Identify the Fourier series for the half-wave rectified sine
function with period 2π. This is the...
Identify the Fourier series for the half-wave rectified sine
function with period 2π. This is the function that is sin(x) when
sin(x) is positive, and zero when sin(x) is negative
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.
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)
Write a program in ecmascript, of Maclurin series of a sine
function that declares two variables:
x is the value of the argument, h is the accuracy that you want
test the program with
x= 1; h= .00001
print out the approximation using as many terms of the Maclaurin
series that you need, but no more than that, to get within the
required accuracy. While you are at it you might as well also print
out Sine(x) BUT do not...
3) Find the Fourier series of ?(?), which is assumed to have the
period 2?. Specify the relationships for Fourier coefficients, and
illustrate the pattern for the first several terms within the
series ?(?). You may use software to solve for the integrals, but
show the complete result and illustrate the simplification process
to a reduced form. [35 pts]
?(?) = ?2 (0 < ? < 2?)