MAC 2313 - Section 03 - Fall 2003
Related Pages: Course Home Page | Syllabus | Schedule and Homework
As stated in class, you are allowed to bring to the test one 8.5x11 inch
page, written on both sides. You can write whatever you want on this page:
eg. definitions, formulas, examples, etc. Calculators will be allowed for
the test.
Chapter 17 - Parameterization and Vector Fields
parameterize lines, circles, curves in general, planes, surfaces
motion, velocity and acceleration vectors
applications: intersection and collision of particles, length of a curve,
velocity, acceleration, uniform circular motion, parameterizations using
spherical and cylindrical coordinates, tangent lines
visualize/draw vector fields and flow fields
types of vector fields: velocity fields, force fields, gravitional fields,
gradient vector fields
applications: compute gradient vector fields, compute flow lines
See also Chapter 17 Summary on page 819
Review Homework for Chapter 17, pg 819: #1-21 all odds, 25
Chapter 18 - Line Integrals
definition
properties
interpretations: work, circulation
compute line intergral over a parameterized curve
path-independent fields: gradient fields are path-independent
path-independent fields: if a curve is closed and circulation is zero,
vector field is path-independent and so is a gradient field
determine whether a vector field is path-independent (i.e. same as
computing a potential function for a vector field)
compute a potential function for a vector field
Fundamental Theorem of Calculus for Line Integrals
Green's Theorem
curl test for path independence
See also Chapter 18 Summary on page 856
Review Homework for Chapter 18, pg 857: #1-23 all odds
Chapter 19 - 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
area of a parameterized surface
See also Chapter 19 Summary on page 882
Review Homework for Chapter 19, pg 882: #1-23 all odds
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