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plugin-Chapter17Overview

# plugin-Chapter17Overview - Math 255 Winter 2010 Fernando...

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Math 255 Winter 2010 Fernando Carreon Chapter 17 overview 1. Line integrals: (a) In the x - y plane i. Of a scalar function f ( x, y ): Z C f ( x, y ) ds, Z C f ( x, y ) dx, Z C f ( x, y ) dy. ii. Of a vector field F ( x, y ) = < P ( x, y ) , Q ( x, y ) > Z C F ( x, y ) · dr Used to compute the work done by a force field F ( x, y ) along a curve C . (b) In 3 D i. Of a scalar function f ( x, y, z ): Z C f ( x, y, z ) ds, Z C f ( x, y, z ) dx, Z C f ( x, y, z ) dy, , Z C f ( x, y, z ) dz. ii. Of a vector field F ( x, y, z ) = < P ( x, y, z ) , Q ( x, y, z ) , R ( x, y, z ) > : Z C F ( x, y, z ) · dr Used to compute the work done by a force field F ( x, y, z ) along a curve C . Methods that can be used to compute them: By direct computation (with a parametrization of C). If F is conservative then use Fundamental Theorem of Line integrals (without a parametrization for C). For closed curves C: Green’s Theorem in two variables and Stokes Theorem in 3D. 1

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2. Double integrals: Z D Z f ( x, y ) dA Applications: mass, center of mass, moment of inertia, probability, areas.
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