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A Fourier series is a way to express a periodic function as a sum of simple sine and cosine waves. The core idea is that even complicated repeating patterns can be built from basic oscillations of different frequencies, amplitudes, and phases. In a typical Fourier series course, you compute coefficients by using orthogonality of sine and cosine on an interval like negative pi to pi. Each coefficient tells you how much of a particular frequency is present in the original function. Conceptually, i
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