Discrete calculus by analogy / F.A. Izadi, N. Aliev, G. Bagirov.

Includes bibliographical references (pages 141-142) and index.

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Annotation. With origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathematics. It is exactly this viewpoint which distinguishes this text from the previous ones. Although the topics are discrete, our approach is absolutely analytic. As in continuous mathematical analysis, we first introduce the main concepts such as the definition of a function, power and exponential functions, discrete differentiation and integration, series expansion, complex analytic functions and their integrals, the Cauchy theorem for analytic functions, as well as the harmonic functions in discrete cases. Then we relate these concepts to the theory of discrete differential equations.

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