Differential Forms

  • David Bachman


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
$$\int \limits_R f(\phi (r, \theta)) {\rm Area}\left[{\frac{\partial \phi}{\partial r}}{(r, \theta)},{\frac{\partial \phi}{\partial \theta}}{(r, \theta)} \right]dr \ d\theta$$


Negative Sign Unit Sphere Tangent Vector Variable Formula Rectangular Lattice 
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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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