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Chapter 14: Q. 18 (page 1132)

ComputethedivergenceofthevectorfieldsinExercises17鈥�22.G(x,y)=xcos(xy),ycos(xy)

Short Answer

Expert verified

divG=2cos(xy)-2xysin(xy)

Step by step solution

01

Step 1. Given information is: 

G(x,y)=xcos(xy),ycos(xy)

02

Step 2. Divergence of vector field

IfG(x,y)=g1(x,y)i+g2(x,y)j,thendivG=鈭�g1鈭�x+鈭�g2鈭�yHere,G(x,y)=xcos(xy),ycos(xy)Comparethiswith,G(x,y)=g1(x,y)i+g2(x,y)jThen,g1(x,y)=xcos(xy),g2(x,y)=ycos(xy)divG=鈭�g1鈭�x+鈭�g2鈭�y=鈭�(xcos(xy))鈭�x+鈭�(ycos(xy))鈭�y=2cos(xy)-2xysin(xy)

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