The third course in the Calculus sequence. Students continue to investigate the application of the Calculus to the solution of problems of both physical and historical importance including the resolution of Zeno's paradox, convergence and divergence of infinite sums, motion in the plane and in space, the shortest time curve between two points (the brachistochrone problem) and centers of mass. Topics include parameterization of curves, vectors, sequences, infinite sums, power series, approximation of functions using the Taylor polynomial, solid analytic geometry, partial derivatives and gradients, multiple integrals, and their application to areas in the plane and volumes beneath surfaces. This course demonstrates how the Calculus unified seemingly diverse concepts from geometry, algebra, the study of motion and other physical problems.
