Associate Professor of Mathematics
Rose-Hulman Institute of Technology

MA 330 Vector Calculus
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).

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.

"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
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.
Questions, Comments, Queries? Send an email david.finn@rose-hulman.edu