Analysis II

I taught Analysis II (Math 3151) in Spring 2017 at UConn. Although our main two textbooks were Spivak’s “Calculus on Manifolds” and Kolmogorov and Fomin’s “Introductory Real Analysis,” I supplemented the course with Munkres’ “Analysis on Manifolds” and Bryant’s “Metric Spaces: Iteration and Application.” If I were to teach a similar course again, I would use the latter two books instead of the first two. I recorded videos for this course, which are available here. I also wrote supplementary notes for this course, which are available here (Warning: the notes are very rough).


The height function together with its level sets on the torus (done in Mathematica)

An irrational slope curve on the torus is not a submanifold of the torus (done in Mathematica)

"You can never verify a theory, you can only verify its predictions." – Venkataraman Balakrishnan