Unformatted text preview: 3. Problem 18.3:19. I ²nd the language of the text somewhat confusing. In the language I have used in class, I would say that: • One ²rst introduces the particular solution z ( x ) = ( xL ) 2 / 2 L , writes v ( x, t ) = u ( x, t )z ( x ), and determines what problem v ( x, t ) satis²es; • For the v problem one introduces another particular solution v 2 ( t ), reducing to a problem for v 1 ( x, t ) = v ( x, t )v 2 ( t ) which one knows how to solve. 4. In 18.4:8(b) one should use the Laplace transform (in the variable t ), not the Fourier transform, although in fact one can guess the form of the solution, and then ²nd it completely, by elementary reasoning....
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 Fall '08
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 Math, Eigenvalue, eigenvector and eigenspace, Eigenfunction, Differential operator, 2L

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