2011_Tutorial_11 - NATIONAL UNIVERSITY OF SINGAPORE...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
NATIONAL UNIVERSITY OF SINGAPORE Department of Mathematics MA 1505 Mathematics I Tutorial 11 1. Evaluate RR S f ( x,y,z ) dS and RR S F dS , where f ( x,y,z ) = x + y + z and F = x 2 i + y 2 j + z 2 k and S is the surface defined parametrically by r ( u,v ) = (2 u + v ) i + ( u - 2 v ) j + ( u + 3 v ) k , (0 u 1 , 0 v 2) . The orientation of S is given by the normal vector r u × r v . Ans : 40 3; - 430 3 2. Evaluate RR S z dS , where S is the portion of the paraboloid z = 4 - x 2 - y 2 lying on and above the xy plane. Ans : 289 60 π 17 - 41 60 π 3. Evaluate RR S F dS , where F = y i + x 2 j + z 2 k and S is the portion of the plane 3 x +2 y + z = 6 in the first octant. The orientation of S is given by the upward normal vector. Ans : 31 4. Use Stoke’s Theorem to evaluate
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/05/2012 for the course MATHEMATIC MA1505 taught by Professor Freudleong during the Spring '10 term at National University of Singapore.

Ask a homework question - tutors are online