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Carslaw H.S. — Operational methods in applied mathematics
Carslaw H.S. — Operational methods in applied mathematics

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Название: Operational methods in applied mathematics

Автор: Carslaw H.S.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1963

Количество страниц: 382

Добавлена в каталог: 15.08.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Air column, longitudinal vibrations of      162
Alternating current bridges      37
Artificial transmission line      47 312—316
Asymptotic expansions for large values of the time      279
Bar, longitudinal vibrations of      137—145
Bar, transverse vibrations of a finite bar      145
Bar, transverse vibrations of a semi-infinite bar      152
Bateman      299
Bessel functions, Laplace Transforms of      351
Bessel functions, note on, and collection of results      348
Boundary value problems      321
Bromwich      xiii 63
Carson's integral equation      xv
Chain hanging under gravity, vibrations of      155
Chain processes      299—303
Charged particle moving in electric and magnetic fields      57
Circular membrane, vibrations of      158—161
Collision of equal rods      143
Conduction of heat in a finite circular cylinder      287—290
Conduction of heat in a semi-infinite solid      91 110—117 254 283
Conduction of heat in a slab      94 117 249 275—276 295
Conduction of heat in a sphere      129
Conduction of heat in a wire carrying electric current      120—122
Conduction of heat in an infinite circular cylinder      123—129 278 286—287
Conduction of heat in the region bounded internally by a circular cylinder      277
Conduction of Heat, equation of      106
Deflexion of beams      324—333
Difference equations, solution by Laplace Transformation method      316
Differential equations (ordinary linear with constant coefficients), application of Laplace Transformation method to      1—8
Differential equations (ordinary linear with constant coefficients), application of Laplace Transformation method to, assumptions involved in this method      8
Differential equations (ordinary linear with constant coefficients), application of Laplace Transformation method to, justification of solutions      8 81
Differential equations (ordinary linear with constant coefficients), application of Laplace Transformation method to, worked examples      9—13
Differential equations (ordinary linear with constant coefficients), connexion with Heaviside's method      19—20
Differential equations (ordinary linear with constant coefficients), solution using the Inversion Theorem      77
Differential equations (ordinary linear with variable coefficients)      258
Differential equations (ordinary linear), two-point boundary value problems for      321
Differential equations (partial), application of Laplace Transformation method to      88—91
Differential equations (partial), application of Laplace Transformation method to, assumptions involved in the method      90
Differential equations (partial), application of Laplace Transformation method to, introductory examples      91—105
Differential equations (partial), application of Laplace Transformation method to, verification of solutions      90 131
Differential equations (simultaneous ordinary linear), application of Laplace Transformation method to      14
Differential equations (simultaneous ordinary linear), application of Laplace Transformation method to, cases in which there must be relations between initial conditions      16—18 241—246
Differential equations (simultaneous ordinary linear), application of Laplace Transformation method to, justification of solutions      83 241—246
Differential equations (simultaneous ordinary linear), application of Laplace Transformation method to, worked examples      14
Differential-difference equations      299
Diffusion of magnetic field in a circular cylinder for longitudinal alternating field      215
Diffusion of magnetic field in a circular cylinder for transverse alternating field      222
Diffusion of magnetic field in a circular cylinder for transverse field      219
Diffusion of magnetic field in a hollow cylinder      216
Diffusion of magnetic field, in a slab      211
Dirac's $\delta$ function      232
Dirac's $\delta$ function, its derivatives      243
Doetsch      xv 250
Duhamel's theorem      252—254
Electric cable      185—186
Electric cable, finite cable with alternating applied EMF      186
Electric cable, finite cable with terminal impedances      189
Electric cable, semi-infinite cable      185
Electric circuits: circuit containing inductance, resistance, and capacity in series      24
Electric circuits: electrical networks      28
Electric circuits: impulsive applied EMF      236 239—243
Electric circuits: problems on electrical networks      30—47 239—246
Electric circuits: various types of EMF applied to such a circuit      25
Electric oscillations on a sphere      223—226
Electric transmission lines      184
Electric transmission lines, artificial transmission lines      47 312—316
Electric transmission lines, doubly infinite line with given initial conditions      204
Electric transmission lines, finite line with constant applied      190
Electric transmission lines, finite line with impulsive applied EMF      246
Electric transmission lines, finite line with non-zero initial conditions      195 247—248
Electric transmission lines, finite line with terminal impedances      188
Electric transmission lines, line with resistance and capacity only      185—189
Electric transmission lines, non-uniform lines      208
Electric transmission lines, semi-infinite line with arbitrary applied EMF      202
Electric transmission lines, semi-infinite line with constant applied EMF      197
Electric transmission lines, solution for finite line expressed in wave form      192 208 246—248
Filter circuits      41—47
Filter circuits, alternating EMF applied to filter circuit      46
