Dynamic Equations on Time Scales: An Introduction with Applications Allan Peterson

ISBN: 9781461266594

Published: October 23rd 2012

Paperback

358 pages


Description

Dynamic Equations on Time Scales: An Introduction with Applications  by  Allan  Peterson

Dynamic Equations on Time Scales: An Introduction with Applications by Allan Peterson
October 23rd 2012 | Paperback | PDF, EPUB, FB2, DjVu, audiobook, mp3, RTF | 358 pages | ISBN: 9781461266594 | 8.24 Mb

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 measureMoreThe 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, e.g., 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 serve as a reference to stimulate the development of new kinds of equations with potentially new applications.



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