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.
Our projects, under the rubric of Case Studies in Calculus (CSCs), will involve modeling aspects of real-world
phenomena with calculus. There will be a total of three CSCs--Rates of Change: Torricelli's Law; Population Modeling with Differential Equations; and
Integrals as Limits of Sums: River Flooding. In these projects, we will behave as mathematicians attempting to answer questions
posed by population demographers 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.
Together with the ideas of calculus, the computer is an indispensable tool in the analysis process, and by using the computer program Maple students will learn the formidable capabilities 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 develop mathematical models in three different case studies, and we will
be learning the conceptual, analytical, and manipulative techniques that make that possible. Moreover, we will be using the computer as a problem-generator to give students lots of practice and immediate feedback on calculus techniques and problem-solving. Calculus is truly a
marvelous intellectual achievement, and we plan to have a lot of fun studying it.