Discrete Calculus by Analogy
Discrete Calculus by Analogy
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类比离散微积分
DOI：
10.2174/97816080508641090101
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
G. Bagirov
中科院分区：
文献类型：
--
作者：
F. Izadi;N. Aliev;G. Bagirov
描述：它的起源可以追溯到几个世纪以前，离散微积分现在是与离散系统和算法相关的许多问题的日益重要的方法论。这里所涉及的主题通常出现在科学和技术的许多分支中，特别是在离散数学、数值分析、统计和概率论以及电气工程中，但我们在这里的观点是，这些主题属于更一般的数学领域；即微积分和微分方程，因为这门学科与数学的这一分支有着显著的相似性。正是这种观点使这一文本区别于以前的文本。虽然主题是离散的，但我们的方法是分析性的。与连续数学分析一样，我们首先介绍函数的定义、幂函数和指数函数、离散微分和积分、级数展开、复解析函数及其积分、解析函数的柯西定理以及离散情况下的调和函数等主要概念。然后，我们将这些概念与离散微分方程理论联系起来。这本书是为了证明数学的各个方面与离散微分方程的关系。它应该证明是有用的数学毕业生和研究人员，不管他们的背景离散微积分。
Description: With its 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 precisely this viewpoint which distinguishes this text from the previous ones. Although the topics are discrete, our approach is analytical. 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. The book serves to demonstrate the relationship of various aspects of mathematics with discrete differential equations. It should prove to be useful for mathematics graduates and researchers, regardless of their background on discrete calculus.