MAA207 - Series of Functions, Differential Equations (2022-2023)

Prerequisite: MAA202
Series of functions, differential equations
(MAA207) builds upon the topology
notions studied in Topology and multivariable
calculus (MAA202) 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.



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.