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)
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
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.
Find the Taylor series or polynomial generated by the following
functions
a. )f(x) √ x centred at x=4 , of order 3
b.) f(x) cosh x= e^x+e^-x/(2), centred at x=0
c.) f(x) = x tan^-1x^2 , centred at x=0
d.) f(x) = 1/(√1+x^3) , centred at x=0 , of order 4
e.) f(x) = cos(2x+pie/2) centred at x= pie/4