010-102-en-2003-2-fin - > o 2 (009-030) K e 2003 12 13{...

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Unformatted text preview: > o 2 (009-030) K e 2003 12 13{ 1r 3r 4 Z 9 < : s2: M K+ c a Z @\ %V IU lǣ k k( 200). \ 1. (30&) 6 4&_ ` #. h h ͤr 1 1+ 1-y 2 1 dxdy (a) 2 + y2 x 0 1 1 1 y (b) 0 sin x dxdy x 2. (30&) h (a) 7' F(x, y) = (cos y+y cos x, -x sin y+sin x)_ F (x, y)\ < #. (b) X (cos y + y cos x)dx + (-x sin y + sin x)dy\ #. #l" X f H xy-_ " x2 + y 2 = 1, y 0` r>@~ / Ͷ /Ӽ B HG s. 3. (20&) C =t&s (0, 0), (1, 1), (0, 1) y+_ Y\ r>@~ h G h A t U / ' B9: h 3 /{M, 6 &` #. H G r xdx - x2 y 2 dy. C 4. (20&) "& O = (0, 0, 0)\" 6 %%_ {^y` #. h h f i 9 R := {(x, y, z) : x2 + y 2 z 2 , 3x2 + 3y 2 z 2 }. 5. 6. (20&) X z = 1 z = 2s\ e " z = h H r 9: h {M & X x2 + y 2 _ r y 2 z 2 dS_ ` #. (20&) &o\ s6 # 6 &` #. x h 1 h r (x2 + y + z)dS. R f A #l" R 0 x2 + y 2 + z 2 1s. r 7. (30&) 7'\ F(x, y, z) = (x2 + y - 4, 3xy, 2xz + z 2 )\ @ # 6 h / t 6\ #. (a) curl F\ #. (b) / S = {(x, y, z) : x2 +y 2 +z 2 = 16, z 0}\ @ # G B / #. , S_ n k > 0 s2 &. r S curl FdS\ 8. (30&) 6` 7" #. h x f h "o_ Us 1s ds "& ^ R_ > R\ @ & / 1 1 7' E(X) := A(0,0, 10 ) (X) + A(- 10 ,0,0) (X)_ e! 8s. # 3 H X -P f l" AP (X) = s. |X - P |3 ...
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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.

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