s11_mthsc208_ws6c-Parseval

s11_mthsc208_ws6c-Parseval - MthSc 208 (Spring 2011)...

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Unformatted text preview: MthSc 208 (Spring 2011) Worksheet 6c MthSc 208: Differential Equations (Spring 2011) In-class Worksheet 6c: Parseval's Identity NAME: Recall that Parseval's identity says that 1 f (x) - 2 1 dx = a2 + 2 0 (a2 + b2 ) . n n n=1 We will use this to compute n=1 1 1 1 1 1 1 =1+ + + + + + . n2 4 4 9 16 25 1. Let f (x) = x on [-, ] and extend f (x) to be 2-periodic. Write f (x) as a Fourier series. (See Example 2 on pages 5-6 of the lecture notes.) 2. Compute 1 f (x) - 2 dx. (The left-hand side of Parseval's identity.) 3. Compute 1 2 a + 2 0 (a2 + b2 ). (The right-hand side of Parseval's identity.) n n n=1 4. Equate your answers to the previous two parts and solve for n=1 1 . n2 Written by M. Macauley 1 ...
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This note was uploaded on 03/11/2012 for the course MTHSC 208 taught by Professor Staufeneger during the Spring '09 term at Clemson.

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