Differential Equations Lecture Work Solutions 45

Differential Equations Lecture Work Solutions 45 - 5 0 −L...

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: 5 0 −L L −5 −10 −5 0 5 10 5 10 5 0 −L L −5 −10 −5 0 Figure 30: Sketch of the even extension of f (x) and its periodic extension for problem 3 4. x [ −L, L ] y [ a, b ] − then y = a + b + b2La x (∗) is the transformation required (Note that if x = −L then 2 y = a and if x = L then y = b) g (y ) is periodic of period b − a g (y ) = G(x) = a0 + 2 1 L an = ∞ n=1 L −L nπ nπ x + bn sin x) L L (an cos G(x) cos nπ x dx L solving (*) for x yields x= an = 1 L Therefore 2L b−a b y− g (y ) cos a an = 2 b−a bn = 2 b−a b a+b 2 ⇒ n π 2L L b−a dx = y− 2L dy b−a a+b 2 2L dy b−a g (y ) cos 2n π b−a y− a+b 2 dy g (y ) sin 2n π b−a y− a+b 2 dy a Similarly for bn b a 45 ...
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