Medical radionuclides, generators, and dose

Does eigendecomposition of the decay matrix agree with scipy.linalg.expm for a four-member branching chain, and what happens to each route as two decay constants are driven together? Useful evidence includes activities of every chain member over time from both routes, agreement to a stated tolerance, the eigendecomposition error growing without bound as two lambda values approach each other while expm stays stable, and the defective non-diagonalisable matrix and its t exp(−λ t) solution named as the cause.

This GioPhysics course map is an adaptable learning sequence, not academic credit, accreditation, or a universal university syllabus. It is written for a four-credit course of roughly three lecture hours plus two to three laboratory or computational hours a week across fifteen weeks, and it is deliberately more mathematical than University Physics I–IV: linear algebra and differential equations are working tools here, not background. Twenty units are mapped against a suggested fifteen-week delivery, so several units share a teaching week. Departments differ widely in how much formalism they expect at this stage; follow your institution's published scope, notation, laboratory programme, and assessment rules. A result should be checked against units, signs, limiting cases, and the conditions under which its model was derived.