Calculus: Dynamics and Integration

The goal of the course is to provide a bridge from “some exposure to single-variable calculus” to “readiness for multivariable calculus”. We will do this by covering some topics that are rarely seen in single-variable calculus courses: discrete dynamical systems and differential equations. These topics are widely applicable in the natural and social sciences, but, more to the point, also provide a way of reviewing ideas from early in single-variable calculus (what is a derivative and what is it good for), and introducing the main ideas from later in single-variable \ud calculus (Taylor expansions and especially integrals). The last few weeks of the course are a more traditional treatment of computing integrals and some of their applications.\ud \ud The course will involve a focus on “modeling”, since discrete dynamical systems and differential equations are tools for describing real-world process that evolve in time (discrete time in the first case, continuous time in the second)