Normal Mode Expansion and Bessel Series

  • Kurt Bernardo Wolf
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 11)


The eigenfunctions of the Laplacian operator in function spaces with certain sets of boundary conditions constitute orthogonal sets of functions on the region enclosed by the boundaries. This is developed in Section 6.1 for rectangular boundaries and in Sections 6.2 and 6.3 for circular, sectorial, and annular boundaries in the plane. These are a few of the systems which appear in physics and engineering, where a great variety of operators and boundaries occur. The Laplacian applies mainly to wave and diffusion phenomena, which makes it specially relevant. As for boundary value problems, the above have been chosen for simplicity and because Fourier and Bessel 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.


Bessel Function Normal Mode Nodal Line Eigenfunction Expansion Neumann Function 
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Copyright information

© Springer Science+Business Media New York 1979

Authors and Affiliations

  • Kurt Bernardo Wolf
    • 1
  1. 1.Instituto de Investigaciones en Matemáticas Aplicadas y en SistemasUniversidad Nacional Autónoma de MéxicoMéxico D.F.México

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