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  function 232
Dirac's 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
|
|
|
О проекте