Fourier Series Examples

Remember:
uk=Cos[kx], k=0,1,2,3, . . .
vk=Sin[kx], k=1,2,3, . . .


  u[x_]:=Table[Cos[k x],{k,10}]
  ColumnForm[u[x]]
  v[x_]:=Table[Sin[k x],{k,10}]
  ColumnForm[v[x]]

Please take note: there are some very important theoretical ideas illustrated in these examples. Please take note of them as you go along!