Line integrals - University of Alberta
Line integrals - University of Alberta
Line integrals - University of Alberta
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MATH 209—<br />
Calculus,<br />
III<br />
Volker Runde<br />
<strong>Line</strong> <strong>integrals</strong><br />
in R 2<br />
Types <strong>of</strong> line<br />
<strong>integrals</strong><br />
<strong>Line</strong> <strong>integrals</strong><br />
in R 3<br />
<strong>Line</strong> <strong>integrals</strong><br />
<strong>of</strong> vector fields<br />
<strong>Line</strong> <strong>integrals</strong> <strong>of</strong> vector fields, II<br />
The general case<br />
Divide C into n subarcs Pj−1, Pj with lengths ∆sj by dividing<br />
the parameter interval [a, b] into n subintervals <strong>of</strong> equal length.<br />
, y ∗ ) on the j-th subarc, and let<br />
Choose a point P∗ j (x ∗ j j , z∗ j<br />
t∗ j ∈ [tj−1, tj] be the corresponding parameter.<br />
If ∆sj is small: as the particle moves from Pj−1 to Pj, it<br />
), the unit<br />
proceeds approximately in the direction <strong>of</strong> T(t∗ j<br />
tangent vector to C at P∗ j (x ∗ j , y ∗<br />
j , z∗ j ).
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