lecture21

lecture21 - MATH 100 Class 21 Line Integral independent of...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
2006 Fall MATH 100 Lecture 14 1 MATH 100 Class 21 Line Integral independent of path (1,1) to (1,0) then (1,0), to (0,0) from (c) (1,1) to (0,0) from (b) (1,1) to (0,0) from (a) over evaluate , ) , ( : Ex path of t independen integral Line 21. Class 3 x y x y xdy ydx r d F j x i y y x F C C = = + = + = G G G G G
Background image of page 1

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

View Full DocumentRight Arrow Icon
2006 Fall MATH 100 Lecture 14 2 MATH 100 Class 21 Line Integral independent of path only. endpoints on depends integral the because same, the All 1 1 ) 1 ( ) 0 ( 0 1 0 , , 1 : 1 0 , 0 , : (c) 1 4 3 , (b) 1 2 , (a) 1 0 1 0 2 1 1 0 3 1 0 2 3 3 1 0 1 0 2 1 = + + + = + = = = = = = = + = + = = = = + = + = = ∫∫ dt d t td dt t t y x C t y t x C dt t dt t t dt t xdy ydx t y t x tdt tdt tdt xdy ydx t y t x CC C C C Sol:
Background image of page 2
2006 Fall MATH 100 Lecture 14 3 MATH 100 Class 21 Line Integral independent of path ) , ( ) , ( ) , ( region, in the entirely lies and ), , ( at and , ) , ( at starts that curve smooth piecewise any for then region, the of point each at ) , ( ) , ( If ). , ( & ) , ( points the continuing region open some in continuous are & where ) , ( that Suppose integral) line of Theorem l fundamenta (The 0 0 1 1 C 1 1 0 0 1 1 0 0 y x y x r d y x F y x y x C y x y x F y x y x g f j g i f y x F φφ φ = = + = G G G G G G Thm:
Background image of page 3

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

View Full DocumentRight Arrow Icon
2006 Fall MATH 100 Lecture 14 4 MATH 100 Class 21 Line Integral independent of path j y i x y x F b y b x y x a y a x y x b t a t y y t x x C G G G + = = = = = = φφ φ ) , ( Since )). ( ), ( ( ) , ( )), ( ), ( ( ) , ( s.t. ), ( ), ( by e Parmeteriz 1 1 0 0 Proof:
Background image of page 4
2006 Fall MATH 100 Lecture 14 5 MATH 100 Class 21 Line Integral independent of path [] for function potential : function ve conservati : case In this . if path of t independen -Integral - ) , ( ) , ( )) ( ), ( ( )) ( ), ( ( )) ( ), ( ( )) ( ), ( ( ) , ( So 0 0 1 1 0 C C C C F F F y x y x a y a x b y b x t y t x dt t y t x dt d dt dt dy y dt dx x dy y dx x r d y x F b t G G G G G φ φφ = = = = = + = + = =
Background image of page 5

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

View Full DocumentRight Arrow Icon
2006 Fall MATH 100 Lecture 14
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/17/2011 for the course MATH 100 taught by Professor Qt during the Fall '09 term at HKUST.

Page1 / 22

lecture21 - MATH 100 Class 21 Line Integral independent of...

This preview shows document pages 1 - 7. Sign up to view the full document.

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