Since I don't expect you want to learn UNIX and all the stuff that goes along with it, all the information that I will give you here is related to WINPP which you can download by clicking the above link.

- If you don't have access to the internet, you can borrow a CD with it in the library (4th floor). Copy the file: windows/winpp/winpp.zip and uncompress it. I think Windows XP has winzip compatibility built in. If you can't unzip it and you can't download winpp.exe from the internet, please see me and I will put it on a floppy.
- If you have the ZIP file, uncompress it and make a shortcut to winpp.exe on your desktop.
- If you just downloaded the executable above, just leave it on the Desktop.

- First create an ODE file
- Open a text editor, like Notepad (it is under Applications in the Start Menu) or if you are really a masochist, Word.
- Type the following lines into it
# a generic first order equation with parameters param a,b,c,d ds/dt=1 dy/dt=y*(1-y) @ xp=s,yp=y,xlo=-5,xhi=20,ylo=-2,yhi=2,total=25 done

- Save the file as example1 in plain text (
**DO NOT SAVE AS RTF or DOC - It wont work**)

- Now run and play with it
- Double click on winpp.exe and open your example1 file. If this doesn't work, make a folder in My Computer C: and call it myodes. Copy your example into this folder. Drag and drop it into winpp.exe
- You should see:
**s**along the bottom and the variable**y**along the side. (You may ask, why not put time itself along the bottom; this is because winpp only does direction fields for 2-dimensional systems so we have to fake it out.)This file solves equations of the form

s'=1, y'=f(y,s) and you can change the f(y,s). The default is f(y,s)=y(1-y)

- Click on Phaseplane Grid parameters and change Dir. Fld.Grd to 20
- Click on Phasplane DirFld and direction fields will show up
- Click on Run Mouse and click somewhere in the plane. It will draw a solution. Click on Run Mice and click al over the place. Click on STOP to quit.
- Click on Edit Copy. Now it is saved to the clipboard and you can paste it into a Paint or Word file to print out.
- Try plotting the directions fields for the more interesting model
f(y,s)=y*(1-sin(s)-y).
- Click on Edit Edit RHS and click on the dY/dt box. Type in y*(1-sin(t)-y) and then OK.
- Click on Ctrl E (Graphics Erase) and the on Phaseplane Dir Fld.
- Plot several trajectories using the Run Mice option

- Quit: Ctrl Q (File Exit)
- Put initial conditions in: Find the little window that says Initial Data, type in the values, and Click Go.
- Change parameters: Find the little window that says Parameters, type them in and press Go.
- Change the view and window: Click on Graphics View and edit the parameters: mainly you waill change what is on the axes and the values Xlo,XHi, YLo,YHi
- Change the numerical parameters: Click on Numerics Int Par to change the total time to integrate, etc.
- Do the &$#%!! home work: I will ask you to draw direction fields
for equations of the form: dy/dt = f(y,t). You rewrite them as:
s'=1, y'=f(y,s) and plug them into the Winpp.

- Draw direction fields for
- dy/dt = -y + .5*sin(y)
- dy/dt = -y + sin(y)
- dy/dt = -y + 2*sin(y)

- Try the following as well with a window |s|<2 and |y|<3; use
initial conditions y(0)=0, 2, -2. Do these seem to exist for all
values in the window?
- y'=-y+3*t
- y'=y+cos(t)
- y'=sin(t*y)
- y'=sin(t)*sin(y)
- y'=sin(t)+sin(y)
- y'=sin(t+y)