Paradigm Lost: A Modern Approach to Teaching Ordinary Differential Equations

Thomas G. Wangler

Illinois Benedictine College
5700 College Road
Lisle, IL 60532-0900
USA
Phone: (708) 829-6554
Fax: (708) 960-1126
wangler@eagle.ibc.edu

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ABSTRACT

Differential Equations has traditionally been taught as a 'methods' course. Different types of differential equations are discussed along with the method of obtaining their solution. The student is then left to work through the concomitant details of this new method; at this point they usually experience first-hand, the truthfulness of the old adage, 'the devil is in the details'. These diabolical details can involve lengthy algebraic manipulations, a healthy dose of differential calculus, and of course, the correct order of execution of the new technique. All in all, this can be a daunting task fraught with peril for the unwary student. As a result, it does little to pique the interest or curiosity of most students.

In order to counter this undesirable state of affairs and make the course more interesting and less daunting for the students, I've adopted a new pedagogical paradigm. The new paradigm de- emphasizes (but does not eliminate) methods, and emphasizes (1) mathematical modeling, (2) analysis of the o.d.e., and (3) addressing the qualitative behavior of the solution. I earnestly endeavored to effect this paradigm shift without emasculating the course or making any major contributions to the 'dumbing down of America'!

In this talk I will discuss a variety of things ranging from my basic teaching philosophy to the prodigious amount of work involved in incorporating a computer lab component into a course. Some of the topics I'll touch on are given below.

teaching philosophy and course objectives
different media used in class
how to incorporate a lab experience into a course and its impact on the course
how the students respond to the way o.d.e.'s is taught
introducing contemporary topics into the course
student talks on d.e. topics at a local student symposium
giving the class 'real life' applications involving soluble differential equations
old paradigm/new paradigm--- a contrast
why bother using computer technology?
good news/bad news
what's so hard about creating a good lab

Keyword(s): differential equations, software