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| Авторизация |
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| Tranter C.J. — Integral transforms in mathematical physics |
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| Предметный указатель |
Asymptotic formulae, for integrals 63
Boussinesq, problem of 46
Bromwich, T. J. IA. vii
Busbridge, I. W. 52
Carslaw, H. S. 4 18 23 29 61
Carson, J. vii
Combined use of relaxation methods and transforms 104
Complex Fourier transform I 3
Complex Fourier transform, inversion formulae for 8 10
Contour integral of inversion formula, evaluation of 23
Cosine transform 1 32
Cosine transform, example of use 8
Cosine transform, finite 78
Cosine transform, inversion formulae for 6 79
Craggs, J. W. 44
Dirichlet’s conditions 4 61
Disc, electrified, solved by Hankel transform 50
Doetsch, G., vii 21 77
Dual integral equations 52
Edwards, J. 57
Electrified disc, solved by Hankel transform 50
Electrified disc, solved by Legendre transform 99
Evaluation of contour integral in inversion formula 23
Evaluation of integrals in solutions 60
Filon, L. N. G. 60 68 70 71
Filon’s method for evaluation of integrals 67
Finite transforms 1 77
Formula, Fourier’s integral 2
Formulae, inversion 4
Fourier, complex transform 1 38
Fourier, complex transform, example 38
Fourier, finite transforms 78
Fourier, finite transforms, examples 81 83 84
Fourier, J. B. J. vii
Fourier, sine and cosine transforms 1 32
Fourier, sine and cosine transforms, examples 34 35
Fourier’s integral formula 2
Fox, L. 107
Goldstein, S. 28
Hankel transform 2 46
Hankel transform, example 91
Hankel transform, examples 46 50
Hankel transform, finite 88
Hankel transform, inversion formulae for 11 88 89
Hankel transform, solved by Legendre transform 99
Hartree, D. R. 29
Heat conduction problems by finite cosine transform 84
Heat conduction problems by finite Hankel transform 91
Heat conduction problems by finite sine transform 81
Heat conduction problems by Laplace transform 21 26
Heat conduction problems by repeated use of finite transforms 83
Heat conduction problems by repeated use of transforms 35
Heat conduction problems by sine transform 34
Heat conduction problems of relaxation methods and transforms 106
Heat conduction problems with radiation boundary condition 86 93
Heaviside, O. vii 21
Humbert, P. 21
Integral formula, Fourier’s 2
Integral transforms 1
Inversion formulae 4
Inversion formulae for complex Fourier transform 8 10
Inversion formulae for finite Hankel transforms 88 89
| Inversion formulae for finite sine and cosine transforms 78 79 81
Inversion formulae for Fourier sine and cosine transforms 6
Inversion formulae for Hankel transform 11
Inversion formulae for Laplace transform 4
Inversion formulae for Legendre transform 97
Inversion formulae for Mellin transform 13
Jaeger, J. C. 18 23 29
Kernel, of transform i
Laplace transform i
Laplace transform, application to ordinary differential equations 18
Laplace transform, applications to partial differential equations 21 26
Laplace transform, evaluation of contour integral in inversion formula 23
Laplace transform, inversion formula for 4
Laplace transform, table of 20
Laplace, P. S. de vii
Legendre transform 96
Legendre transform, example of use 99
Love, A. E. H. 40 46 54 57
McLachlan, N. W. 21
Mellin transform 2
Mellin transform, example of use 53
Mellin transform, inversion formula for 13
Numerical evaluation of integrals 60
Numerical evaluation of integrals, Filon’s method 67
Numerical evaluation of integrals, values at end points 60
Numerical evaluation of integrals, worked example 72
Ordinary differential equations, solution by Laplace transform 18
Procedure in using transforms 18
Radial flow of heat 26
Radiation boundary condition 86 93
Relaxation method, combined use with transforms 104
Repeated use, of finite transforms 83
Repeated use, of transforms 35
Riemann-Lebesgue theorem 61
Sine transform 1 32
Sine transform, example of use 81
Sine transform, finite 78
Sine transform, inversion formulae for 6 78
Small values of time, solutions for 28
Sneddon, I. N. 77 88 89
Southwell, R. V. 104
Stresses in long cylinder 40
Stresses in wedge 53
String, motion of 38
Summary, transforms and inversion formulae 14
Table of constants for use with Filon’s formula 71
Table of Laplace transforms 20
Titchmarsh, E. C. 3 52 61
Transforms, complex Fourier 1 38
Transforms, finite 1 77
Transforms, Hankel 2 46
Transforms, Laplace 1 18
Transforms, Legendre 96
Transforms, Mellin 2 53
Transforms, sine and cosine 1 32
Tranter, C. J. 44 53
Van der Pol, B. vii
Verification of solution 29
Viscous fluid, motion of 94
Watson, G. N. 12 42 50 52 67 88 89 96 97
Weber, H. 50
Whittaker, E. T. 96 97
Willis, H. F. 63
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