Curl of a gradient is 8711 x y z 8706x 8706y 8706z 8706t 8706x 8706t 8706y 8706t 8706z x 8706y8706z 8706z8706y y 8706z8706x 8706x8706z z 87 ID: 9251 Download Pdf

By the way the gradient of isnt always denoted sometimes its denoted grad As you know the gradient of a scalar eld is f x f x f x We can abstract this by leaving out the to get an operator x x x which when applied to yields This is called t

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So if PQR then div 8711 8706x 8706y 8706z PQR 8706P 8706x 8706Q 8706y 8706R 8706z Notice that div is a scalar Find div for each of the following vector 64257elds i xyyzxz ii yzxzxy iii where iv grad where is a function with continuous second der

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CURL(3D).Thecurlofa3DvectoreldF=(P;Q;R)isdenedasthe3Dvectoreldcurl(P;Q;R)=(RyQz;PzRx;QxPy):CURL(2D).Recall,thecurlofa2DvectoreldF=(P;Q)isQxPy,ascalareld. WANTED!Isthereamultivariablecalculusb

By de64257nition if M then the two dimensional curl of is curl Example If x y then x y and so curl 1 x y Notice that x is vector valued function and its curl is scalar valued function It is important that we label this as the two dimensional curl

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Curl of a gradient is 8711 x y z 8706x 8706y 8706z 8706t 8706x 8706t 8706y 8706t 8706z x 8706y8706z 8706z8706y y 8706z8706x 8706x8706z z 87

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