9.1b Fourier series labs

Source: Lab ideas from Computational Physics (Landau, Páez, Bordeianu), §9.1. Original drills. Continues 9.1.

Pure Python. No NumPy / VPython. Use math only.

Formula refresh

Warm up: pick the matching equation among lookalikes (same walk as the theory lesson).

Labs

Activity: First sine coefficient

For the odd sawtooth with $b_n=\dfrac{2}{n\pi}(-1)^{n+1}$, print $b_1$ with 10 decimals.

No input.

Write-ups

0/3 solved

9.1b.W1

Using “gibbs”, “overshoot”, and “jump”, explain:

What visual artifact do you expect near a jump when you truncate a Fourier series at finite N?

Minimum 3 words. Your answer must include: “gibbs”, “overshoot”, “jump”.

0 words/ 3 min

Meet the writing requirements, then you can open the model answer.

Explorers

Tune $N$ and watch the sawtooth partial sum vs the true ramp:

Next: 9.2 Fourier transforms.