2008级(下)第17次è¯&frac34

2008级(下)第17次课

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Unformatted text preview: * * * * (F : y B L M i -1xi yi M i M n -1 L : A B, A F ( x , y ) = P ( x , y )i + Q ( x , y ) j o ( W = F AB M2 M1 x A = M 0 , M 1 ( x1 , y1 ), , M n-1 ( x n-1 , y n-1 ), M n = B . M i - 1 M i = ( x i )i + ( y i ) j . F ( i , i ) = P ( i , i )i + Q( i , i ) j , Wi F ( i , i ) M i -1 M i , y F (i ,i ) B L A M2 M1 M i -1 xi yi M i M n-1 Wi P ( i , i )xi + Q ( i , i )yi . o x W = Wi i =1 n n [ P ( i , i ) x i + Q ( i , i ) y i ]. i =1 W = lim [ P ( i , i ) x i + Q ( i , i ) y i ]. 0 i =1 n 1. 2 ('* 2 2 L2 xoy2 , 2 . 2 L2 A2 B2 P ( x , y ), Q( x , y )2 L M 1 ( x1 , y1 ), M 2 ( x2 , y2 ), n('* , M n-1 ( xn-1 , yn-1 )2 L2 M i -1 M i ( i = 1,2,, n; M 0 = A, M n = B ). 2 xi = xi - xi -1 , yi = yi - yi -1 , 2 ( i , i )2 M i -1 M i ('* ('* 02 , . ('* w P ( i , i )xi i =1 n , ]w* L , n P ( x , y ) ]w* (h x L P ( x, y)dx = lim P ( i , i )xi . 0 i =1w 2 Q( x , y )dy = lim Q( , )y . L 0 i =1 i i i n P ( x , y ), Q ( x , y] )* w w] , L . 2. (ſ A 2 3. 2 , 2 P ( x , y ), Q( x , y A)(ſ* . L L P ( x , y )dx + L Q( x , y )dy = P ( x , y )dx + Q( x , y )dy = F ds . L L F = Pi + Qj , ds = dxi + dyj . 4. * w ^ n Pdx + Qdy + Rdz . P ( x , y , z )dx = lim P ( i , i , i )xi . 0 i =1 Q( x , y, z )dy = lim Q( i , i , i )yi . 0 i =1 R( x , y, z )dz = lim R( i , i , i )zi . 0 i =1 n n 5. (1) x Lx 1 L1x L2 , x 2 B h L Pdx + Qdy = L Pdx + Qdy + L Pdx + Qdy . ,- Lx , x BLh ( 2) x BLh* -L P ( x , y )dx + Q( x , y )dy = - L P ( x , y )dx + Q( x , y )dy . I !*PBſ 2 P ( x , y ), Q ( x , y )2 x = ( t ), 2 , Lȫ* , 2 y = ( t ), 2 2 , 2 M ( x , y ) 2 L2 A2 Lȫ , Lȫ* , t2 2 B, 2 ( t ), ( t )2 2 2 P , 2 ( t ) + 2 ( t ) 0,, ȫ ,2 L P ( x, y)dx + Q ( x, y)dy2 L P ( x , y )dx + Q ( x , y )dy = { P[ ( t ), ( t )] ( t ) + Q[ ( t ), ( t )] ( t )}dt (1) L : y = y( x ) xx b a ax b. L Pdx + Qdy = { P[ x , y( x )] + Q[ x , y( x )] y( x )}dx . yx d ( 2) L : x = x ( y ) cx d. L Pdx + Qdy = c { P[ x( y), y]x( y) + Q[ x( y), y]}dy. ( 3) x = (t ) : y = ( t ), t z = (t ) , . Pdx + Qdy + Rdz = { P[ ( t ), ( t ), ( t )] ( t ) + Q[ ( t ), ( t ), ( t )] ( t ) + R[ ( t ), ( t ), ( t )] ( t )}dt (4) 뵿 P L 2 ( x , y )P L x = (t ) , y = (t ) , , L Pdx + Qdy = L ( P cos + Q cos )ds ( t ) ( t ) cos = ,cos = , 2 2 2 2 ( t ) + ( t ) ( t ) + ( t ) 2 I * 2 ( x , y , z ) , , , Pdx + Qdy + Rdz = ( P cos + Q cos + R cos )ds = A t ds = A dr = At ds , A = { P , Q , R} t = {cos , cos , cos }, ( x , y , z )^n * * ^n * dr = t ds = {dx , dy , dz } ^n At2 A2 t2 . 1 2 L xydx , 2 L2 . y 2 = x2 B(1,1) A(1,-1)2 B(1,1)2 (1) x y AO 0 OB y = x. y2 = x L xydx = xydx + xydx 1 A(1,-1) = x ( - x )dx + x xdx 1 0 4 = 2 x dx = . 0 5 1 3 2 ( 2) y x= y , 2 y2 - 12 1. B(1,1) L xydx = AB xydx = y 2 y( y 2 )dy -1 1 y2 = x A(1,-1) 4 = 2 y dy = . -1 5 1 4 22 L y 2 dx , 2 L2 ~) B ( - a ,0 ) 2 . (1) 2 ~) ( 2) 2 2 axK ; A(a ,0) 2 x 2 (1) x x = a cos L: , y = a sin x 0x 2 0 x B( - a, 0 ) = a 2 sin 2 ( - a sin )d A(a,0) =a 3 0 4 3 (1 - cos )d (cos ) = - a . 3 2 ( 2) x L : y = 0, xx ax 2 = 0dx = 0. a -a - ax B( - a, 0 ) A(a,0) b*v . 32 (1) 2 ( 2) 2 L 2 xydx + x 2dy , 2 L2 ; ; (0,0) y = x 22 x = y 22 OAB2 x2 2 O(0,0)2 B(1,1)2 O(0,0)2 B(1,1)2 O , A, B2 . ( 3) 2 (1,0), (1,1). x (1) 2 1 B(1,1) L : y = x , x2 02 x = 1, y = x2 0 ( 2 x x 2 + x 2 2 x )dx 1 = 4 x 3 dx = 1. 0 A(1,0) ( 2) 2 y2 . x = y2 B(1,1) L : x = y 2 , y2 0 2 x = 1, A(1,0) 1 0 ( 2 y 2 y 2 y + y 4 )dy 1 = 5 y 4 dx = 1. 0 ( 3) 2 = OA 2 xydx + x dy 2 B(1,1) + AB 2 xydx + x 2 dy A(1,0) 2 OA 2 , y = 0, x2 0 2 1, B(1,1) OA 2 xydx + x dy = 2 1 0 ( 2 x 0 + x 2 0)dx = 0. 2 AB 2 , x = 1, y 2 0 2 2 1 1, A(1,0) AB 2 xydx + x dy = 0 ( 2 y 0 + 1)dy = 1. = 0 + 1 = 1. x 諿o Pb*v . 1 2 3 P158 2 9-2 1 2 2 2 3 2 4 2 5. 2 14* n [ [end] ...
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