 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/14/a/i/solution

To distinguish the old and new coordinate descriptions, write

u (x, y) = U (ξ (x, y), η (x, y))

. Since

ξ_{x} = η_{x} = 1

u_{x} = U_{ξ} + U_{η} .

Equivalently, the differential operator is

\partial_{x} = \partial_{ξ} + \partial_{η}

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