Hi!
I've studied ODE's but not Partials DE.
in ODE one uses linearization method to linearize an non-linear system of equations.
My question is:
The method of finding normal coordinates for say, a dynamical system, is that the correspondent of the method i described above but for...
That's what i was thinking
\frac{1}{\pi}\int_{-\pi}^{\pi}f(t)\sin(nt) dt = \frac{1}{\pi}\int_{-\pi}^{0} 0· dt+\frac{1}{\pi}\int_{0}^{\pi}\sin(t)\sin(nt) dt
but the above is zero!
i'm doing something wrong.
Homework Statement
Hi i would just like some fast hints, I'm doing the integrals wrong, I am splitting up the integral below and get the wrong answer.
well it's about finding the Fourier series for f(t)={0 for -π<t<0 and sint for 0≤t≤π}
Homework Equations
a_{n} =...
suppose, s_{n}(f;t) = \sum_{k=-n}^{n}\widehat{f}(k)e^{ikt}
and
\sigma_{N}(f;t)= \frac{1}{N+1}\sum_{n=0}^{N}s_{n}(f;t).
how do i get from this \sigma_{N}(f;t)= \frac{1}{N+1}\sum_{n=0}^{N}s_{n}(f;t).
to this
\sigma_{N}(f;t)= \sum_{n=-N}^{N}(1-\frac{|n|}{N+1})\widehat{f}(n)e^{int}...
Hi i tried in the other section with no luck.
Let me try here if there are anyone here that can help me.
the question is:
Suppose one catches in 5000-Na atoms in a spherical-shaped cloud with diameter of 2mm.
And suppose that the atoms are uniformly distributed in that sphere.
At what...