010.102-2006-2-fin - 2 eK o > 2006 12 9{ 13r 15r 4 Z...

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

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

Unformatted text preview: 2 eK o > 2006 12 9{ 13r 15r 4 Z 9 < : s2: %V IU lǣ k k( 200). M K+ c a Z @\ \ 1. (20&) 6 &` r. h h r 1 -1 1 |y| sin(1 + x2 )dxdy. 2. (20&) F+d # / r = 1 - cos (0 2)_ ?\ D M, 6 &` r. h G Q B A G / + : h r xydA. D 3. (25&) {^ R : (x - y)2 + (4y - z)2 + (z - x)2 1 \ @ # 6 &` r. h 9 / h r |x - y|dV. R a f м t 4. \" x- s9s x = a(t - sin t), Q i %%` D . t h , (a) (15&) D_ Vs\ r. (b) (15&) ' F(x, y) = (6x + ey , 4y - ln(x + 1)) D_ > D\ : (flux)\ r. h 7 x H 1 5. (25&) / S _ {" x2 + y 2 + z 2 = 1 (z 2 ) &_. / S_ >d_ z- B a a G G h B 9Ҽf r r \ . y = a(1 - cos t) (0 t 2) 6. (25&) { {/ & / S & P \ @ # 6 7" r. L G h 2 9 B < h / ` x 1 4 X -P dS = |X - P |3 1 P S_ ?\ e, / 0 P S_ \ e. @ S 7. (25&) / S\ " z = 1 - x2 + y 2 z 0 s /_ n k 0 # G h B r B G r Q 7 . ' F(x, y, z) = (x + y 2 z, y + ex , x2 + y 2 + z) S\ 4 ` r. R H 8. # 7' Q F(x, y, z) = / 9 \ @ # 6 |\ r. , r = H (a) (15&) F_ curl F\ r. h r / h G / (b) (15&) B S : (x - 1)2 + (y - 2)2 + z 2 = 1 (z 0)\ @ # curl F dS S r(x2 yz -xz , ,0 2 ) r(x2 + y 2 ) +y x2 + y 2 + z 2 . \ r. , S_ n k 0 2 &. r & ...
View Full Document

This note was uploaded on 09/09/2009 for the course MATHMATICS 010-102 taught by Professor Cho during the Spring '09 term at Seoul National.

Ask a homework question - tutors are online