vctut02s - The University of Sydney School of Mathematics...

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Unformatted text preview: The University of Sydney School of Mathematics and Statistics Solutions to Tutorial 2 MATH2061: Vector Calculus Summer School 2012 1. Find grad f if f ( x, y ) = x 2 cos xy . Solution: grad f = f = f x i + f y j = (2 x cos xy x 2 y sin xy ) i x 3 sin xy j . 2. Find grad if ( x, y, z ) = 3 x + 4 y 8 z . Solution: grad = = x i + y j + z k = 3 i + 4 j 8 k . 3. Find if ( x, y, z ) = e x y + 3 xyz . Solution: = grad = x i + y j + z k = ( e x y + 3 yz ) i + ( e x + 3 xz ) j + 3 xy k . 4. Calculate Curl F if F = (sinh x ) i + (cosh y ) j xyz k . Solution: F = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle i j k x y z sinh x cosh y xyz vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = xz i + yz j . 5. Let S be the surface defined by z = xy ....
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This note was uploaded on 02/06/2012 for the course MATH 2061 taught by Professor Notsure during the Three '09 term at University of Sydney.

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vctut02s - The University of Sydney School of Mathematics...

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