1. In the plane, let D be a simply-connected region whose boundary OD is a piecewise C1, simple, closed curve, oriented counterclockwise. Let în be the outward unit normal vector to D. Given two functions, f(x,y) and g(x, y), both C² on an open set containing the domain D, show that: (a) · ds = - · ds, C

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Chapter2: Second-order Linear Odes
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Please don’t use stoke’s theorem to solve this
1. In the plane, let D be a simply-connected region whose boundary ðD is a piecewise C1, simple, closed curve,
oriented counterclockwise. Let în be the outward unit normal vector to D. Given two functions, f(x,y) and
g(x, y), both C² on an open set containing the domain D, show that:
(a)
· ds = -
· dš,
C
Transcribed Image Text:1. In the plane, let D be a simply-connected region whose boundary ðD is a piecewise C1, simple, closed curve, oriented counterclockwise. Let în be the outward unit normal vector to D. Given two functions, f(x,y) and g(x, y), both C² on an open set containing the domain D, show that: (a) · ds = - · dš, C
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