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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
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 $J_n(x)$      179 (28)
Generating function, for $P_n(x)$      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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