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MA 330 Vector Calculus |
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Have you ever watched and wondered about the weather patterns?
For instance, why there is stillness in the eye of a hurricane?
Have you ever watched and wondered at the swirl patterns in rivers
and other fluid flow? Have ever been intrigued by electricity
and magnets, and how they effect their surroundings? The
mathematics needed to answer such questions are contained in the
subjects of vector calculus and advanced calculus. In this
course, we develop and apply the calculus of vector fields to
answer such questions. Other questions that involve vector
fields involve geometry. For instance, "Can you comb the hair
on a billiard ball?" (see picture below). |
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Polar Orbiting Data on Wind Speed over the Oceans from National
Oceanographic and Atmospheric Administration SSM/I Microwave
Data
Image taken from
http://www.nhc.noaa.gov/graphics.html
The image to right is a representation of some information
about a vector field.
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"Can you comb the hair on a billiard ball?"
To answer this question involves an analysis of what kind
of vector fields can be on a sphere?
Image taken from
http://www.icase.edu/docs/hilites/viz.vector.html
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The course will begin with a review of selected topics from Calculus
III and then develop the calculus of vector fields, covering the
divergence and curl of vector field and their physical significance,
and the major mathematical theorems of vector calculus, the Divergence
theorem, Green's Theorem, and Stokes' Theorem. Applications
from geometry, mechanics, fluid mechanics, electricity and magnetism,
and astrophysics (gravity) will be given throughout the course.
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Questions, Comments, Queries? Send an email
david.finn@rose-hulman.edu
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