FM5002-HW5-2.22.12

11 let a dx dy b dx dz c dy dz p dx dt q dy dt

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Unformatted text preview: y d z Adz dx dy t Adt dx dy u Adu dx dy t z Adt dz dx dy u z Adu dz dx dy z t Adz dt dx dy u t Adu dt dx dy Adz du dx dy Adt du dx dy Adt dz dx dy zu tu tz z t Adt dz dx dy Adu dz dx dy Adu dz dx dy Adu dt dx dy uz zu ut t u Adu dt dx dy 0042 12. Defin e f : 2 Define u, v : z by f z by f x y sin u x, y 2 z . 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 xy a. If z x y, then f z sin x2 y2 U x cos y sin x2 y2 a n d V x sin y . b. They do n ot : x x U 0042 13. Defin e f : 2 Define u, v : 2 xcos x2 cos y y U y cos y y2 , while Van d x V V y sin x2 sin y y x U hold. y2 . Therefore, cos y . sin z 2 . by f z by f x x x 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 z2 z2 a. If z x sin z 2 y, then f z x2 y2 x2 y2 2 xy 2 xy 2 U 1 2 2 xy sin x2 sin x2 1 2 y2 b. They do : x U 1 2 2 xy x Cos x2 yV 2 y2 2 xy y2 U y x2 y2 2 x y 2 2 xy 2 1 x 2 xy sin y2 2 x V y U hold. x2 y2 2 x y 2 cos x2 sin y2 y2 x2 x Cos x2 sin x2 2 xy 2 1 x2 a nd V 2 xy Van d 2 xy 2 y2 2 y2 cos x2 cos x2 2 xy 2 xy y2 y2 y Sin x2 cos y2 2 xy 2 xy y2 2 x2 cos y2 cos...
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