Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Exercise (3-2): find Fourier series on [0,2n]
Question
Answer
(1) f(x)= x/2
sin nx
(2) f(x)= -x
sin nx
(3) f(x)=sin.x
sin x
(4) f(x)=cosx
COS X
(5) f(x)=xsin x
-1+
COS nx
(6) f(x)=xcos x
2n(-1)
(n-1)(n +1)
sin(nx)
0<x<A
151-- sin nx
(7) f(x) =.
1 T<x<2n
-1
0<xくて
2テ-1+(-1)
(8) f(x) =.
1
sin nx
0<x<T
3
1-(-1)"
(9) f(x) =-
sin nx
2 くx<2元
2.
-n/4
(10) f(x)=
ーTくX<0
ミ-1+(-1)"
-sin nx
0<x<r
0<x<T
37 (-1)" -1
sin nx
(11) f(x) =
COS LX -
|T くX<2元
0<x<T
sin nx
(12) f(x) = {
COS nx +
0<x<T
(-1)"
(13) f(x) =
|2ォーx
COS NX
Transcribed Image Text:Exercise (3-2): find Fourier series on [0,2n] Question Answer (1) f(x)= x/2 sin nx (2) f(x)= -x sin nx (3) f(x)=sin.x sin x (4) f(x)=cosx COS X (5) f(x)=xsin x -1+ COS nx (6) f(x)=xcos x 2n(-1) (n-1)(n +1) sin(nx) 0<x<A 151-- sin nx (7) f(x) =. 1 T<x<2n -1 0<xくて 2テ-1+(-1) (8) f(x) =. 1 sin nx 0<x<T 3 1-(-1)" (9) f(x) =- sin nx 2 くx<2元 2. -n/4 (10) f(x)= ーTくX<0 ミ-1+(-1)" -sin nx 0<x<r 0<x<T 37 (-1)" -1 sin nx (11) f(x) = COS LX - |T くX<2元 0<x<T sin nx (12) f(x) = { COS nx + 0<x<T (-1)" (13) f(x) = |2ォーx COS NX
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