 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ia/paper-2/7a/a/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

For a compactly supported test function

f

⟨ H^{'}, f ⟩ = - ⟨ H, f^{'} ⟩ = - \int_{0}^{\infty} f^{'} (t) d t = f (0) = ⟨ δ, f ⟩ .

Thus this is the distributional derivative of the Heaviside step function: $H^{'} = δ$ .

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