Question

Derive the Fourier series for the function f(x) = x + 1/2 for −1 < x < 1; plot the function and its Fourier series for −3 < x < 3.

Answer #1

f(x) = 2x - 7
x ∈ (0,7)
Draw a plot of the periodic Fourier Series expansion of f(x).
What is its value at x=0 and why? Is it odd or even?
Expand the given function in a Fourier Series also

Expand the function f(x) = x^2 in a Fourier sine series on the
interval 0 ≤ x ≤ 1.

a. Let f be an odd function. Find the Fourier series of f on
[-1, 1]
b. Let f be an even function. Find the Fourier series of f on
[-1, 1].
c. At what condition for f would make the series converge to f
at x=0 and x=1?

Find the Fourier series of the function f(x) = |x|, −π/2 < x
< π/2 , with period π.

Calculate the Fourier series expansion of the function:
f(x)
=1/2(π-x) , when 0
< x ≤ π and
f(x) = -
1/2(π+x), when -π
≤ x < 0

sketch the function f and obtain fourier series
1. f(x)=|x|, -2pi<x<2pi

Find the Fourier series for the following function (which has
period 2): f(x)= −x if −1<x<0
x if 0 < x < 1

Find the Fourier series of the function:
f(x) =
{0, -pi < x < 0
{1, 0 <= x < pi

Compute the complex Fourier series of the function f(x)= 0 if −
π < x < 0, 1 if 0 ≤ x < π
on the interval [−π, π]. To what value does the complex Fourier
series converge at x = 0?

Find the Fourier series of the function f on the given
interval.
f(x) =
0,
−π < x < 0
1,
0 ≤ x < π

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