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| Авторизация |
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| Hildebrand F.B. — Advanced Calculus for Applications |
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| Предметный указатель |
Abel’s formula 29 31 42 47 36)
Absolute value 509
Acceleration 273
Acceleration in polar coordinates 319 (31)
Acceleration, normal 274
Acceleration, tangential 274
Acoustics 427
Adams’ method 96
Adams’ method, modified 100
Admissible function 355
Algebra, fundamental theorem of 593 (53)
Alternating series 120
Amplitude, of complex number 511
Analytic continuation 531
Analytic function 521 535
Analytic function, residues of 547 594 595
Analytic function, singularities of 535
Angle, between vectors 265
Angular velocity vector 267 294
Approximate solution of differential equations, by graphical methods 93
Approximate solution of differential equations, by numerical methods 93
Arc length, differential of 273 300
Arc length, differential of, on surface 371 (22)
Area, differential of 300 347 370
Argument, of complex number 511
Ascending differences 112
Associated Legendre functions 165
Associative law 263
Asymptotic approximation for Bessel functions 151
Asymptotic approximation for Gamma function 81
Asymptotic expansion 170
Asymptotic expansion of Bessel functions 170
Average value 217
Axial load 198
Backward differences 108
Base curve, characteristic 395 404
Beam, bending of 193
Beam, buckling of 198
Beam, rotating 193
Beam, vibrating 244 (10)
Bending moment 194 320
Bending stiffness 320 (38)
Ber and Bei functions 156
ber and bei functions, asymptotic approximations for 181 (37)
ber and bei functions, derivative formulas for 181 (38)
Bernoulli’s differential equation 37 43
Bernoulli’s equation 314 609
Bessel functions, asymptotic approximations for 151
Bessel functions, asymptotic expansions of 170
Bessel functions, derivative formulas for 151
Bessel functions, differential equations satisfied by 155
Bessel functions, expansions in 226 448
Bessel functions, integral formulas for 178 (26 27) 254
Bessel functions, integrals of 177 (24)
Bessel functions, modified 150
Bessel functions, of first kind 143
Bessel functions, of order n + 1/2 7 153
Bessel functions, of second kind 147
Bessel functions, of third kind 149
Bessel functions, Wronskian of 179 (29)
Bessel functions, zeros of 154 617 619
beta function 91 (43)
Bi-Laplacian equation 326 (73) 427
Binormal vector 274
Boundary-value problem, for ordinary differential equation 187
Boundary-value problem, for ordinary differential equation, nonhomogeneous 213
Boundary-value problem, for partial differential equations 469
Branch 516 535
Branch point 132 516 535 540
Bromwich integral 602 (87)
Buckling mode 199
Buckling, of long column 198 246
Calculus of variations 355
Capacity, of condenser 615 (122)
Cauchy principal value 558
Cauchy — Riemann equations 522 587
Cauchy’s inequality 590 (33)
Cauchy’s integral formula 528
Cauchy’s integral theorem 524
Cauchy’s residue theorem 551
Central differences 112
Central force 317 (27)
Chain rules 335
Characteristic base curve 395 404
Characteristic curve 380 394 400 404 410
Characteristic cylinder 395 404
Characteristic equation 8
Characteristic functions 188
Characteristic functions, expansions in series of 210
Characteristic functions, orthogonality of 206
Characteristic strip 404
Characteristic values 188
Characteristics 404 411
Charge density 584 615 (121)
Chebyshev polynomials 142
Circle of convergence 512 530
Circular cylindrical coordinates 298 303
Circular functions 512
Circulation 284 490 570
Column, buckling of 198 246
Commutative law 17 263 265 266
Compatibility, equation of 404
Complementary solution 7 388
Complete solution 4
Completeness 212
Complex number 509
Complex plane 509
Complex plane, extended 542
Complex potential 566
Complex variable, function of 509
Complex velocity 567
Components, of vector 263
Compressible fluid, flow of 309 409 475
Condenser, capacity of 615 (122)
Conductor 584 615
Confluent hypergeometric function 141 169 174
Conformal mapping 562
Conjugate complex numbers 509
Conjugate flows 307
Conjugate functions 523
Conservative force 285
Constraints 352 359
Continuity, equation of 310
Contour integration 551 558
Convergence, of series 119 511 530
Convolution 62
Coordinates, circular cylindrical 298 303
Coordinates, curvilinear 298 346
Coordinates, curvilinear, nonorthogonal 346
Coordinates, curvilinear, orthogonal 298
Coordinates, elliptical cylindrical 327 (82)
Coordinates, parabolic cylindrical 328 (84)
Coordinates, spherical 304
Cosine-integral function 32
Cramer’s Rule 20
Critical length, of column 246 (16)
Critical load, for column 199
Critical speed, of rotating shaft 197
Critical speed, of rotating string 191
Cross product 266
Crosscut 525
Curl 277 294
Curl in curvilinear coordinates 303
Curl theorem 325 (67)
Curvature 195 273
Curvature of beam 195
Curvature, radius of 273
Curvilinear coordinates 298 346 480
Curvilinear coordinates, arc length 300
