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Unformatted text preview: 18.02 Multivariable Calculus (Spring 2009): Lecture 21 Vector Fields and Line Integrals on the Plane March 31 Reading Material: From Simmons : 21.1. From Course Notes : V1 and V3. Last time: General Change of Variables. Today: Vector Fields and Line Integrals on the Plane. 2 Work of a force and line integrals on a plane Assume that ~ F is a constant vector field representing a force on a plane. Let A and B be two pints on the plane. Special Case: We want to compute the work W of ~ F done while moving an object from A to B on a straight line. We have that W = ~ F ·--→ AB = | ~ F ||--→ AB | cos θ where θ is the angle between ~ F and--→ AB . This makes sense since the work should only depend on the component of ~ F along the direction of the displacement and on the length of the displacement itself. We want to generalize this concept to the more physical situation in which the force ~ F is not a constant vector field and the displacement is not along a straight line....
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