Fourier Series Examples

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

In[45]:=

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

Out[45]=

  Cos[x]
  Cos[2 x]
  Cos[3 x]
  Cos[4 x]
  Cos[5 x]
  Cos[6 x]
  Cos[7 x]
  Cos[8 x]
  Cos[9 x]
  Cos[10 x]

Out[46]=

  Sin[x]
  Sin[2 x]
  Sin[3 x]
  Sin[4 x]
  Sin[5 x]
  Sin[6 x]
  Sin[7 x]
  Sin[8 x]
  Sin[9 x]
  Sin[10 x]

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