Title page for ETD etd-05052008-134530


Type of Document Master's Thesis
Author Arnold, Rachel Florence
Author's Email Address rachel.arnold@vt.edu
URN etd-05052008-134530
Title Complex Analysis on Planar Cell Complexes
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Haskell, Peter E. Committee Chair
Green, Edward L. Committee Member
Thomson, James E. Committee Member
Keywords
  • Cell Decomposition
  • Cauchy-Riemann Equation
  • Discrete Differential Forms
  • Hodge Decomposition
  • Cauchy Integral Formula
Date of Defense 2008-04-29
Availability unrestricted
Abstract
This paper is an examination of the theory of discrete complex analysis that arises from the

framework of a planar cell complex. Construction of this theory is largely integration-based.

A combination of two cell complexes, the double and its associated diamond complex, allows

for the development of a discrete Cauchy Integral Formula.

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