Unformatted text preview: 6 ... 4 1 3 1 2 1 1 1 2 2 2 2 2 5. Show, graphically, that a Fourier series can only be differentiated if f ( x ) is continuous and f (0) = f ( L ) = 0. Consequently, verify that the temperature distribution in a one-dimensional rod (that we previously derived in class) could be expanded in terms of a Fourier sine series, if and only if both ends of the rod have a temperature of zero. 6. Show (using the de Moivre relations) that an alternate representation of the function, f(x) expressed as a Fourier series over an interval (-L, L ), i.e., f(x) ~ ) sin( ) cos( 1 1 L x n b L x n a a n n n n o is: f(x) ~ ) ( L x n i n n e c where ) ( 2 1 n n n b i + a c...
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- Spring '09
- Fourier Series, Periodic function, Mathematical Physics