# Maple - Direction Fields

Maple makes it relatively easy to create direction field plots for
differential equations. One simply loads the `DEtools` package,
and then uses the `dfieldplot` command.

First, we define a differential equation, and assign it to a Maple
variable. We could just do all this in the `dfieldplot` command,
but this gives us a chance to talk about it.

de1 := diff(y(t),t)=r*y(t)-h;Note that

`de1`is an expression encompassing the entire differential equation. Observe too that the definition of the DE requires us to note explicitly the independent variable. Finally, pay attention to the difference between the assignment operator := and the plain equation operator =. The := means "Evaluate the right hand side and put it into the variable on the left hand side" while the second means that "symbolically, the expressions on the left and right of this are equal".

If we tried to use the `dfieldplot` command right now, we would
have two problems. First, we have not loaded the `DEtools`
package yet.

with(DEtools):The colon at the end of the line causes the output to be suppressed - saves space on our output. The second problem is that

`r`and

`h`are still symbolic variables, which Maple cannot plot. We need to nail them down.

r := 0.5; h := 15

We can now plot the direction field.

dfieldplot(de1,y,t=0..3,y=0..50);This gives the result

It is possible to do direction fields for 2-D autonomous
equations as well. Consider the system

*x' = y
y' = -x*
We can do the direction field for this using the following command.

dfieldplot([diff(x(t),t)=y(t),diff(y(t),t)=-x(t)],[x,y],t=0..3,x=-3..3,y=-3..3);Note the use of brackets to group the system, and to show that there are two dependent variables. The result is below.

This class will run from Monday, 7 June, until Friday, 30 July.

I have started posting homework. It will be due each week on
Wednesday, during class. I will usually not post the entire week's
homework at once. Check this every day to see what is up. Homework
assigned on Tuesdays will not be due until the following week.

The TA for this class is Giang Trinh. He holds office hours
from 3:00 to 4:20 every Monday and Friday. Go see him if you
have questions about homework grading, or if you cannot make the
instructor's hours, or if you just prefer his explanations.

The final exam will take place on Thursday, 29 July, from
6-9 PM in our usual classroom, Wegner G1. Class will be cancelled
on Thursday and Friday, 29 and 30 July, to compensate for this
special lengthened exam time. The instructor will be present
in the classroom at the normal class time on Thursday for an
optional help session.

There is a
sample final exam posted. The tables
you will have available are
also posted.