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
See also
-No Additional Notes-