Curvilinear coordinates, curl 303
| Curvilinear coordinates, del 301 608
Curvilinear coordinates, divergence 302
Curvilinear coordinates, gradient 301
Curvilinear coordinates, Laplacian operator 302
Curvilinear coordinates, nonorthogonal 346
Curvilinear coordinates, orthogonal 298 480
Curvilinear coordinates, surface area element 300 370
Curvilinear coordinates, volume element 300 346
Cut 536
Damping 88 (35)
Dashpot 88 (35)
De Moivre’s Theorem 513
Definite integrals, evaluation of, by calculus of residues 551 558
Definite integrals, evaluation of, by Laplace transforms 83 (12)
Deflection, of beam 193
Deflection, of membrane 446
Deflection, of string 189
DEL 277
Del in curvilinear coordinates 301 608
Delta function 64
Dependence, functional 344
Dependence, linear 3
Derivative, of complex function 520
Derivative, of vector function 270 278
Descending differences 112
Differences, ascending 112
Differences, backward 108
Differences, central 112
Differences, descending 112
Differences, forward 98 108
Differential distance vector 281
Differential equation, Bernoulli 37 43
Differential equation, Bessel Cauchy — Riemann 522 587 see
Differential equation, complementary solution of 7 388
Differential equation, complete solution of 4
Differential equation, confluent hypergeometric 144 169 174
Differential equation, equidimensional 13
Differential equation, exact 34
Differential equation, Hermit 176 (18)
Differential equation, homogeneous 35 37
Differential equation, homogeneous solution of 7
Differential equation, hypergeometric 165
Differential equation, Jacobi 184 (45)
Differential equation, Laguerre 176 (17)
Differential equation, Legendre see "Legendre functions"
Differential equation, linear 1 7 8 388 392
Differential equation, nonlinear 2 33
Differential equation, numerical solution of 93
Differential equation, order of 2
Differential equation, ordinary 2
Differential equation, partial 2 376
Differential equation, partial, classification of 388
Differential equation, partial, normal form of 406
Differential equation, quasi-linear 376
Differential equation, Riccati 50 (48)
Differential equation, separable 33 36
Differential equation, series solutions of 119
Differential surface area vector 288 300 370
Differentiation, Numerical 111
Differentiation, of integral containing parameter 359
Differentiation, of vector 270 278
Diffusion 427
Diffusivity 429
Digamma function 90 (42)
Dirac delta function 64
Direction cosines 264
Direction ratios 264
Directional derivative 276
Dirichlet problem 430
Discontinuity, finite 54
Distributions, theory of 65
Distributive law 17 265 266 279
Divergence 277
Divergence in curvilinear coordinates 302
Divergence, Theorem 290 324
Division, of series 122
Dot product 265
Double Fourier series 442
Doublet 65 570
Doublet function 65
Doublet, orientation of 570
Doublet, strength of 570
Drag force 609 (101)
Duhamel’s integral see "Superposition integral"
Duplication formula, for Gamma function 92 (48)
d’Alembert’s solution 392 454
Eigenfunction see "Characteristic function"
Eigenvalue Elastic end support 195 see
Electric field intensity 615 (121)
Electromagnetic theory 427
Electrostatic potential 426 584 615
Elementary functions 511
Elliptic integrals 192
Elliptic partial differential equation 388 409 469
Elliptic partial differential equation, normal form of 406
Elliptical cylindrical coordinates 327 (82)
Entire function 547
Envelope, of curves 34
Equations of motion, for fluids 310
Equidimensional differential equation 13
Equipotential line 306
Equipotential surface 286
Equivalent contours 527
Error function 464
Essential singularity 540
Essential singularity, nonisolated 541
Euler equation 357
Euler load, of column 199
Euler’s constant 90 (42) 146
Euler’s differential equation see "Equidimensional differential equation"
Euler’s equations, of fluid motion 310
Euler’s formula 10 513
Even function 218
Exact differential equation 34
Expansion, asymptotic 170
Expansion, in series of characteristic functions 210
Exponent, of differential equation 131
Exponential function 512
Exponential function, generalized 518
Exponential order, function of 54
Exponential-integral function 32
Extrapolation 108
Extremal 358
Factorial function see "Gamma function"
Factorization, of operators 17
Faltung see "Convolution"
Family 11
Field intensity vector 615 (121)
Fixed end support 195
Fluid flow 305 566
Fluid flow, about cylinder 489 (36—38) 571 609 611
Fluid flow, about plate 579 613
Fluid flow, about sphere 443
Fluid flow, compressible 309 409 475
Fluid flow, from channel 581
Fluid flow, supersonic 312 475
Fluid pressure 309 609
Flux 292 480
force 281
Force potential 285
Force, conservative 285
Forced vibration 68
Formulation of problems 469
Forward differences 98
Fourier cosine integral 238
Fourier cosine series 220
Fourier integral 236
Fourier integral, applications of 460
Fourier integral, complex form of 239
Fourier series 216 221
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