# Differentiation of Forms

## Abstract

The goal of this section is to figure out what we mean by the derivative of a differential form. One way to think about a derivative is as a function which measures the variation of some other function. Suppose *ω* is a 1-form on ℝ^{2}. What do we mean by the “variation” of *ω*? One thing we can try is to plug in a vector field *V*. The result is a function from ℝ^{2} to ℝ. We can then think about how this function varies near a point *p* of ℝ^{2}. But *p* can vary in a lot of ways, so we need to pick one. In Section 1.5, we learned how to take another vector, *W*, and use it to vary *p*. Hence, the derivative of *ω*, which we shall denote “*dω*,” is a function that acts on both *V* and *W*. In other words, it must be a 2-form!

## Keywords

Differential Form Tangent Plane Directional Derivative Correct Formula Algebraic Computation## Preview

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