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Fourier Series Demonstration

Fourier Series Demonstration
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2017-07-24 18:55
FunctionTrigonometryCoordinate GeometryCalculusGraphing
In collections UQ-Applied Mathematical Analysis
This example demonstrates how to approximate a given function using Fourier series; core math concepts include Fourier series, trigonometric functions, and function approximation; construction highlights involve GeoGebra commands like Midpoint, Textfield, Sequence, Append, and Sum to build Fourier coefficients and function approximation graphs; suitable for high school and above mathematics learners to understand the application and principles of Fourier series and function approximation.

GeoGebra Commands & Parameters

  1. Midpoint(A, B) → C
  2. Textfield(f) → InputBox1
  3. Textfield(initial) → InputBox2
  4. Textfield(final) → InputBox3
  5. Sequence((1 / (period / 2) * Integral[(f(x) * cos(((i * x) * π / (period / 2)))), initial, final]), i, 1, 20) → an
  6. Sequence((1 / (period / 2) * Integral[(f(x) * sin(((i * x) * π / (period / 2)))), initial, final]), i, 1, 20) → bn
  7. Sequence((1 / (period / 2) * Integral[(f(x) * cos(((i * x) * π / (period / 2)))), initial, final]), i, 2, 20) → an'
  8. Sequence((1 / (period / 2) * Integral[(f(x) * sin(((i * x) * π / (period / 2)))), initial, final]), i, 2, 20) → bn'
  9. Append(A1, an') → an''
  10. Append(B1, bn') → bn''
  11. Sequence((Element[an'', i] * cos(((π * i / (period / 2)) * x))) + (Element[bn'', i] * sin(((π * i / (period / 2)) * x))), i, 1, 20) → list2
  12. Textfield(A0) → InputBox4
  13. Textfield(A1) → InputBox5
  14. Textfield(B1) → InputBox6
  15. Textfield(n) → InputBox7
  16. Append(A0 / 2, list2) → list3
  17. Sequence((Element[an, i] * cos(((π * i / (period / 2)) * x))) + (Element[bn, i] * sin(((π * i / (period / 2)) * x))), i, 1, 20) → list1
  18. Sum(list3, n + 1) → p