Welcome to Calculus 1. This course will cover the basics of derivatives and integrals, and also include some interesting applications of derivatives. It culminates in the profound and surprising connection between derivatives and integrals, which is called the Fundamental Theorem of Calculus.
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Students of this course can expect to acquire specific mathematical skills, to grapple with important scientific ideas, and learn how to use a computer to implement these skills and ideas. The course involves a nice balance between working individually and also working in groups. The development of calculus by Isaac Newton and Gottfried Leibniz in the latter part of the seventeenth century was one of the most exciting and important developments in the history of science. Today, the ideas of calculus permeate almost every scientific endeavor, whether a physicist is predicting the path of an astronomical object, or a biologist is modeling the population growth, or an economist is studying a firm’s allocation of resources. Thus, the study of calculus is both an exciting intellectual journey, and also the practical acquisition of tools used throughout science.