Chapter 5. Vibration and Eigenvalue Problems

  1. R. Courant,
  2. D. Hilbert

Published Online: 24 DEC 2007

DOI: 10.1002/9783527617210.ch5

Book Title

Methods of Mathematical Physics, Volume I

Methods of Mathematical Physics, Volume I

Additional Information

How to Cite

Courant, R. and Hilbert, D. (2007) Vibration and Eigenvalue Problems, in Methods of Mathematical Physics, Volume I, Wiley-VCH Verlag GmbH, Weinheim, Germany. doi: 10.1002/9783527617210.ch5

Publication History

  1. Published Online: 24 DEC 2007
  2. Published Print: 19 APR 1989

ISBN Information

Print ISBN: 9780471504474

Online ISBN: 9783527617210

SEARCH

CHAPTER TOOLS

Get PDF (5109K)

Keywords:

  • derivatives;
  • algebraic;
  • frequency;
  • motions;
  • orthogonal;
  • decomposing

Summary

This chapter contains sections titled:

  • Preliminary remarks about linear differential equations

  • Systems of a finite number of degrees of freedom

  • The vibrating string

  • The vibrating rod

  • The vibrating membrane

  • The vibrating plate

  • General remarks on the eigenfunction method

  • Vibration of three-dimensional continua. Separation of variables

  • Eigenfunctions and the boundary value problem of potential theory

  • Problems of the Sturm-Liouville type. Singular boundary points

  • The asymptotic behavior of the solutions of Sturm-Liouville equations

  • Eigenvalue problems with a continuous spectrum

  • Perturbation theory

  • Green's function (influence function) and reduction of differential equations to integral equations

  • Examples of Green's function

  • Supplement to Chapter V

Get PDF (5109K)