Guest lecture · UC Merced

Numerical Differentiation

PHYS 181/281 · September 18, 2024 · 75 minutes

An inquiry-based Jupyter lesson developing finite-difference methods through prediction, coding, error analysis, and pre/post assessment.

The central question

When a derivative cannot be taken symbolically, how can we approximate it—and know whether the answer is trustworthy?

Forward difference
Backward difference
Central difference
Truncation error
Roundoff error
Optimal step size

Lesson design

How the class unfolded

Engage

Students began with a pre-class concept check and predictions about slopes from discrete data.

Explore

The notebook let students implement and compare finite-difference formulas on smooth and perturbed datasets.

Explain & evaluate

Error curves exposed the tradeoff between truncation and roundoff before a post-class assessment closed the loop.

Assessment & evidence

How learning was made visible

Pre-class

15 responsesA ten-question baseline assessment.

Post-class

14 responsesThe same concepts were revisited after instruction.

Observation

COPUSThree observers documented engagement and instructional practice.

The classroom observation notes that the lesson implemented the 5E inquiry model and encouraged student interaction throughout the session. The observation record and paired assessments provide complementary evidence of classroom practice and student understanding.

Student-response files are summarized here but are not published as downloads, even when responses appear anonymous.

Class materials