Discrete Calculus Applied Analysis on Graphs for Computational Science [Paperback]

This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.

Discrete Calculus: History and FuturePart I: A Brief Review of Discrete CalculusIntroduction to Discrete CalculusCircuit Theory and Other Discrete Physical ModelsPart II: Applications of Discrete CalculusBuilding a Weighted Complex from DataFiltering on GraphsClustering and SegmentationManifold Learning and RankingMeasuring NetworksRepresentation and Storage of a Graph and ComplexOptimizationThe Hodge Theorem: A Generalization of the Helmholtz Decomposition

From the reviews:

The book introduces some best practices and advanced techniques in the field of discrete calculus. The articles are written by a team of experts in the field and are aimed at scientists and engineers. The book shows how the theory can be applied to solving a wide variety of real-world problems. & All the examples are well described and illustrated with source code and screen shots. I recommend this book to anyone interested in discrete calculus and its application. (Todor Jordanov Todorov, Mathematical Reviews, Issue 2012 d)

This book illustrates the concepts of discrete calculus with examples in circuit theory, chosen because of its natural connection to algebraic topology and maturity. & this is a unique book that brings together research in complex networks and algorithm content extraction. I have no doubt that the book will be a valuable addition to the libraries of many researchers and graduate students working in the areas of complex networks, graphics, and algorithm design. (Alexander Tzanov, ACM Computing Reviews, July, 2011)

The field of discrete calculus, also known as discrete exterior calculus , focuses on finding a proper set of definitions and diffelĐ