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Mathematical Foundations of Network Analysis pp 76–94Cite as

Boundary Operator and Coboundary Operator

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Part of the book series: Springer Tracts in Natural Philosophy ((STPHI,volume 16))

Abstract

We now start to develop our circuit theory by combining our linear algebra and network theory. In this Chapter such a combination yields the boundary operator and coboundary operator, leading to a precise formulation in Chapter Six of Kirchhoff’s Laws, upon which all circuit theory is based.

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References

  • Bourgin, D. G.: Modern Algebraic Topology. New York: MacMillan 1963.

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  • Nerode, A., and H. Shank: An Algebraic Proof of Kirchhoff’s Network Theorem. American Math. Monthly 68, 3, March, 1961.

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  • Nerode, A., and H. Shank: Topological Network Theory. WADC Technical Report 57–424, Astia Document Number AD 155730, Wright Air Development Center, November, 1957.

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  • Pontryagin, L. S.: Foundations of Combinatorial Topology. Translated by F. Bagemihl, W. Komm, and W. Seidel. Rochester, New York: Graylock Press 1952.

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Authors and Affiliations

  1. Department of Mathematics, Rensselaer Polytechnic Institute, Troy, New York, USA

    Paul Slepian

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  1. Paul Slepian
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© 1968 Springer-Verlag Berlin · Heidelberg

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Slepian, P. (1968). Boundary Operator and Coboundary Operator. In: Mathematical Foundations of Network Analysis. Springer Tracts in Natural Philosophy, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-87424-6_6

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  • DOI: https://doi.org/10.1007/978-3-642-87424-6_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-87426-0

  • Online ISBN: 978-3-642-87424-6

  • eBook Packages: Springer Book Archive

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