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Fourier Series Example 3

Fourier Series Example 3
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2016-09-15 19:43
FunctionTrigonometrySequenceCoordinate GeometryCalculus
In collections UQ-Applied Mathematical Analysis
This example demonstrates how Fourier series approximates a given function's graph. Core math concepts include Fourier coefficients, trigonometric sequences, and series convergence. Construction highlights involve commands like Sequence and Append, with objects such as s, p, n, f, g, an, bn, list1, etc. Suitable for high school and above learners to understand Fourier series applications and visualization.

GeoGebra Commands & Parameters

  1. Sequence((2 / p * Integral[(s(x) * cos((((i * x) * 2) * π / p))), 0, p]), i, 1, n) → an
  2. Sequence((2 / p * Integral[(s(x) * sin((((i * x) * 2) * π / p))), 0, p]), i, 1, n) → bn
  3. Sequence((Element[an, i] * cos((((π * i) * 2 / p) * x))) + (Element[bn, i] * sin((((π * i) * 2 / p) * x))), i, 1, n) → list1
  4. Sequence((2 / p * Integral[(s(x) * cos((((i * x) * 2) * π / p))), 0, p]), i, 2, n) → an'
  5. Sequence((2 / p * Integral[(s(x) * sin((((i * x) * 2) * π / p))), 0, p]), i, 2, n) → bn'
  6. Append(A1, an') → an''
  7. Append(B1, bn') → bn''
  8. Sequence((Element[an'', i] * cos((((π * i) * 2 / p) * x))) + (Element[bn'', i] * sin((((π * i) * 2 / p) * x))), i, 1, n) → list2
  9. Textfield(A0) → InputBox1
  10. Textfield(A1) → InputBox2
  11. Textfield(B1) → InputBox3
  12. Textfield(n) → InputBox4