This function is always increasing and concave down. This will then serve as a gateway course for students from all fields so that they can have a broader view about calculus.įigure 1. We will design a new first-semester calculus course which would break this tradition and contain a balanced set of application examples in biology, chemistry, economics and physics. Although calculus textbooks nowadays contain some problems in economics and business, chemistry and biology applications are rare and instructors usually do not mention them at all in class, being somewhat unfamiliar with those fields. However, the traditional first-semester calculus focuses on applications in mechanics and physics. They would also appreciate mathematics more if they felt that they were connected with the applications as well as the theories. We believe that most of the students would learn calculus well if they were motivated by the prospective usefulness of calculus in their future studies and careers. It is also important because of its wide applicability in many fields, from science and engineering to economics and social science, allowing students to broaden their horizons of investigation and career options. This course is important because it transitions from high school mathematics to higher mathematical thinking with analytical rigor. The objective of the first semester calculus is to train the students in the basic concepts and techniques of calculus: limit, continuity, differentiation and integration. In fact, this course could be more efficient than the traditional Calculus I. With careful planning, this is not difficult to do. Because of the applications as mentioned above, it is essential for us to discuss these two functions in our first Calculus course. Traditionally, the first Calculus course does not include exponential functions and logarithm functions. Consequently, they are more motivated to study Calculus. By using these examples, the students would feel the connection between mathematics and their major subjects. These include: growth/decay problems in any organism population, gene regulation and dynamical changes in biological events such as monitoring the change of patients’ temperature along with the medications. We have developed a set of application examples for Calculus, which are more biology oriented. These examples have been proved to be very efficient for engineering students but not for the life science majors.
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Classical applications for teaching Calculus include: moving objects, free fall problems, optimization problems involving area or volume and interest rate problems. The reforms in STEM education demand a redesign of foundation courses in mathematics, among which calculus is the key to quantitative analysis in sciences.Īlthough we can teach and learn calculus from the pure and abstract mathematical point of view, the general consensus is that the most efficient way to study/teach Calculus is connecting the mathematical concepts with their applications. All these changes have increased concerns over science, technology, engineering and mathematics (STEM) education. Thus, the most challenging question for this project is: why do we need to develop a new calculus course? The straightforward answer is that although the basic concepts and techniques of calculus have not changed, many fields where mathematics is applied have developed and advanced, especially in the biological sciences, and most importantly the students have changed. The teaching materials for calculus, from traditional textbooks to modern computer software, have been reinvented and refined over the years and have become classical and standard.
What is special about this Calculus course?Ĭalculus courses have been taught at universities around the world for hundreds of years.
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