261-F11-sg3

261-F11-sg3 - MA 261 - Spring 2011 Study Guide # 3 You also...

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Unformatted text preview: MA 261 - Spring 2011 Study Guide # 3 You also need Study Guides # 1 and # 2 for the Final Exam 1. Line integral of a function f ( x, y ) along C , parameterized by x = x ( t ) , y = y ( t ) and a t b , is C f ( x, y ) ds = b a f ( x ( t ) , y ( t )) ( dx dt ) 2 + ( dy dt ) 2 dt . (independent of orientation of C , other properties and applications of line integrals of f ) Remarks : (a) C f ( x, y ) ds is sometimes called the line integral of f with respect to arc length (b) C f ( x, y ) dx = b a f ( x ( t ) , y ( t )) x ( t ) dt (c) C f ( x, y ) dy = b a f ( x ( t ) , y ( t )) y ( t ) dt 2. Line integral of vector field F ( x, y ) along C , parameterized by r ( t ) and a t b , is given by C F d r = b a F ( r ( t )) r ( t ) dt . (depends on orientation of C , other properties and applications of line integrals of f ) 3. Connection between line integral of vector fields and line integral of functions: C F d r = C ( F T ) ds where T is the unit tangent vector to the curve C . 4. If F ( x, y ) = P ( x, y ) i + Q ( x, y ) j , then C F d r = C P ( x, y ) dx + Q ( x, y ) dy ; Work = C F d r ....
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261-F11-sg3 - MA 261 - Spring 2011 Study Guide # 3 You also...

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