Surface Integrals

  • James J. CallahanEmail author
Part of the Undergraduate Texts in Mathematics book series (UTM)


We turn now to integrals over curved surfaces in space. They are analogous,in several ways, to integrals over curved paths. Both arise in scientific problems as ways to express the product of quantities that vary. The first surface integral we consider measures flux, the amount of fluid flowing through a surface. The integrand of a surface integral, like a path integral, can be either a scalar or a vector function: flux is the integral of a vector function, whereas area—another surface integral—is the integral of a scalar. Also, orientation matters, at least when the integrand is a vector function.


Differential Form Scalar Integral Oriented Surface Surface Patch Coordinate Change 
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Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsSmith CollegeNorthamptonUSA

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