l_notes21 - 1 C 2 Lecture XXI Line Integrals Conservative...

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Unformatted text preview: 1 C 2 Lecture XXI Line Integrals; Conservative Fields Line integrals Let us recapitulate the basic notions reffering to line integrals. For both scalar and vector fields, we can define line integrals. For a scalar field f on a curve fds . C For a vector field F , it is denoted C , the line integral is denoted by d F R . We can evaluate line integrals either by their definition as limits of · Riemann sums, or by parameters. Let us consider a path R ( t ) for the curve C , t going from a to b . Then we can evaluate the line integral using parameter t : dR dt dt, b b dR d F R = F fds = f dt. · · dt C C a a For vector fields we can also define other line integrals as well. If F ( x, y ) = R F ds M ( x, y ) ˆ i + N ( x, y ) ˆ j , then ˆ i + ˆ j . Also, is C R F ds = Mds Nds C C C ds C the average value of F on C . We can also define the line integral R F × d = C R d dt. C F × dt Conservative fields F . We say that Let D be the domain of a vector field F has independence of F R = 0. If = 0....
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This note was uploaded on 09/24/2011 for the course MATH 1802 taught by Professor Duorg during the Two '04 term at Macquarie.

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l_notes21 - 1 C 2 Lecture XXI Line Integrals Conservative...

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