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Hildebrand F.B. — Advanced Calculus for Applications
Hildebrand F.B. — Advanced Calculus for Applications

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Название: Advanced Calculus for Applications

Автор: Hildebrand F.B.

Аннотация:

This volume offers an integrated treatment of mathematical topics which can be developed from results of elementary calculus, and which are of common importance in many fields of application.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1962

Количество страниц: 646

Добавлена в каталог: 30.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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