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Fourier Series Example 1

Fourier Series Example 1
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2016-09-15 13:46
FunctionTrigonometrySequenceCalculusGraphing
This example demonstrates how to approximate a periodic function using Fourier series. It involves core mathematical concepts like Fourier coefficients, trigonometric functions, sequences, and integrals. The construction uses GeoGebra commands such as Sequence, Append, Textfield, and objects like f, g, a_0, n, an, bn, list1, i, j, h, p, text1, A0, A1, B1, an', bn', an'', bn'', list2, q, InputBox1, InputBox2, InputBox3, a, b, c, text2, button1, button2, InputBox4. Suitable for high school and above students to understand the application and visualization of Fourier series.

GeoGebra Commands & Parameters

  1. Sequence((1 / π * Integral[(f(x) * cos((i * x))), (-π), π]), i, 1, n) → an
  2. Sequence((1 / π * Integral[(f(x) * sin((i * x))), (-π), π]), i, 1, n) → bn
  3. Sequence((Element[an, i] * cos(((π * i / π) * x))) + (Element[bn, i] * sin(((π * i / π) * x))), i, 1, n) → list1
  4. Sequence((1 / π * Integral[(f(x) * cos((i * x))), (-π), π]), i, 2, n) → an'
  5. Sequence((1 / π * Integral[(f(x) * sin((i * x))), (-π), π]), i, 2, n) → bn'
  6. Append(A1, an') → an''
  7. Append(B1, bn') → bn''
  8. Sequence((Element[an'', i] * cos(((π * i / π) * x))) + (Element[bn'', i] * sin(((π * i / π) * x))), i, 1, n) → list2
  9. Textfield(A0) → InputBox1
  10. Textfield(A1) → InputBox2
  11. Textfield(B1) → InputBox3
  12. Textfield(n) → InputBox4