Assignment 1

To do this problem, you need to have access to a program that graphs 
direction fields for first order ODE's, and which also will graph the
plots of several solutions to an ode on a direction field.  You can
do this be getting a computer account on the 8th floor of RLM in the
computer lab.  After you get your account and log in, you access
matlab by typing matlab.  Type and you will see what is done in class.


The first assignment uses dfield.  Go into matlab and type dfield. A
window appears in which you can type the equation and the range of the
variables t and x (or y).

The discrete systems can be handles by writing a simple program. There
is information on how to do this under problem 3.  Also, typing logistics1(3.4)
computes the logistics equation with parameter 3.4.  Typing logistics brings
up the bifurcation diagram.

Assignment 5 asks for two types of computer graphics.  One is a phase plane
diagram for second order equations.  You will have to convert the second order
equation
            x" + 3x'  + sin(x) = 0


to a system:

            x' = y

            y' = -3y - sin(x).

Now go to matlab and type pplane.  A window will appear with a place to
type in the system.  The plot shows the curve in the plane, but not the
speed with which the curve is traversed.

The second type of computer graphics uses the ode solver ode45 in matlab.
There is a link to instructions on how to use this after problem set 5.