Fourier Series Examples

Remember:

In[27]:=

  Clear[u,v,L]

In[28]:=

  u[x_,L_,n_]:=Cos[n Pi x/L]

In[29]:=

  ColumnForm[Table[u[x,L,k],{k,0,10}]]

Out[29]=

  1
      Pi x
  Cos[----]
       L
      2 Pi x
  Cos[------]
        L
      3 Pi x
  Cos[------]
        L
      4 Pi x
  Cos[------]
        L
      5 Pi x
  Cos[------]
        L
      6 Pi x
  Cos[------]
        L
      7 Pi x
  Cos[------]
        L
      8 Pi x
  Cos[------]
        L
      9 Pi x
  Cos[------]
        L
      10 Pi x
  Cos[-------]
         L

In[30]:=

  v[x_,L_,n_]:=Sin[n Pi x/L]

In[31]:=

  ColumnForm[Table[v[x,L,k],{k,1,10}]]

Out[31]=

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

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

Fourier Series Examples

The Delta Function

f(x)=x

f(x)=|x|

A Different Looking Sine Function

Another Example