Suppose $f(x)=H(x-.5)$ where H = Heaviside function on $0<x<1$ is approximated by the first five nonzero terms of its Fourier sine series. Compute the uniform error (i.e maximum error, max p(x) for all $0<x<1$) in this approximation
I know how to do (absolute) pointwise error $p(x)=|f(x)-S_n(x)|$ where $S_n(x)$ is the Fourier sine series, but I have no notes on how to do uniform error.