Mathematics 3 this term is a lecture course in introductory calculus that we have revised to make
leaner, livelier, and case studies 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.
Our Case Studies in Calculus (CSCs) will involve modeling aspects of real-world
phenomena with calculus. The CSCs range from modeling the AIDs data to analyzing issues of river flooding. In these projects, we will behave as mathematicians attempting to answer questions
posed by epidemiologists or earth scientists, for example. The purpose of the CSCs is to illustrate the
power of calculus as a tool in real-world problem-solving. Students may work either individually or as part of a
group, though the write-ups must be in each individual's own words.
We will be turning to the on-line components of the textbook to make the ideas and applications of calculus come alive. Together with the concepts and techniques of calculus, the computer is an indispensable tool in the analysis process. By using the World Wide Web to access calculus tools that we have developed for our course, students will learn the formidable capabilities of a computer system in doing calculus. We will even be using the computer as a problem-generator to give students lots of practice and immediate feedback on calculus techniques and problem-solving. And we will have examples, quizzes, and tutorial videos on line as well.
This term, we will be using calculus to develop mathematical models in case studies, 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.