A major priority in the design of this course is the engagement of students as scientists and citizens. This is accomplished through the variety of techniques described below.
Course Syllabus (Acrobat (PDF) 54kB Nov7 08)
The course meets twice a week for 80 minutes. I prefer this format, as compared to meeting three times a week for 50 minutes, as I regularly have the students engage in interactive group activities during the class and the longer time block facilities such activities.
The text for the course is Differential Equations by Blanchard, Devaney, and Hall, 3rd edition, published by Brooks/Cole. The authors are all researchers in the field of dynamical systems and they apply a dynamical systems perspective to their presentation of differential equations. There is a strong emphasis on quantitative analysis of equations using graphical and numerical methods and a corresponding decrease in emphasis on analytical techniques. The text includes a strong focus on mathematical modeling.
Formats and Pedagogies
A computer disk comes with the text. This disk, that can be used on both PC and MacIntosh computers, contains a variety of easy to use simulations and demonstrations that illustrate many of the ideas in the course. Most of the programs are menu driven, with the user selecting from a set of pre-programmed examples, so there is no learning curve required to use them. The output is displayed in a beautiful visual form. In a few important cases, such as to graph slope fields or vector fields and draw their associated solutions curves, the user can enter her own formulas into the programs.
The class format is an integrated mixture of lecture, seminar and lab. Part of the time I lecture, there is also a lot of group work, often using the computer programs, and classroom discussion. In earlier versions of the course, I would use the computer programs to demonstrate ideas, via a computer projection system, to the class. The class would have a separate computer laboratory component in which students would do assignments in our computer lab. Several years ago, the math department purchased a set of ten laptop computers. Now the students, in teams of two or three, use these laptops during class time to explore the concepts themselves and at present we do not have a separate computer lab component. There are still some more extensive computer assignments that students do on their own time.
For the group work, I have both open-ended discovery work and guided work. For the discovery work, I have the students use the computer programs to investigate a new situation and respond to prompts such as "what do you observe?", "do you see any patterns?", "what questions do you have?", "can you make some predictions or conjectures? ". In the guided work, the students practice a technique that I have presented during lecture.
I regularly assign homework problems from the textbook. Students read out of the book Collapse: How Societies Choose to Fail or Succeedby Jared Diamond, and write short response papers in which they describe the ways that they see the material in our math course applying to the social issues being discussed in the chapter. There is a more focused assignment on over-population and the Rwandan genocide (See Appendix for Rwanda Assignment). There is a final project in which student teams learn about a topic of interest that involves differential equations, give a short oral presentation on their project and write a 10 – 15 page report on their findings. (See Appendix for description of final project and list of potential project topics.)
We have a special three hour class meeting one evening in which we learn about over harvesting of resources by playing the simulation game Fishing Banks, Ltd created by Dennis Meadows. (See Appendix for Fishing Simulation Game).
Below is the course "play-by-play" in which I briefly describe the topic for each class and also have links to the handouts for group work and computer work that we used in class that day. Also below is an example of a group modeling project.
Class Schedule (Acrobat (PDF) 100kB Nov7 08)