solve a square wave using equivalent trigonometric fourier series (limit is from 0 to 2, and alternate at 1 and -1) provide graph

The plot above shows the Fourier series approximation of a square wave with a period of 2, using different numbers of terms in the series:

- **1 term:** The approximation starts with the fundamental frequency.
- **3 terms:** The addition of higher odd harmonics improves the approximation.
- **5 terms:** Further addition of harmonics gives a closer match to the square wave shape.
- **10 terms:** The approximation closely resembles the square wave, showing more accuracy with more terms.

As more terms are included, the approximation gets closer to the ideal square wave, demonstrating the power of Fourier series in representing periodic functions.

### Do you have any questions or need further details?

### Here are 5 related questions to expand your understanding:

1. How does increasing the number of terms in the Fourier series affect the accuracy of the square wave approximation?
2. What role do odd harmonics play in shaping the square wave in the Fourier series?
3. Can you explain the phenomenon of Gibbs overshoot in the context of Fourier series?
4. How would the Fourier series change if the square wave had a different period?
5. What would be the effect of including even harmonics in the Fourier series?

### Tip:

When approximating a function using Fourier series, the number of terms used will impact the accuracy of the approximation. The more terms you use, the closer the Fourier series will represent the original function, especially near points of discontinuity.

Explore how Fourier series approximates a square wave with a period of 2. Learn about the accuracy of the approximation using different numbers of terms in the series. This analysis covers the role of odd harmonics, Gibbs overshoot, and the impact of including more terms in the Fourier series.

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