How to use Netmath to do your first computer assignment!


NOte that there is probably at least one mistake in these instructions.
Check the news and announcements on my web page to see the latest news.


The first part of the exercise is to use a symbolic manipulator.
(Essentially the answer to IC  is that the algebraic  answers aren't
too helpful, while IIC is easy, i.e. graphical descriptions help a lot!)

Hopefully you have tried netmath, but if not, let me remind you to log
in (and if it is your first time, take a knowledgeable friend or get the
attention of a friendly  lab proctor).

Type netmath. Hit return.

Click on the small window, and then the large window. Center the large
window by clicking in the upper corner, clicking the cursor on "move"
and adjusting the window until you can see both sides.

Click on course materials (for ordinary differential equations.)

Click on symbolically.  Read the entire page once.  

Go to any of  the first blue equations.  Change it to read:


   ode2('diff(y,x) + 3*y = sin(4*x), y,x)

The area below will turn pink while you do this. Hit return.  Either 
you will be told you made an error (forget a *, a comma, a ) and all is
lost) or the answer will be displayed.  It should not take you long to
do the five problems, but you might want to do the initial condition
bit at the same time.

To solve an initial condition problem, modify either the equation you are
looking, or the one lower down on the page which is an initial condition
problem for a second order equation.  Choose your favorate name 
(Professor Schelter uses soln, I'll use key). Type in red or blue

(key:ode2('diff(y,x)= -3*y + sin(4*x),y,x), tmp:IC1(key,x=0,y=1))

Check your parentheses, stars, commas, etc and press return!  Good luck!




To do part II, either start again, or go back to the previous page by
clicking on back  at the top.  Now click on one of the direction field
programs.  Probably the first is best.  Read the entire description
(although the end stuff won't make any sense).  Change one of the blue
equations to read

plotdf -ode  {d(y,x) =- 3*y+ sin(4*x)}

Double click and wait for the direction field to come up. Click on the
point x = 0, y = 1.  Pretty dull, and the green line doesn't even fill out
the plane because we didn't plot enough points.  Move your cursor over to
the right until a rectangle of boxes  appears out of the shadows. 
The top slot says "dismiss".  Click on this 
to get rid of your direction field and start again.  Move your cursor
down to "config" and click.  When the box comes up, you will want to
change some of the settings.  To get more of the solution curve, change the
default setting of 100 steps to 200, or, say, 300.  Click on OK, bring the
box up again and click on "replot."  The green curve should extend to both
sides of the page.  But it is a little small...clearly the interesting part
of the curve is between x = -1 and x = + 5 and of height about 1 in y.
Change the x radius to 3, the x center to 2   and the y radius to 2.
Click on"OK" and" replot".  Experiment to see if any of the other settings
help you. Try a different color (the printer prints black).

Notice you can plot the curve as a function of t.  The scale resets 
automatically   depending on how many t steps you gave the problem
...you can't reset the   parameters at the momment.  Also, when you are
 finished with this plot window, don't dismiss it!  You'll never see it
again.  Move to the upper left little box and close as you close any
file. (This took a lot of learning).  We will worry about the graphs
another day, and this is only a suggestion for those who try it.

To print, go to "config" again, and click on "print options".  Turn your 
printer button on and check that you are going to print in the right
place.  Click "OK" twice.  What used to be "save"  in the 
set of shadow boxes  is now "print".  Click ONLY ONCE on "print".
(You get a graph for every click).  Find the printer and look for your
printout.