FM5002-HW5-2.22.12

If z x sin z 2 y then f z x2 y2 x2 y2 2 xy 2 xy 2 u 1

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Unformatted text preview: y2 2 xy sin y2 x2 2 xy x2 . Therefore, x2 . y Sin x2 y2 a nd x V 0. FM5002−HW5−2.22.12.nb y 1 U 2 2 xy 2 y Cos x2 0042 14. Defin e f : 2 Define u, v : y2 by f z by f x y 2 xy 2 2 z y Cos x2 y2 2 xy 2 x Sin x2 y2 2 2 xy y x Sin x2 y2 . U hold. cos z . u x, y v x, y . Let U = u (x, y) an d V = v (x, y). a. Fin d U and V. b. Determin e whether the Cauchy Riemann equations x a. If z x x4 2 x2 y2 y4 y y x y2 2 x2 y, then f z x y x 2 x4 1 V 2 2 x2 y2 y4 y 2 b. They do n ot : y y4 y 2 Therefore, U but U 1 U x 4 x2 y 4 x3 2 4 y3 y 0042 15. Defin e f : 2 Define u, v : 4 x y2 by f x y y Sin x by f z y y cos x Van d y x V y 2 2 x2 y2 x4 x cos x x4 cos x a nd V y Cos x 1 Sin x 2 2 x2 y2 y4 1 x4 2 2 x2 y2 2 x2 y2 y4 cos x y 2 Cos x x4 y sin x sin x y4 y Sin x V y sin x y y y sin x . Sin x y Sin x , Sin x . cos z . u x, y v x, y . Let U = u (x, y) an d V = v (x, y). a. Fin d U and V. b. Determin e whether the Cauchy Riemann equations z a. If z x y, then f z xy cos z xy xy 2 y U cos x xy y U 1 2 y Van d x x y cos x sin x 2 and V sin x x y U hold. 2 xy y b. They do not : U z 2 2 x y . Sin x , but cos x 2 y 2 y y V 1 2 y y Sin x . sin x y . Therefore, 7 8 FM5002−HW5−2.22.12.nb 0042 16. Write x z y3 dx 3 y z dy z 4 x y z dz 8 2 x y z 3 dx in the form f x, y, z dx dy g x, y, z dx dz h x, y, z dy dz. xz 4y 3 dy y7 x d...
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This note was uploaded on 01/19/2014 for the course MATH 5002 taught by Professor Adams during the Spring '08 term at Minnesota.

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