Vector Analysis Versus Vector Calculus pp 207-267 | Cite as

# Surfaces with Boundary

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## Abstract

One of the objectives of this book is to obtain a rigorous proof of a version of Green’s formula for compact subsets of \(\mathbb{R}^2\) whose topological boundary is a regular curve of class *C* ^{2}. These sets are typical examples of what we will call regular 2-surfaces with boundary in \(\mathbb{R}^2\). The analogous three-dimensional example would consist of a compact set of \(\mathbb{R}^3\) whose topological boundary is a regular surface of class *C* ^{2}. The following example is perhaps instructive.

## Keywords

Coordinate System Normal Vector Open Subset Tangent Space Open Neighborhood
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## Copyright information

© Springer Science+Business Media, LLC 2012