4 added 63 characters in body
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You examples are easy, I was hoping for harder ones ;) This is from the definition.

f3[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}];
FourierSeries[f3[x], x, 3]

Mathematica graphics

A quick Manipulate:

enter image description here

Manipulate[
 r = FourierSeries[f[x], x, n];
 Show[Plot[r, {x, -2 Pi, 2 Pi}, Frame -> True], Plot[f[x], {x, -2 Pi, 2 Pi}, 
      PlotStyle -> {Thick, Red}]],
 Grid[{
   {Control[{{n, 3, "how many terms?"}, 1, 20, 1}], Dynamic[n]}
   }],
 ContinuousAction -> False,
 SynchronousUpdating -> True,
 Initialization :>
  (
   f[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}]
   )
 ]

Mathematica graphics

And if you meant them to be different functions:

f1[x_] := Piecewise[{{1 - x^2 , x < 0}, {0, True}}];
f2[x_] := Piecewise[{{1 + x^2 , x > 0}, {0, True}}];
FourierSeries[f1[x], x, 3]

Mathematica graphics

FourierSeries[f2[x], x, 3]

Mathematica graphics

You can use the definition of the $c_k$ also by using FourierParameters to make it match the textbook you are using. So make sure to look at FourierParameters and adjust it as needed else you'll get different looking result from the textbook if the textbook does not use the default setting used by Mathematica.

You examples are easy, I was hoping for harder ones ;) This is from the definition.

f3[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}];
FourierSeries[f3[x], x, 3]

Mathematica graphics

A quick Manipulate:

enter image description here

Manipulate[
 r = FourierSeries[f[x], x, n];
 Show[Plot[r, {x, -2 Pi, 2 Pi}, Frame -> True], Plot[f[x], {x, -2 Pi, 2 Pi}, 
      PlotStyle -> {Thick, Red}]],
 Grid[{
   {Control[{{n, 3, "how many terms?"}, 1, 20, 1}], Dynamic[n]}
   }],
 ContinuousAction -> False,
 SynchronousUpdating -> True,
 Initialization :>
  (
   f[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}]
   )
 ]

And if you meant them to be different functions:

f1[x_] := Piecewise[{{1 - x^2 , x < 0}, {0, True}}];
f2[x_] := Piecewise[{{1 + x^2 , x > 0}, {0, True}}];
FourierSeries[f1[x], x, 3]

Mathematica graphics

FourierSeries[f2[x], x, 3]

Mathematica graphics

You can use the definition of the $c_k$ also by using FourierParameters to make it match the textbook you are using. So make sure to look at FourierParameters and adjust it as needed else you'll get different looking result from the textbook if the textbook does not use the default setting used by Mathematica.

You examples are easy, I was hoping for harder ones ;) This is from the definition.

f3[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}];
FourierSeries[f3[x], x, 3]

Mathematica graphics

A quick Manipulate:

enter image description here

Manipulate[
 r = FourierSeries[f[x], x, n];
 Show[Plot[r, {x, -2 Pi, 2 Pi}, Frame -> True], Plot[f[x], {x, -2 Pi, 2 Pi}, 
      PlotStyle -> {Thick, Red}]],
 Grid[{
   {Control[{{n, 3, "how many terms?"}, 1, 20, 1}], Dynamic[n]}
   }],
 ContinuousAction -> False,
 SynchronousUpdating -> True,
 Initialization :>
  (
   f[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}]
   )
 ]

Mathematica graphics

And if you meant them to be different functions:

f1[x_] := Piecewise[{{1 - x^2 , x < 0}, {0, True}}];
f2[x_] := Piecewise[{{1 + x^2 , x > 0}, {0, True}}];
FourierSeries[f1[x], x, 3]

Mathematica graphics

FourierSeries[f2[x], x, 3]

Mathematica graphics

You can use the definition of the $c_k$ also by using FourierParameters to make it match the textbook you are using. So make sure to look at FourierParameters and adjust it as needed else you'll get different looking result from the textbook if the textbook does not use the default setting used by Mathematica.

3 added 564 characters in body
source | link

You examples are easy, I was hoping for harder ones ;) This is from the definition.

f3[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}];
FourierSeries[f3[x], x, 3]

Mathematica graphics

A quick Manipulate:

enter image description here

Manipulate[
 r = FourierSeries[f[x], x, n];
 Show[Plot[r, {x, -2 Pi, 2 Pi}, Frame -> True], Plot[f[x], {x, -2 Pi, 2 Pi}, 
      PlotStyle -> {Thick, Red}]],
 Grid[{
   {Control[{{n, 3, "how many terms?"}, 1, 20, 1}], Dynamic[n]}
   }],
 ContinuousAction -> False,
 SynchronousUpdating -> True,
 Initialization :>
  (
   f[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}]
   )
 ]

And if you meant them to be different functions:

f1[x_] := Piecewise[{{1 - x^2 , x < 0}, {0, True}}];
f2[x_] := Piecewise[{{1 + x^2 , x > 0}, {0, True}}];
FourierSeries[f1[x], x, 3]

Mathematica graphics

FourierSeries[f2[x], x, 3]

Mathematica graphics

You can use the definition of the $c_k$ also by using FourierParameters to make it match the textbook you are using. So make sure to look at FourierParameters and adjust it as needed else you'll get different looking result from the textbook if the textbook does not use the default setting used by Mathematica.

