vcprac05s - The University of Sydney School of Mathematics...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The University of Sydney School of Mathematics and Statistics Solutions to Practice Session 5 MATH2061: Vector Calculus Summer School 2012 1. Evaluate the following surface integral: integraldisplayintegraldisplay S ( z + 2) dS, S : x 2 + y 2 + z 2 = a 2 . Solution: In spherical co-ordinates, the surface S is represented by x = a cos sin , y = a sin sin , z = a cos , (0 , 2 ) , and dS = a 2 sin d d. So we have integraldisplayintegraldisplay S ( z + 2) dS = integraldisplay 2 integraldisplay ( a cos + 2)( a 2 sin ) d d = integraldisplay 2 integraldisplay ( a 3 sin cos + 2 a 2 sin ) d d = integraldisplay 2 bracketleftbigg a 3 sin 2 2 2 a 2 cos bracketrightbigg =0 d = 4 a 2 integraldisplay 2 d = 8 a 2 . 2. Find the flux of F = x i + y j + z k across the surface S , where S is the triangular region with vertices (1 , , 0) , (0 , 1 , 0) , (0 , , 1) . Solution: The surface S is the plane given by x + y + z = 1 ....
View Full Document

Page1 / 3

vcprac05s - The University of Sydney School of Mathematics...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online