exterior derivative

(30 minutes to learn)

Summary

The exterior function is a generalization of the differential of a function to differential forms. It appears in the statement of Stokes's Theorem for manifolds.

Context

This concept has the prerequisites:

differential forms (The exterior derivative is an operator on differential forms.)
partial derivatives (The exterior derivative is defined in terms of partial derivatives.)

Goals

Define the exterior derivative of a function and of a differential form

Show that d(dw) = 0 for any differential form w

Be able to manipulate exterior derivatives algebraically

Core resources (read/watch one of the following)

-Paid-

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location: Section 2.2, "Differential forms on R^n and the exterior derivative," pages 339-341

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