Calculus I

In this course we study the basic objects of calculus: derivatives and integrals. The course emphasizes physical motivations and intuitive understanding of the concepts.

Topics include: concept of a derivative, connection with problems of motion, properties of derivatives, mean value theorems, simple examples of calculating derivatives, tangents to curves, approximation using derivatives, maxima and minima of functions, convexity and concavity, points of inflection, derivatives in polar coordinates, concept of an integral, calculation of area, fundamental theorem of calculus, properties of integrals.