## Computer stuff

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.

## Installing

• 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.

## Running

• First create an ODE file
1. Open a text editor, like Notepad (it is under Applications in the Start Menu) or if you are really a masochist, Word.
2. 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
```
3. Save the file as example1 in plain text ( DO NOT SAVE AS RTF or DOC - It wont work )
• Now run and play with it
1. 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
2. You should see:
This is a phase-plane plot with the time-like variable, 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)

3. Click on Phaseplane Grid parameters and change Dir. Fld.Grd to 20
4. Click on Phasplane DirFld and direction fields will show up
5. 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.
6. 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.
7. 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

### How do I ...

• 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.

### Finally some homework

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