This page contains some links to pages with material relevant to the
multivariable and vector calculus course.
You will also find links to Mathematica notebooks which you
can download and modify for further exploration.
Functions
of two and three variables.
Examples of
surface,
contour,
and density
plots of multi-variable functions are available.
Limits and
continuity of functions
of two and three variables.
Some surfaces plotted in three dimensions for which the
limits
as (x, y) approach (0,0) do not exist.
Notebook:
LimitsContinuity.nb.
The directional derivative
and the
gradient.
This material includes an alternative means to find the tangent plane
and normal line to a surface in three-dimensional space.
Finding the extrema of functions of two
variables (equally instructive may be a brief exploration of a
wrong way to locate
extrema of functions of two variables).
An outline of the method of least
squares for fitting a line to a collection of ordered pairs is
also presented.
Finally the steepest ascent
algorithm for locating maxima is described.
Some examples of the method of
Lagrange multipliers applied to
constrained optimization problems.