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
R
2
and
R
3
, including their symbolic, numerical, and graphical representations
Familiarity with geometric interpretation dot products of vectors in
R
2
and the projection of one vector onto another
The
Vectors in Two and Three Dimensions
module
modules at math.duke.edu
Copyright CCP and the author(s), 2001
Last Modified: Nov. 8, 2002
