Suppose F = (P(x, y, z), Q(x, y, z,), R(x, y, z)), is conservative vector field. Here P, Q, R are such that their second derivatives are continuous. Prove that ƏQ - Əx ӘР ду = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Suppose \(\vec{F} = (P(x, y, z), Q(x, y, z), R(x, y, z))\) is a conservative vector field. Here \(P, Q, R\) are such that their second derivatives are continuous. Prove that

\[
\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} = 0
\]
Transcribed Image Text:Suppose \(\vec{F} = (P(x, y, z), Q(x, y, z), R(x, y, z))\) is a conservative vector field. Here \(P, Q, R\) are such that their second derivatives are continuous. Prove that \[ \frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} = 0 \]
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