Multivariable Calculus

We will explore how to extend the fundamental notions of calculus to functions of several variables and vector fields. In particular, we will discuss how to describe and visualize them, and how to differentiate and integrate them. Of particular interest will be how to generalize two central ideas of single- variable calculus: optimization and the Fundamental Theorem, but generally, you should be able to make analogies between single- and multi-variable calculus and to see where these analogies break down.\ud You should be able to think about these subjects in multiple ways, understand relationships between them, recognize when they can be used, and be fluent enough at computing to apply them effectively. That is, the goal is to develop a powerful, hierarchical, and connected framework for understanding the material