Unformatted text preview: u ( x, t ): ± u t + 5 u x = 0 u ( x, 0) = cos(3 x ) 4. Using the method of characteristics solve the following PDE for u ( x, t ): ± u t16 u x =5 u u ( x, 0) = e2 x 2 5. For the following onedimensional wave equation ∂ 2 u ∂t 2 = 7 ∂ 2 u ∂x 2 show explicitly that u 1 = cos(2 x2 √ 7 t ) is a solution, and so is u 2 = ( x + √ 7 t ) 3 . Is u 1 + u 2 also a solution? 6. For the same wave equation, given the Gaussian initial condition u ( x, 0) = 3 exp(x 2 ), what do you expect will happen at later times? Sketch u ( x, t )....
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 Fall '06
 BELMONTE
 Math, Calculus, Laplace, Magnetic Field, following PDE, closed current loop

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