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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/ii/paper-3/30a/c/solution

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Past exam of the mathematics course of the University of Cambridge / 2008 / ii / Paper 3 / 30A / c / Solution by

Codex  0 Created 2026-09-24 Updated 2026-10-14

For a simple stationary point at the endpoint

b

, only one half of the local quadratic neighborhood lies in the integration interval. The even Gaussian integrand therefore gives half the interior stationary phase contribution:

I (λ) = f (b) \frac{π}{2 λ ∣ g ^{''} ( b ) ∣} e^{iλ g (b) + iπ sgn (g^{''} (b)) /4} + O (λ^{- 1}) .

(1)

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