Fundamental theorem, of algebra 593 (53)
Gamma function 73
Gamma function, asymptotic approximation for 81
Gamma function, duplication formula for 92 (48)
Gamma function, table of 619
Gauss’s hypergeometric function 165
Gauss’s interpolation formula 117 (22)
Gauss’s test, for infinite series 120
Generalized factorial function see "Gamma function"
Generating function, for  179 (28)
Generating function, for  182 (42)
Geodesics 373 (37)
Geometry, of space curve 271
Gradient 275
Gradient in curvilinear coordinates 301
Gradient theorem 325 (67)
Graphical integration, of differential equations 93
Gravitational potential 426
Green’s theorem, first form 293
Green’s theorem, in the plane 297
Green’s theorem, second form 293
Gregory’s backward difference formula 110
Grounded line 465
Hankel functions 149 457
Harmonic functions 295
Harmonics 217
Heat flow 428
Heat flow in column 488 (33—35)
Heat flow in cylinder 487 (30—32)
Heat flow in plate 430 433 460
Heat flow in rectangular parallelepiped 441
Heat flow in rod 449 462
Heat flow in rod with radiation 479 (6)
Heat flow in sphere 439
Heat-flow equation 427
Heaviside unit step function 87 (27)
Helix 319 (32)
Helmholtz equation 394 420 496
Hermite polynomials 142 176
Hinged end support 195
Homogeneous boundary condition 187 431
Homogeneous differential equation, linear 5 389
Homogeneous differential equation, of first order 35 37
Homogeneous differential equation, partial 389
Homogeneous function 35
homogeneous solution 7
Hyperbolic functions 43 (15) 513
Hyperbolic partial differential equation 388 409 469
Hyperbolic partial differential equation, normal form of 406
Hypergeometric function 165
Hypergeometric function, confluent 141 169 174
Hypergeometric series 165
Imaginary number 509
Imaginary part, of complex quantity 438 509
Imaginary unit 509
Implicit functions 340
Improper integral, principal value of 558
Impulse functions 64
Incompressible fluid 291
Indented contours 558
Independence, functional 344
Independence, linear 3
Indicial equation 131
Infinite series see "Series"
Infinity, point at 542
Infinity, residue at 594 (60) 595
Initial conditions 32 384
Initial-value problem 32 386 394 400 409 469
Inner product 265
Insulated boundary 483 (16) 492
Integral equation 86 (24)
Integral function 547
Integral power function 511
Integral surface 380
Integral transcendental function 547
Integral, elliptic 192
Integral, improper 558
Integral, improper, principal value of 558
Integral, line 281 523
Integral, of differential equation 379
Integral, surface 287
Integrating factor 7 37
Integration, numerical 111 116 117 25) 118
Intermediate variable 336
Interpolation 110 117
Interval of convergence 120
Inverse circular functions 519
Inverse hyperbolic functions 519
Inverse Laplace transform 60 601
Inverse tangent, addition formula for 578
Inversion, of plane 606 (95)
Irregular singular point, of differential equation 128 168
Irrotational flow 294
Isoclines 93
Isolated singular point 538
Iteration, methods of, in solving transcendental equations 193
Iteration, methods of, Newton — Raphson method 362
Iteration, methods of, Picard’s method 106
Iteration, methods of, Stodola — Vianello method 200 214
Jacobi polynomials 142 184
Jacobian determinants 340 346
| Jacobi’s differential equation 184 (45)
Jordan’s lemma 556
Ker and Kei functions 158
ker and kei functions, asymptotic approximations for 181 (37)
ker and kei functions, derivative formulas for 181 (38)
Kutta see "Runge — Kutta method"
Lagrange multipliers 352 359
Lagrange, identity of 270
Laguerre polynomials 82 (6) 142 176
Laguerre polynomials, associated 142
Laplace transforms 51 464
Laplace transforms, inversion of, by contour integration 601 (87—94)
Laplace transforms, table of 74
Laplace’s equation 295 426 429 523
Laplace’s equation, polynomial solutions of 484 (17)
Laplacian operator 280
Laplacian operator in curvilinear coordinates 302 608
Laurent series 531
Least squares, method of 252 (39) 256
Legendre functions 159
Legendre functions, associated 165
