Exercise 2.10: Fourier series of a triangle waveConsider the Fourier sine series approximation for the triangle wave depicted in Fig-ure 2.32.MfM (x) = an sin(nnx)хе [0, 11n=1(a) Find the coefficients an, n = 1,2,... To save time you may find the following 1integral formulas useful%3D(mx + b) sin(nnx)dx =тx + bsin(nnx)cos(nnx) +(nT)2sin(nnx) sin(Mnx)dx =Snm.2n, m = 1,2, ...2.10 Exercises2230 ..+2а1Figure 2.32: Triangle wave on [0, 1].a Plot the function fM (x) for M 5,10, 50 with parameter a 0.1 to demonstrateconvergence to f(x). How many terms are required to obtain good accuracy?

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Consider the Fourier sine series approximation for the triangle wave depicted in Fig- ure 2.32. M fM (x) = an sin(nnx) xE [0,1] %3D n=1 (a) Find the coefficients an, n = 1,2,... To save time you may find the folowne integral formulas useful %3D

Consider the Fourier sine series approximation for the triangle wave depicted in Fig- ure 2.32. M fM (x) = an sin(nnx) xE [0,1] %3D n=1 (a) Find the coefficients an, n = 1,2,... To save time you may find the folowne integral formulas useful %3D

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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Exercise 2.10: Fourier series of a triangle wave
Consider the Fourier sine series approximation for the triangle wave depicted in Fig-
ure 2.32.
M
fM (x) = an sin(nnx)
хе [0, 11
n=1
(a) Find the coefficients an, n = 1,2,... To save time you may find the following 1
integral formulas useful
%3D
(mx + b) sin(nnx)dx =
тx + b
sin(nnx)
cos(nnx) +
(nT)2
sin(nnx) sin(Mnx)dx =
Snm.
2
n, m = 1,2, ...
2.10 Exercises
223
0 ..+
2а
1
Figure 2.32: Triangle wave on [0, 1].
a Plot the function fM (x) for M 5,10, 50 with parameter a 0.1 to demonstrate
convergence to f(x). How many terms are required to obtain good accuracy?

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