2. (10 分) Let C be a positively oriented, piecewise-smooth, simple closed curve in the plane and let D be the region bounded by C. If f(x, y) is a scalar function with continuous first and second partial derivatives in D, derive the following formula:
∬
D ( f
xx + f
yy )dxdy =
where
= ∇f⋅N is the normal derivative, N is an outer unit normal, s is the arc-length.
阿摩線上測驗
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