On a differentiable manifold, the exterior derivative extends the concept of the differential of a function to differential forms of higher degree. The exterior . The exterior derivative of a function is the one-form. (1) written in a coordinate chart . Thinking of a function as a zero-form, the exterior derivative extends linearly to all differential k-forms using the formula. 10 thg 8, 2010 - For 1-forms, you can get some intuition for exterior differentiation from how it shows up in In this approach the exterior derivative is a very simple operation. 13.4 The exterior derivative. 123. 13.3 Differential forms. Definition 13.3.1 A k-form ω on a differentiable manifold M is a smooth section of the bundle of . Chapter 14. Exterior derivative. The exterior derivative is a generalization of the gradient of a func- tion. It is a map from p-forms to (p + 1)-forms. This should be a. 1 thg 11, 2011 - Before jumping into the exterior derivative, it's worth reviewing what the basic vector derivatives , , and do, and more importantly, what they look . 4.1 The exterior derivative. Differential forms are equipped with a natural differential operator, which extends the exterior derivative of functions to all forms: d . 1 thg 4, 2013 - Yes. The same holds true for any differential form whose coefficients are constant functions. For example, if ω=3(dx∧dy)+5(dx∧dz)+7(dy∧dz), .