Legendre functions, of second kind 162
Legendre functions, recurrence formula for 162
Legendre polynomials 161
Legendre series 231 440
Leibnitz’s rule 360
Lerch’s theorem 61
Lift force 609 (101) 611
Limiting contours 555
Line integral 281 523
Line integral of a complex function 523
Line integral, independent of path 284 524
linear combination 3
Linear combination, nontrivial 3
Linear dependence 3
Linear differential equations see "Differential equations"
Linear fractional transformation 606 (97)
Lines of flow 306
Lines of force 584 615
Liouville’s theorem 545 593
Logarithm, complex 514
Long line, equations for 464
Loop integral 603 (90)
Mach number 312 475
Mapping, conformal 562
Maxima and minima, absolute 352
Maxima and minima, of functions 351
Maxima and minima, of integrals 355
Maxima and minima, relative 351
Maxwell’s equations 326 (77)
Mean value see "Average value"
Membrane, deflection of 446
Membrane, vibration of 446
minimax 351
Modified Bessel functions 150
Modulus, of complex number 509
Moment, bending 194 320
Moment, of momentum vector 317 (27)
Moment, vector 267
Momentum vector 317 (27)
Multiple products, of vectors 268
Multiplication, of series 122
Multivalued function 536
Natural boundary 541
Natural frequencies, of vibrating beam 244 (10)
Natural frequencies, of vibrating membrane 449 491
Natural frequencies, of vibrating string 244 (7)
Natural mode, of vibration 244 (7 10)
Neumann problem 430 443
Neumann’s function 146
Newton — Gauss formula 117 (22)
Newton — Raphson method 362
Newton’s backward difference formula 110
Newton’s Law of Cooling 474 492 46)
Newton’s method 362
Nodal lines, of membrane 491 (42)
Normal acceleration 274
Normal derivative 293
Normal form, of partial differential equation 406
Normal plane 275
Normal vector 287
Normalization, of characteristic functions 209
Normalizing factor 210
Numerical methods, of differentiation 111
Numerical methods, of integration 111 116 117 25) 118
Numerical methods, of interpolation 110 116 22)
Numerical methods, of solving differential equations 93
Numerical methods, of solving differential equations, characteristic-value problems 200
Numerical methods, of solving nonlinear equations 193 362
Odd function 218
Odd-harmonic function 226
Open line 465
Operational calculus see "Laplace transforms"
Operator, linear dfferential 5 16 339
Order, of differential equation 2
Order, of pole 538
Ordinary differential equation 2
Ordinary point, of differential equation 127 168
Orthogonal coordinates 298
Orthogonal functions 206
Orthogonal functions, expansions in series of 210
Orthogonal set, of functions 206
Orthonormal set, of functions 209
Osculating plane 275
Outer product’ 266
Parabolic cylindrical coordinates 328 (84)
Parabolic partial differential equation 388 409 470
Parabolic partial differential equation, normal form of 406
Parabolic rule 118 (27)
Paraboloidal coordinates 329 (85)
Parseval equalities 252 (42)
Partial derivative 335
Partial differential equation 376 426
Partial fractions 67 84
Particular solution 6 388
Picard's theorem 541
Picard’s method 106
Piecewise continuity 54
Piecewise smooth curve 281
Piecewise smooth surface 288
Plane, equation of 315 (10)
Plasticity 412
Poisson’s equation 426
Poisson’s integral 437
Pole 132 538
Pole, order of 538
Pole, residue at 548
Pole, simple 539
Polygonal mapping see "Schwarz — Christoffel transformation"
Polynomial 511 546
Polynomial, existence of zero of 593 (53)
Polynomials, Chebyshev 142
Polynomials, Hermite 142 176
Polynomials, Jacobi 142 184
Polynomials, Laguerre 82 (6) 142 176
Polynomials, Legendre 161
Position vector 272
Position vector, derivative of 272
Potential 284
potential energy 285
Potential, complex 566
Potential, electrostatic 426 584 615
Potential, existence of 285
Potential, gravitational 426
Potential, velocity 305 566
Potential, velocity deviation 311
Power function, generalized 516
Power function, integral 511
Power series 119 511 528
Power series, convergence of 119 511 529
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