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The Fourier Method (for the Vibrating String)

  • Vladimir I. Arnold
Part of the Universitext book series (UTX)

Abstract

Consider the periodic boundary-value problem for the vibrating string:
$$ {u_{tt}}= {a^2}{u_{xx}},x \in {S^1} = \mathbb{R}/2\pi \mathbb{Z}$$
(5.1)
$$ u{\backslash _{t = 0}} = \varphi \left( x \right),{u_t}{\backslash _{t = 0}} = \psi (x) $$
(5.2)
.

Keywords

Fourier Series Original Density Hermitian Product Suitable Linear Combination Double Tangent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vladimir I. Arnold
    • 1
    • 2
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.CEREMADEUniversité de Paris-DauphineParis Cedex 16France

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