Differential Equations Lecture Work Solutions 37

Differential Equations Lecture Work Solutions 37 - 6 4 2 0...

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 6 4 2 0 −L L −2 −4 −6 −8 −6 −4 −2 0 2 4 6 8 4 6 8 6 4 2 0 −L L −2 −4 −6 −8 −6 −4 −2 0 2 Figure 15: Sketch of f (x) and its periodic extension for 1a 6 4 2 0 −L L −2 −4 −6 −8 −6 −4 −2 0 2 4 6 8 4 6 8 6 4 2 0 −L L −2 −4 −6 −8 −6 −4 −2 0 2 Figure 16: Sketch of the odd extension and its periodic extension for 1a 1. a. The Fourier series is the same as the periodic extension except for the points of discontinuities where the Fourier series yields 1 1+0 = 2 2 For the Fourier sine series we take ONLY the right branch on the interval [0, L] and extend it as an odd function. Now the same discontinuities are there but the value of the Fourier series at those points is 1 + (−1) =0 2 For the Fourier cosine series we need an even extension Note that the periodic extension IS continuous and the Fourier series gives the exact same sketch. 37 ...
View Full Document

This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

Ask a homework question - tutors are online