Analysis (MAA 207) builds upon the topology notions studied in Analysis (MAA 202) to allow for a more profound study of functions. Examining functions as limits of simpler ones (e.g. for approximation problems) is made possible in a rigorous manner thanks to topological ideas. This provides the possibility of using crucial tools in many scientific fields; the most striking one being Fourier series (first designed to solve the heat equation and now ubiquitous in science and, in a hidden manner, in daily life). The second part of the course deals with a wide array of differential equations, permitting students to better understand complex physical questions.