Suppose you are assigned to teach a college-level first-semester calculus class (including a properly-taught AP Calculus class in high school) and you are given the following parameters to follow:
- The course actually needs to be a course in first-semester calculus and not some related field;
- It is to be the equivalent of a 4-credit hour college class (four 50-minute meetings per week for 14 weeks);
- The students in the course need to be prepared to enter a second-semester calculus course that starts with techniques of integration (i.e., you should cover basic integration concepts and u-substitution); and
- The audience is a general audience of students needing calculus — i.e. not just engineers and scientists.
But apart from those parameters, you may do whatever you want in the course, in whatever way you see fit.
What would your course do, or look like? Especially, what departures would you make from the “standard” calculus course? Anything really radical you have in mind?