Expand in Fourier series:
Expand in fourier sine and fourier cosine series of: f(x) =
x(L-x), 0<x<L
Expand in fourier cosine series: f(x) = sinx, 0<x<pi
Expand in fourier series f(x) = 2pi*x-x^2, 0<x<2pi,
assuming that f is periodic of period 2pi, that is,
f(x+2pi)=f(x)
Find the Fourier Series for the function defined over -5 < x
< 5
f(x) = -2 when -5<x<0 and f(x) = 3 when 0<x<5
You can use either the real or complex form but must show
work.
Plot on Desmos the first 10 terms of the series along with the
original
function.
Calculate the fourier series of these periodic functions f(x) =
cosh(2πax + πa), x ∈ [0, 1) and f(x) = cos(2πax − aπ) x ∈ [0, 1).
The period of these functions is 1.
1-periodic
I know if f(x) is even the fourier series expansion will
consists of consnx, for like f(x)=x^2sinx, or f(x)=2/(3+cosx). but
if the f(x) is neither even or odd, would fourier expansion have
both cosnx and sinnx? This is PDE.
Both parts.
a) identify Fourier series for full wave rectified sine function
f(x) = | sin(x) |.
b) f(t) = cos(t) but period of 6, so t = [-3,3] (L = 6) Find the
Fourier series of the resulting function.