Foundations of Iso-Differential Calculus. Volume 4 Iso-Differential Equations

Foundations of Iso-Differential Calculus. Volume 4 Iso-Differential Equations Synopsis

This book is intended for readers who have had or currently have a course in difference equations or iso-differential calculus. It can be used for a senior undergraduate course. Chapter 1 deals with the linear first-order iso-difference equations, equilibrium points, eventually equilibrium points, periodic points and cycles. Chapter 2 are introduces iso-difference calculus and the general theory of the linear homogeneous and nonhomogeneous iso-difference equations. Chapter 3 studies the systems of linear iso-difference equations and the linear periodic systems. Chapter 4 is devoted to the stability theory. They are considered the non-autonomous linear systems, Lyapunov's direct method, and stability by linear approximation. Chapter 5 discusses the oscillation theory. The oscillation theory is defined as the iso-self-adjoint second-order iso-difference equations and they are given some of their properties. They are considered some classes of nonlinear iso-difference equations. Chapter 6 studies the asymptotic behavior of some classes of iso-difference equations. Time scales iso-calculus is introduced in Chapter 7. They are given the main properties of the backward and forward jump iso-operators. They are considered the iso-differentiation and iso-integration. They are introduced as the iso-Hilger's complex plane and the iso-exponential function.