发帖
雷达卡
Prem K. Kythe
University Of New Orleans Louisiana, USA
This coursebook starts in Chapter 1 with an introduction to some basic results and definitions from topics such as Euclidean space, specially the metric space and the concept of inner product; classes of continuous functions and those that are infinitely differentiable with compact support; convergence of sequences, their weak and strong convergence, convergence in the mean, and convergence of infinite series; linear func-tionals, and linear transformations; Cramer’s rule; divergence theorem and Green’s identities; Leibniz’s rule for differentiation of integrals and for the nth derivative of product of two functions; formulas for integration by parts; Bessel’s inequality for Fourier series and for square-integrable functions; Schwarz’s inequality for infinite sequences; and Parseval’s equality or completeness relation.
The concept of a Green’s function is presented in Chapter 2 by first introducing the ‘generalized function’ known as the Dirac delta function through a limiting process for certain admissible ‘test functions’ which are infinitely differentiable with compact support. This approach to define the Dirac delta function seems to be the simplest as compared to more advanced definitions, available prior to 1945, that arose out of Schwarz’s theory of distributions, namely.
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Greens Functions and Linear Differential Equations Theory, Applications, and Com.pdf
(5.05 MB, 需要: RMB 19 元)
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