Vector Fields and Line Integrals
Oliver Knill and Dale Winter, Harvard
University
with the assistance of David Smith,
Duke University
Purposes:
- To introduce the idea of a vector
field and illustrate some of the practical uses of vector fields
- To introduce the notion of ``work''
from physics and make a link between vector fields and the calculation of
physical work
- To develop a notion of the definite
integral of a vector field around a curve in the plane
- To examine some of the properties
of the line integral of a vector field
Prerequisites:
- Familiarity with the fundamental
concepts of Newtonian physics (distance, direction, force)
- The
Accumulation module (or an understanding of definite integrals and Riemann
sums)
- Familiarity with vectors in R2
and R3, including their symbolic, numerical, and graphical
representations
- Familiarity with geometric interpretation
dot products of vectors in R2 and the projection of one
vector onto another
- The Vectors
in Two and Three Dimensions module
