A differential form is simply this: an integrand. In other words, it is a thing which can be integrated over some (often complicated) domain. For example, consider the following integral: \(\int\limits_0^1 {x^2 } dx\). This notation indicates that we are integrating x2 over the interval [0, 1]. In this case, x2dx is a differential form. If you have had no exposure to this subject, this may make you a little uncomfortable. After all, in calculus we are taught that x2 is the integrand. The symbol “dx” is only there to delineate when the integrand has ended and what variable we are integrating with respect to. However, as an object in itself, we are not taught any meaning for “dx.” Is it a function? Is it an operator on functions? Some professors call it an “infinitesimal” quantity.


Real Number Linear Function Line Segment Correct Answer Differential Form 
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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsPitzer CollegeClaremontUSA

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