 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ia/paper-3/11b/b/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Fix the first index

i

and form the vector field with components

F_{j} = T_{ij}

\int_{S} F_{j} n_{j} d S = \int_{V} \partial_{j} F_{j} d V .

\int_{S} T_{ij} n_{j} d S = \int_{V} \frac{\partial T _{ij}}{\partial x _{j}} d V .

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