含铁
发表于 2025-3-25 05:22:12
Ordinary Differential EquationsLinear differential equations with constant coefficients are an important area of application of the Laplace transform. As a prelude to the discussion of such problems we discuss first two particularly simple examples, since the connection with the classical methods of solution is readily apparent in these cases.
纹章
发表于 2025-3-25 10:32:31
Partial Differential EquationsAs an example to show how the Laplace transform may be applied to the solution of partial differential equations, we consider the diffusion of heat in an isotropic solid body.
偶像
发表于 2025-3-25 12:36:28
The Inversion IntegralAnalytic information about the inversion integral is usually obtained by “closing the contour”, as in Section 2.4 for rational functions.
rheumatology
发表于 2025-3-25 16:54:12
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琐事
发表于 2025-3-25 23:31:44
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somnambulism
发表于 2025-3-26 01:08:32
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带子
发表于 2025-3-26 05:23:24
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有杂色
发表于 2025-3-26 09:29:30
Dual Integral EquationsTo motivate this section, we first solve a classical problem of electrostatics. We wish to find the electrostatic potential φ created by an isolated thin conducting disc of radius a, whose potential is V.
肮脏
发表于 2025-3-26 15:37:26
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Nefarious
发表于 2025-3-26 17:38:43
Methods Based on Cauchy IntegralsThe major difficulty in using the Wiener-Hopf technique is the problem of constructing a suitable factorization. We consider here a method based on contour integration which leads by natural extensions to the use of Cauchy integrals in the solution of mixed boundary-value problems.