• Corpus ID: 14063518

Differential complexes and exterior calculus

@article{Harrison2006DifferentialCA,
  title={Differential complexes and exterior calculus},
  author={Jenny Harrison},
  journal={arXiv: Mathematical Physics},
  year={2006}
}
  • J. Harrison
  • Published 9 January 2006
  • Mathematics
  • arXiv: Mathematical Physics
In this paper we present a new theory of calculus over $k$-dimensional domains in a smooth $n$-manifold, unifying the discrete, exterior, and continuum theories. The calculus begins at a single point and is extended to chains of finitely many points by linearity, or superposition. It converges to the smooth continuum with respect to a norm on the space of ``pointed chains,'' culminating in the chainlet complex. Through this complex, we discover a broad theory of coordinate free, multivector… 

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Geometric Hodge star operator with applications to the theorems of Gauss and Green

  • J. Harrison
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 2006
The classical divergence theorem for an $n$-dimensional domain $A$ and a smooth vector field $F$ in $n$-space \[\int_{\partial A} F \cdot n = \int_A div F\] requires that a normal vector field $n(p)$

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We present here the fundamentals of a theory of domains that offers unifying techniques and terminology for a number of different fields. Using direct, geometric methods, we develop integration over

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