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Titlebook: Integral Transforms in Science and Engineering; Kurt Bernardo Wolf Book 1979 Springer Science+Business Media New York 1979 Canon.Finite.La

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書目名稱Integral Transforms in Science and Engineering
編輯Kurt Bernardo Wolf
視頻videohttp://file.papertrans.cn/469/468347/468347.mp4
叢書名稱Mathematical Concepts and Methods in Science and Engineering
圖書封面Titlebook: Integral Transforms in Science and Engineering;  Kurt Bernardo Wolf Book 1979 Springer Science+Business Media New York 1979 Canon.Finite.La
描述Integral transforms are among the main mathematical methods for the solution of equations describing physical systems, because, quite generally, the coupling between the elements which constitute such a system-these can be the mass points in a finite spring lattice or the continuum of a diffusive or elastic medium-prevents a straightforward "single-particle" solution. By describing the same system in an appropriate reference frame, one can often bring about a mathematical uncoupling of the equations in such a way that the solution becomes that of noninteracting constituents. The "tilt" in the reference frame is a finite or integral transform, according to whether the system has a finite or infinite number of elements. The types of coupling which yield to the integral transform method include diffusive and elastic interactions in "classical" systems as well as the more common quantum-mechanical potentials. The purpose of this volume is to present an orderly exposition of the theory and some of the applications of the finite and integral transforms associated with the names of Fourier, Bessel, Laplace, Hankel, Gauss, Bargmann, and several others in the same vein. The volume is divide
出版日期Book 1979
關(guān)鍵詞Canon; Finite; Lattice; Mathematica; Volume; equation; form; integral; integral transform; interaction; system
版次1
doihttps://doi.org/10.1007/978-1-4757-0872-1
isbn_softcover978-1-4757-0874-5
isbn_ebook978-1-4757-0872-1
copyrightSpringer Science+Business Media New York 1979
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Normal Mode Expansion and Bessel Seriesbove have been chosen for simplicity and because Fourier and . series appear. Bessel series are a family of expansions in terms of orthonormal sets of functions which include those of Fourier as a particular case. In Section 6.4 we give a broad survey of the variants of eigenfunction expansions and some references.
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Concepts from Complex Vector Analysis and the Fourier Transformill be important in applications. We give, in Section 1.6, the elements of invariance group considerations for a finite N-point lattice. Finally, in Section 1.7 we examine the axes of a transformation and develop the properties of self-adjoint and unitary operators.
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The Application of Fourier Analysis to the Uncoupling of Latticesg properly to analytical mechanics. Sections 2.5 and 2.6 can be read after the first two sections if the reader so prefers. Although examples drawn from Sections 2.3 and 2.4 are used to illustrate examples of the theory, the reader should be able to follow the general presentation easily.
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lly, the coupling between the elements which constitute such a system-these can be the mass points in a finite spring lattice or the continuum of a diffusive or elastic medium-prevents a straightforward "single-particle" solution. By describing the same system in an appropriate reference frame, one
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