Project Page
This semester's project is on separation of variables, details and
due date will be announced later. Tentatively the project will be
assigned on 17 Mar, an outline will be due on Friday 25 Mar and the
project on Friday 8 Apr.
Here is the old why group assignments handout
from back when all homework was group homework.
There are two ways to view separation of variables. Those of you who
are going to take Paritial Differential Equations will see the technique
used many times to solve many PDEs. (You may have already seen it used
in ordinary differential equations.) For us, separation of variables
will be a way of looking at special cases of general multivariable functions,
and not a way of solving differential equations of any kind. These
are functions F(x, y) which can be written f(x)g(y) where f(x) and g(y)
are functions of a single variable.
The Maple file here shows some functions of
two variables that are really functions of one variable. The one variable
could be theta or r from polar coordinates. Also we see a couple of
separated examples of the form f(x)g(y) or f(r)g(theta). These are
special kinds of functions, not every function of two variables can
be written this way.
Some links: