Book Recommendation for Differential Forms

If anyone is seeking a more formal treatment of differential forms than the (admittedly informal!) description given in class, a good reference is

Abraham, Marsden, Ratiu, “Manifolds, Tensor Analysis, and Applications

Note that an electronic version of this book is available for free for CMU students through the library webpage.

A big difference from the treatment we’ve seen in class is that this book first spends several chapters defining and studying manifolds before introducing differential forms. We instead started with differential forms in \(\mathbb{R}^n\), and will later talk about how to work with them on curves and surfaces. Interestingly enough, however, differential forms in \(\mathbb{R}^n\) is essentially all we need to define discrete differential forms, which in turn are sufficiet to work with “curved” polyhedral surfaces. (The joys of being piecewise Euclidean…)

Assignment -1: Favorite Formula

Part of your course grade is determined by participation, which can include both in-class participation as well as discussion here on the course webpage.  Therefore, your first assignment is to:

  1. create an account (you must use your Andrew email address, so we can give you participation credit this semester!),
  2. sign up for Piazza and Discord,
  3. read carefully through the Course Description and Grading Policy, and
  4. leave a comment on this post containing your favorite mathematical formula (see below).
To make things interesting, your comment should include a description of your favorite mathematical formula typeset in $\LaTeX$.  If you don’t know how to use $\LaTeX$ this is a great opportunity to learn — a very basic introduction can be found here.  (And if you don’t have a favorite mathematical formula, this is a great time to pick one!)
(P.S. Anyone interested in hearing about some cool “favorite theorems” should check out this podcast.)