Fourier Series Expansion of f(x) = x | Calculation & Visualization
Автор: Math Infinitum
Загружено: 2025-12-21
Просмотров: 81
#fourierseries #calculus #maths #mathematics #maths #manim #visualization #engineeringmathematics #fourieranalysis #series #calculation #engineering #approximations #python #odd #even #functions
In this video, we derive the trigonometric Fourier Series for the function f(x) = x on the interval (-π, π).
We calculate the coefficients step-by-step and use geometric intuition (Odd/Even symmetry) to simplify the integration. Finally, we visualize how the series converges to the original function as we add more terms.
Timeline:
0:52 - Finding coefficient a₀ (Odd function property)
2:00 - Finding coefficient aₙ (Symmetry check)
3:10 - Calculation of bₙ (Integration by Parts)
4:00 - The Final Fourier Series Formula
4:25 - Visualization of Convergence (N=1 to N=20)
Concepts covered:
Integration by parts
Odd and Even functions
Convergence of infinite series
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