Dynamic Equations on Time Scales
Dynamic Equations on Time Scales
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DOI：
10.1007/978-1-4612-0201-1
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
M. Bohner;A. Peterson
中科院分区：
文献类型：
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作者：
M. Bohner;A. Peterson
测度链（时标）上动力方程的研究可以追溯到其创始人S。Hilger（1988），是一个新的领域仍然相当理论探索数学。激励主题的概念，动态方程测量链可以建立连续和离散数学之间的桥梁。此外，测度链理论的研究导致了一些重要的应用，例如，在昆虫种群模型，神经网络，传热和流行病模型的研究。本书的主要特点：* 测量链理论介绍;讨论它的有用性，允许同时发展的微分方程和差分方程，而不必重复类似的证明 * 许多经典公式或程序的微分和差分方程投在一个新的光 * 新的类似物的许多”特殊功能”的研究 * 检查的性质”指数函数”的时间尺度，它可以用一个特别简单的线性方程来定义和研究 * 自伴方程、线性系统、高阶方程、动态不等式和辛动态系统 * 清晰、有动机的阐述，从字母表开始，逐渐发展到更复杂的文本 * 在整本书中有大量的例子和练习 * 解决选定的问题只需要微积分和线性代数的第一学期，时间尺度上的动态方程可以被认为是一个有趣的方法，通过接触连续和离散分析微分方程。这种方法提供了在生物学、物理学和工程学等领域的许多应用的早期遭遇。本书的部分内容可用于高年级本科生或研究生初级阶段的专题研讨会。最后，工作可以
The study of dynamic equations on a measure chain (time scale) goes back to its founder S. Hilger (1988), and is a new area of still fairly theoretical exploration in mathematics. Motivating the subject is the notion that dynamic equations on measure chains can build bridges between continuous and discrete mathematics. Further, the study of measure chain theory has led to several important applications, eg, in the study of insect population models, neural networks, heat transfer, and epidemic models. Key features of the book:* Introduction to measure chain theory; discussion of its usefulness in allowing for the simultaneous development of differential equations and difference equations without having to repeat analogous proofs* Many classical formulas or procedures for differential and difference equations cast in a new light* New analogues of many of the" special functions" studied* Examination of the properties of the" exponential function" on time scales, which can be defined and investigated using a particularly simple linear equation* Additional topics covered: self-adjoint equations, linear systems, higher order equations, dynamic inequalities, and symplectic dynamic systems* Clear, motivated exposition, beginning with preliminaries and progressing to more sophisticated text* Ample examples and exercises throughout the book* Solutions to selected problems Requiring only a first semester of calculus and linear algebra, Dynamic Equations on Time Scales may be considered as an interesting approach to differential equations via exposure to continuous and discrete analysis. This approach provides an early encounter with many applications in such areas as biology, physics, and engineering. Parts of the book may be used in a special topics seminar at the senior undergraduate or beginning graduate levels. Finally, the work may