MAC 2313 - Section 04 - Spring 2008
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Remainder of Chapter 16 - Vector Calculus
Parameterization of Curves and Surfaces
parameterize lines, circles, curves in general, planes, surfaces
parameterizations using spherical and cylindrical coordinates
surface area of a parameterized surface
Vector Fields
compute gradient vector fields
find potential function of a gradient vector field
Line Integrals
interpretations: work, circulation
compute line intergral over a parameterized curve
determine whether a vector field is path-independent
path-independent fields: gradient fields are path-independent
path-independent fields: if a curve is closed and line integral is zero,
vector field is path-independent and so is a gradient field
path-independent fields: curl test - if curl = 0, field is path-independent
path-independent fields: use Fundamental Theorem of Calculus for Line
Integrals (ie. if curl = 0, find f & apply FTofLI)
Green's Theorem: use if curve closed
Surface/Flux Integrals
definition
interpretation (rate fluid flows through a surface)
calculate flux through a surface given by z=f(x,y), through a cylindrical
surface, through a spherical surface, through a parameterized surface
Curl
definition
interpretation (rotation)
Stokes' Theorem - be able to use this theorem to calculate a line; use if
curve is boundary of a surface
curl test
Divergence
definition
interpretation (net outflow)
the divergence theorem: be able to use this theorem to calculate flux
integral
Review Homework for Chapter 16, pg 1136: #1b, 11-17 odds, 25-35 odds
(previously assigned 1-9 odds)
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