Calculus I: The Study of Motion and Change

Our world is dominated by motion and change. The Earth spins on its axis, as it rotates around the Sun. Stock prices rise and fall. An apple, acting in accordance with the laws of physics, falls onto the head of a modern day Newton. Calculus is the intriguing branch of mathematics whose primary goal is the understanding of the laws governing motion and change. The sum of the calculus—its methods, tools, and ideas—is often cited as one of the greatest intellectual achievements of humanity. Though just a few hundred years old, the calculus has become an indispensable research tool in both the natural and the social sciences. Our study begins with the central concept of the calculus, the limit, and proceeds to explore the dual notions of differentiation and integration. Numerous applications of the theory will be examined. The minimum required preparation for successful study of the calculus is one year each of high-school algebra and geometry. The precalculus topics of trigonometry and analytic geometry will be developed as the need arises. For conference work, students may choose to undertake a deeper investigation of a single topic or application of the calculus or conduct a study in some other branch of mathematics. This seminar is intended for students interested in advanced study in mathematics or science, for students preparing for careers in the health sciences, and for any student wishing to broaden and enrich the life of the mind.