Taking this class is very like a roller coaster. The beginning about Fixed Point and Contraction Mapping is easy, if you took 131AH and has the topology mindset. The second part -- about Inverse Function Theorem and multivariable derivatives -- is hard, because the dense proof presented here, and the frequent use of linear algebra. The third part is about Winding Numbers -- a very interesting topological invariant that gives you a taste of homotopy in algebraic topology. I think this is the most beautiful part of the course (also most geometric and topological). The last part is about Riemann integral and Fourier Series, which are I believe the easiest section of the course.

In general Professor Greene took a very intuitive path to lead you down into the world of differential analysis through powerful topological mindset developed in the previous course. Strongly recommend to take if you wish to enjoy the beauty of mathematics.

EXTREMELY HARD

h a r d

Super HARD

very hard

hard