Dynamic Equations on Time Scales

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, 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