Your next reading assignment will help you review the concepts we’ve been discussing in class: describing “little volumes” or \(k\)-vectors using the wedge product and the Hodge star, and measuring these volumes using “dual” volumes called \(k\)-forms. These objects will ultimately let us integrate quantities over curved domains, which will also be our main tool for turning smooth equations from geometry and physics into discrete equations that we can actually solve on a computer.
The reading is Chapter 4, “A Quick and Dirty Introduction to Exterior Calculus”, up through section 4.5.1 (pages 45–65). It will be due Tuesday, February 11 at 10am Eastern time. See the assignments page for handin instructions.
Your next homework will give you some hands-on practice with differential forms; just take this time to get familiar with the basic concepts.