Mathematics 3 this term is a standard lecture course in introductory calculus that we have revised to make leaner, livelier, and project oriented. The course is taken by mostly first-year students, is taught in two sections in a lecture format, and meets three times per week.
In a new and improved format, we will be developing a single project as a Case Study in Calculus (or CSC). The topic will be modeling and predicting the size of the USA population from census data. This case study will be spread out over the entire term, and will unfold as a series of five chapters which taken together will comprise the completed CSC. By limiting ourselves to one CSC, students will have more time to think carefully about the modeling process and the scientific method. We also will be able to provide feedback on a student's CSC as it develops, rather than only at the end. Students may work either individually or as part of a group, though the write-ups must be in each individual's own words.
Together with the ideas of calculus, the computer is an indispensable tool in the analysis process, and by using Maple students will learn the power of a computer algebra system. We will provide the Maple tools and show how to use them to solve mathematical problems. Students will be filling in a Maple worksheet with graphs, algebra, and numerical analyses, and then reporting on their findings and conclusions.
This term, we will be using calculus to model the size of the USA population, and we will be learning the conceptual, analytical, and manipulative techniques that make that possible. Calculus is truly a marvelous intellectual achievement, and we plan to have a lot of fun studying it.