P1.
Write the Taylor series for f(x) = cos
x about x = 0.
State the Taylor polynomials T2(x),
T4(x), and T6(x) (note that
T3(x)
will be the same as T2(x), and
T5(x) will be the same as
T4(x)).
Plot f(x), T2(x), T4(x), and T6(x), together on one graph,
using demos
or similar (cut-and-paste or reproduce
below).
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