Tool Python Beginner 40 min

Eigenvalues with numpy.linalg: normal modes of coupled oscillators

Afterwards you can turn a physical system into a matrix, solve it with numpy.linalg.solve, pick eigh or eig, and check eigenvectors by what they must satisfy.

Linear algebra Chemistry, Engineering, Physics

Tool Python Beginner 35 min

Numerical integration with scipy.integrate: the area under a measured peak

Afterwards you can integrate data and formulas with scipy.integrate, report a peak area with its uncertainty, and handle singular points and infinite limits.

Numerical calculus Cross-disciplinary

Tool Python Beginner 50 min

scipy.stats from the ground up: is the difference between two samples real?

Afterwards you can describe two samples with scipy.stats, test whether they differ, and report the effect size with a confidence interval, not a bare p-value.

Statistics Cross-disciplinary