The 2002 Winter Term home page for this course is located here.
The functions studied in Calculus I and II all reside on a flat sheet
of paper. But the universe of everyday experience is, at minimum,
three-dimensional. In this course we explore how Calculus can be
extended so as to apply to functions of more than one variable, and
thus apply to the three-dimensional world. We will begin by reviewing
vectors and functions of several variables. We will then discuss
partial derivatives and gradients, and apply these tools to
multivariable optimization. Turning our attention to integral
calculus, we will next cover double and triple integrals and their
applications. As time permits, we will discuss line integrals, flux
integrals, the divergence and curl of a vector field, and Green's,
and Stokes's theorems. Throughout the course, applications of
vector calculus to electromagnetic theory will be emphasized. We will
also discuss how Newton's invention of Calculus enabled him to explain
Kepler's laws of planetary motion in terms of a universal law of
gravitation.
Evaluation will be based on class participation and weekly problem sets. Some computer work will be required, but no computer experience is necessary.
Prerequisites: Calculus II or the equivalent or permission of instructor. Intermediate/Advanced. QR. ES. Lab fee $10.
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