plugin-Chapter17Overview

Plugin-Chapter17Over - 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

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Unformatted text preview: 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. 2. Double integrals: Z D Z f ( x,y ) dA Applications: mass, center of mass, moment of inertia, probability, areas.Applications: mass, center of mass, moment of inertia, probability, areas....
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This note was uploaded on 12/31/2011 for the course MATH 255 taught by Professor Jackwaddell during the Fall '08 term at University of Michigan.

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Plugin-Chapter17Over - 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

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