Introduction to Discrete Calculus



In this chapter we review conventional vector calculus from the standpoint of a generalized exposition in terms of exterior calculus and the theory of forms. This generalization allows us to distill the important elements necessary to operate the basic machinery of conventional vector calculus. This basic machinery is then redefined in a discrete setting to produce appropriate definitions of the domain, boundary, functions, integrals, metric and derivative. These definitions are then employed to demonstrate how the structure of the discrete calculus behaves analogously to the conventional vector calculus in many different ways.


Boundary Operator Differential Form Fundamental Theorem Incidence Matrix Laplacian Matrix 
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© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.Siemens Corporate ResearchPrincetonUSA
  2. 2.Athinoula A. Martinos Center for Biomedical Imaging, Department of RadiologyMassachusetts General Hospital, Harvard Medical SchoolCharlestownUSA

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