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Differential Forms

  • David Bachman
Chapter

Abstract

Let us now go back to the example in Chapter 1. In the last section of that chapter, we showed that the integral of a function, \( f:\mathbb{R}^3 \to \mathbb{R},\) over a surface parameterized by \(\phi: R \subset \mathbb{R}^2 \rightarrow \mathbb{R}^3\) is
$$\int \limits_R f(\phi (r, \theta)) {\rm Area}\left[{\frac{\partial \phi}{\partial r}}{(r, \theta)},{\frac{\partial \phi}{\partial \theta}}{(r, \theta)} \right]dr \ d\theta$$
.

Keywords

Negative Sign Unit Sphere Tangent Vector Variable Formula Rectangular Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsPitzer CollegeClaremontUSA

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