Introduction to Differential Equations
- Students in Section 05, my 9am section, should refer to the D2L Login Page for all course materials.
- Students in other sections should refer to their instructor for course materials pertaining to their section. Click here to locate your section's instructor.
- If you would like to learn more about MATLAB or DFIELD, check out the Graphing Tools section below or see my Useful Links page in the Navigation Bar at the top. Check in the Miscellaneous section.
The purpose of this section is to provide Math 225 students with a little extra help with some of the graphing tools that we use for the qualitative analysis of ODEs. Within the material below, you will find short discussions about Slope Fields and Phase Portraits. There are also a few links to some mathy websites that might help you develop a better understanding of these important topics.
Aside from the discussions, the following content provides students with some getting-started training and the links to use the web-based graphing tools that we hope you find useful and convenient. Plotting slope fields and phase portraits can get a little cumbersome at times. So, once you have the basic concepts down, feel free to use these tools while you are doing your homework or studying. Hopefully, it will save you some time. With all that time you save, you can spend a good portion of it asking yourself: "What does this graph mean?" or "What information can be gathered from this graph?"
Note: Using these graphics tools requires a good amount of organization of your computer's desktop windows. Have a little patience the first couple of times, and experiment with moving windows around so that you can find them all. When all else fails MINIMIZE!
- Graphing Functions
- Slope Fields
- Phase Planes
A big Thank You to Todd Shaw for pointing out the website maintained by Polking and his colleagues.