s11_mthsc208_ws6c-Parseval

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

## This note was uploaded on 03/11/2012 for the course MTHSC 208 taught by Professor Staufeneger during the Spring '09 term at Clemson.

Ask a homework question - tutors are online