Filter circuits, case of an infinite number of sections      47 303—309
Filter circuits, square-wave EMF applied to filter circuit      295
Filter circuits, transients in filter circuits      41—47 242 309—312
Fourier Series for deflexion of beams      330
Fourier Series for steady periodic currents in electric circuits      48 297
Fourier transforms      263—264
Fourier Transforms, applications of      265
Fourier Transforms, comparison with Laplace Transforms      264 266
Fourier — Mellin theorem      71
Fourier's integral theorem      74 262
Green's Functions for ordinary linear differential equations      156—157
Heaviside: operational solution for ordinary linear differential equations      viii
Heaviside: operational solution for ordinary linear differential equations, asymptotic expansions      xii 279—285
Heaviside: operational solution for ordinary linear differential equations, expansion theorem      viii xiii 19—20
Heaviside: operational solution for ordinary linear differential equations, extension to partial differential equations      ix—xiii
Heaviside: operational solution for ordinary linear differential equations, series expansion      ix 20 271—274
Heaviside: operational solution for ordinary linear differential equations, unit function      viii 7 142 233
Heaviside: operational solution for ordinary linear differential equations, use for partial differential equations      xiii
Hertzian oscillator      227 265 267
Impulsive functions      232—234
Impulsive functions, problems involving      234—249
Instantaneous heat sources      107—110
Instantaneous heat sources in a semi-infinite solid      115
Instantaneous heat sources in a slab      117 249
Instantaneous heat sources in an infinite circular cylinder      125—129
Inversion theorem for Laplace Transformation      xiv 71
Inversion theorem for Laplace Transformation, application to ordinary linear differential equations      77
Inversion theorem for Laplace Transformation, application to verification of solutions of problems on impulsive motion of dynamical and electrical systems      237—239 240
Inversion theorem for Laplace Transformation, application to verification of the solution of ordinary linear differential equations      81
Inversion theorem for Laplace Transformation, application to verification of the solution of simultaneous ordinary differential equations      83
Inversion theorem for Laplace Transformation, deduction from Fourier's Integral Theorem      74
Inversion theorem for Laplace Transformation, proof      72
Inversion theorem for Laplace Transformation, use of contour integration to evaluate solutions      75—79 89—96 99—103
Jeffreys      xv
Kirchhoff's laws      29—30
Ladder network, finite      41 309—312
Ladder network, semi-infinite      47 303—309
Ladder network, uniform transmission line as a limiting case of      312
Lagrange's equations      59
Laplace transformation      4 261
Laplace Transformation, theorems on      4—7 72—75 80 250—270
Laplace transforms, tables of      4 353—356
Laplace Transforms, tables of periodic functions      251—252
Laplace Transforms, tables of step functions      317
Lerch's theorem      7 345
Maxwell's equations in cylindrical and spherical polar coordinates      213
Maxwell's equations in vector form      210
Network Theorems      268
Normal modes of vibration      62
Parseval's theorem for Fourier transforms      266
Parseval's Theorem for Laplace Transforms      267
Parseval's Theorem, applications      267
Partial fraction expansion      8 78
Periodic EMF of any wave form applied to a circuit      48 290—298
Periodic functions, Laplace Transforms of      251—252
Poisson distribution      301
Projectile moving relative to the earth      58
Radioactive disintegration, equations of      299
Residues, calculation of      78
Retarded potential formulae      228
Small oscillations of dynamical systems about equilibrium      59—62
Small oscillations of dynamical systems about equilibrium, caused by blows      235 237—239
Small oscillations of dynamical systems about equilibrium, comparison with method of normal coordinates      02
Solutions expressed in wave form for filter circuits      309
Solutions expressed in wave form for plucked string      101—115
Solutions expressed in wave form for transmission lines      192—194 208 240—248
Solutions expressed in wave form for vibrations in a rod      141—145
Solutions suitable for large values of the time      256
Solutions suitable for large values of the time, asymptotic expansions      279
Solutions suitable for large values of the time, linear asymptotes      285
Solutions suitable for large values of the time, steady periodic solutions      290—298
Solutions suitable for small values of the time      255
Solutions suitable for small values of the time for filter circuits      273 309
Solutions suitable for small values of the time for ordinary differential equations      271—274
Solutions suitable for small values of the time for partial differential equations      274
Solutions suitable for small values of the time for partial differential equations in cylindrical coordinates      276
Steady periodic solutions      290—298
Stretched String, Vibrations of      97 101 154
Subsidiary equation      xvi 1—2 88
Switching problems      243
Thevenin's theorem      268
van der Pol      xv 250 261
Variation of parameters      97
Verification of solutions obtained by the Laplace Transformation      9 81—86 236—239 244
Vibration of air due to oscillating sphere      165
Vibration of air due to pulsating sphere      163
Viscous motion between concentric cylinders      172
Viscous motion between parallel planes      169—172
Viscous motion in the region outside a cylinder      174
W.B.F.      348
Water waves in a canal      175
Water waves in an infinite two-dimensional sheet      180
Water waves in infinite liquid produced by initial surface elevation      179
Wave motion of air under gravity      183
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