Would you like to see the Fourier approximations to the graphs below? Mearly click on one of the pictures and you will see some of the approximations. Click on the notebook links to download the appropriate Mathematica notebooks that allow you to make a more extensive study of the process.
The Half-Range Sine Series
you can't see it Click on the graph to see the Half-Range Sine series approximations to
if -1< x< 0 then f(x) = -((x+1)^2)+1
else 0< x< 1 then f(x) = ((x+1)^2) -1
In Mathematica code f[x_]:=If[x<0, -((x+1)^2)+1 , ((x+1)^2)-1 ]
The next link will download the
Mathematica notebook to study the half-range Sine series.

The Half-Range Cosine Series
you can't see it Click on the graph to see the Half-Range Cosine series approximations to
if -2< x< -1 then f(x) = ((x+2)^2)-1
else if -1< x < 1 then f(x) = x^2+1
else if 1 < x < 2 then f(x) = ((x-2)^2) -1
In Mathematica code f[x_]:=If[x<0, -((x+1)^2)+1 , ((x+1)^2)-1 ]
The next link will download the
Mathematica notebook to study the half-range Cosine series.

The Full-Range Fourier Series
you can't see it Click on the graph to see the Full-Range Fourier series approximations to
if -2< x< -1 then f(x) = ((x+2)^2)-1
else if -1< x < 1 then f(x) = x^2+1
else if 1 < x < 2 then f(x) = ((x-2)^2) -1
In Mathematica code f[x_]:=If[x<0, -((x+1)^2)+1 , ((x+1)^2)-1 ]
The next link will download the
Mathematica notebook to study the Full-Range Fourier series.

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