You examples are easy, I was hoping for harder ones ;) This is from the definition.

f3[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}];
FourierSeries[f3[x], x, 3]

Mathematica graphics

And if you meant them to be different functions:

f1[x_] := Piecewise[{{1 - x^2 , x < 0}, {0, True}}];
f2[x_] := Piecewise[{{1 + x^2 , x > 0}, {0, True}}];
FourierSeries[f1[x], x, 3]

Mathematica graphics

FourierSeries[f2[x], x, 3]

Mathematica graphics

You can use the definition of the $c_k$ also by using FourierParameters to make it match the textbook you are using. So make sure to look at FourierParameters and adjust it as needed else you'll get different looking result from the textbook if the textbook does not use the default setting used by Mathematica.

You examples are easy, I was hoping for harder ones ;) This is from the definition.

f3[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}];
FourierSeries[f3[x], x, 3]

Mathematica graphics

A quick Manipulate:

enter image description here

Manipulate[
 r = FourierSeries[f[x], x, n];
 Show[Plot[r, {x, -2 Pi, 2 Pi}, Frame -> True], Plot[f[x], {x, -2 Pi, 2 Pi}, 
      PlotStyle -> {Thick, Red}]],
 Grid[{
   {Control[{{n, 3, "how many terms?"}, 1, 20, 1}], Dynamic[n]}
   }],
 ContinuousAction -> False,
 SynchronousUpdating -> True,
 Initialization :>
  (
   f[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}]
   )
 ]

And if you meant them to be different functions:

f1[x_] := Piecewise[{{1 - x^2 , x < 0}, {0, True}}];
f2[x_] := Piecewise[{{1 + x^2 , x > 0}, {0, True}}];
FourierSeries[f1[x], x, 3]

Mathematica graphics

FourierSeries[f2[x], x, 3]

Mathematica graphics

You can use the definition of the $c_k$ also by using FourierParameters to make it match the textbook you are using. So make sure to look at FourierParameters and adjust it as needed else you'll get different looking result from the textbook if the textbook does not use the default setting used by Mathematica.

2 added 216 characters in body
source | link

You examples are easy, I was hoping for harder ones ;) This is from the definition.

f3[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}];
FourierSeries[f3[x], x, 3]

Mathematica graphics

And if you meant them to be different functions:

f1[x_] := Piecewise[{{1 - x^2 , x < 0}, {0, True}}];
f2[x_] := Piecewise[{{1 + x^2 , x > 0}, {0, True}}];
FourierSeries[f1[x], x, 3]

Mathematica graphics

FourierSeries[f2[x], x, 3]

Mathematica graphics

You can use the definition of the $c_k$ also by using FourierParameters to make it match the textbook you are using. So make sure to look at FourierParameters and adjust it as needed else you'll get different looking result from the textbook if the textbook does not use the default setting used by Mathematica.

You examples are easy, I was hoping for harder ones ;) This is from the definition.

f1[x_] := Piecewise[{{1 - x^2 , x < 0}, {0, True}}];
f2[x_] := Piecewise[{{1 + x^2 , x > 0}, {0, True}}];
FourierSeries[f1[x], x, 3]

Mathematica graphics

FourierSeries[f2[x], x, 3]

Mathematica graphics

You can use the definition of the $c_k$ also by using FourierParameters to make it match the textbook you are using. So make sure to look at FourierParameters and adjust it as needed else you'll get different looking result from the textbook if the textbook does not use the default setting used by Mathematica.

You examples are easy, I was hoping for harder ones ;) This is from the definition.

f3[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}];
FourierSeries[f3[x], x, 3]

Mathematica graphics

And if you meant them to be different functions:

f1[x_] := Piecewise[{{1 - x^2 , x < 0}, {0, True}}];
f2[x_] := Piecewise[{{1 + x^2 , x > 0}, {0, True}}];
FourierSeries[f1[x], x, 3]

Mathematica graphics

FourierSeries[f2[x], x, 3]

Mathematica graphics

You can use the definition of the $c_k$ also by using FourierParameters to make it match the textbook you are using. So make sure to look at FourierParameters and adjust it as needed else you'll get different looking result from the textbook if the textbook does not use the default setting used by Mathematica.

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