Surfaces and Differential Forms in \(\mathbb{R}^{n}\)

  • Vladimir A. Zorich
Part of the Universitext book series (UTX)


In this chapter we introduce and describe the concepts of surface, boundary of a surface, coherent orientations of a surface and its boundary. We derive a formula for calculating the area of a surface, and we give an initial idea of the concept of a differential form. All these concepts are essential when working with curvilinear and surface integrals, which will be the main subject of the next chapter.

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Vladimir A. Zorich
    • 1
  1. 1.Department of MathematicsMoscow State UniversityMoscowRussia

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