In response to your query about resources for teaching differential equations.
First, the Braun book offered above is THE BEST source book and still in print. Get it!!!
I would like to introduce you to an exciting project: SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations.
SIMIODE is about teaching differential equations using modeling and technology upfront and throughout the learning process. Learn more at our dynamic website, www.simiode.org, where we offer a community in which colleagues can communicate, collaborate, publish, teach, explore, contribute, etc.
We are building a complete environment for teachers and learners – communication, groups across and intra/inter campus projects for students and teachers, models, data, videos. For the latter see our YouTube videos at http://www.youtube.com/channel/UC4y1q6ShHIjRUm7NrM9_dOg where students can collect data on Torricelli's Law and model it with a first principle physics approach for building a differential equation.
Once inside www.simiode.org you can see all the material associated with the Torricelli's Law video in the Modeling Scenario section of our Resources found on our home page. Check It out and also check out our very interesting way of starting a differential course with the student version of the Modeling Scenario on M&M Death and Immigration.
Join a group, start a group, begin a discussion, and then collaborate and communicate with others who are interested in teaching differential equations using modeling and technology. Join SIMIODE! It is FREE!
We also have a Manuscript Management system, FastTrack, (http://simiode.expressacademic.org) which handles reviews of material submitted to SIMIODE. We need your help to build this community of innovative educators:
Please register as a referee.
Please contribute to this community as an author.
Even before joining a group you may engage in discussion – click on Join the Discussion under Participate at the bottom of the Home page. Here are the current discussion groups, but you can start your own as well. Once inside your Group you may want to start more specific discussion to enliven SIMIODE and engage colleagues. We welcome and need discussion and your ideas. Thank you.
Here are the Discussions currently available.
(1) Share your ideas on how to improve SIMIODE
Please share your ideas on how to improve SIMIODE. This may be to add content, options, discussions, opportunities to contribute and use materials, etc. You can really help us by making suggestions on the web site itself. We are currently engaged in making the presentation friendlier, less "texty," leaner, more attractive and functional, and more inviting. So your ideas are always welcome.
(2) Thoughts on teaching differential equations
What are your general thoughts about teaching differential equations? What role do you see for the subject for your students? What should students know before entering the course and what should they gain from the course.
(3) Teaching differential equations with modeling
Teaching with modeling scenarios Please discuss how and why you used modeling in your teaching of differential equations. Offer a short description of type, rationale, use, results, recommendations for others, and lessons learned. Describe the nature of your applications and models. Please consider sharing your efforts through submitting materials for others to use in SIMIODE.
(4) Teaching differential equations with technology
Using technology in teaching and learning differential equations Please discuss how and why you used technology in your teaching of differential equations. Offer a short description of type, rationale, use, results, recommendations for others, and lessons learned. Please consider sharing your efforts through submitting materials for others to use in SIMIODE.
Finally be sure to consider joining our SIMIODE Mathematical Association of America Four Hour Minicourse #6: SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations – Building Community 2014 MathFest, Portland OR, 7-9 August 2014 and do encourage colleagues who might have these interests to join us as well. Contact us for details.
If this is not your thing, please share this opportunity with your colleagues who are interested in teaching differential equations and who are interested in exciting students with a new approach.
Brian Winkel, Director - SIMIODE
Founder and Editor Emeritus - PRIMUS
Problems, Resources, and Issues in Undergraduate Mathematics Studies
Founder and Editor Emeritus - Cryptologia
Professor Emeritus, Department of Mathematical Sciences
United States Military Academy, West Point NY 10996 USA