Reading 4: Exterior Calculus — due 2/18

The next reading assignment will wrap up our discussion of exterior calculus, both smooth and discrete. In particular, it will explore how to differentiate and integrate \(k\)-forms, and how an important relationship between differentiation and integration (Stokes’ theorem) enables us to turn derivatives into discrete operations on meshes. In particular, the basic data we will work with in the computational setting are “integrals of derivatives,” which amount to simple scalar quantities we can associate with the vertices, edges, faces, etc. of a simplicial mesh. These tools will provide the basis for the algorithms we’ll explore throughout the rest of the semester.

The reading is the remainder of Chapter 4 from the course notes, “A Quick and Dirty Introduction to Exterior Calculus”, Sections 4.6 through 4.8 (pages 67–83). Note that you just have to read these sections; you do not have to do the written exercises; a different set of written problems will be posted later on. The reading is due Tuesday, February 18 at 10am. See the assignments page for handin instructions.

2 thoughts on “Reading 4: Exterior Calculus — due 2/18”

  1. typo: I’m reviewing the notes and I noticed in 4.6.1 the gradient defined in nabla probably meant to discuss either a scalar function $f$ or a scalar function $\phi$?
    In other words it meant to write $\nabla f = \left(\frac{\partial f}{\partial x^1}, \dots, \frac{\partial f}{\partial x^n}\right)^T$?

    1. Yes, thank you! Probably best to use \(\phi\) instead of \(f\) throughout much of that section, so that \(f\) can be reserved for the immersion of the surface.

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