5.1b Differentiation labs

Source: Lab ideas from Computational Physics (Landau, Páez, Bordeianu), §5.1. Rewritten as original drills. Continues 5.1 Differentiation algorithms.

Implement the two stencils, check the parabola identities, and compare absolute errors on $\sin t$. Stubs fail until filled in.

Formula refresh

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

Labs

Activity: Forward difference

Given $t$, $h$, and coefficients for $y(t)=a+b t^{2}$, print the forward-difference estimate of $y'(t)$ with 6 decimals.

Input: a b t h.

Write-ups

0/3 solved

5.1b.W1

Using “cancel”, “epsilon”, and “h”, explain:

Why can making $h$ extremely small make a numerical derivative worse?

Minimum 3 words. Your answer must include: “cancel”, “epsilon”, “h”.

0 words/ 3 min

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

Explorers

Next: 5.2 Extrapolated difference.