Ravi P. Agarwal is a Professor at the Texas A&M University in Kingsville, USA, and a Distinguished University Professor of Mathematics at the Florida Institute of Technology, Melbourne, FL, USA. Abdullah Özbekler is a Professor at Atilim University, Department of Mathematics, Ankara, Turkey.

An introduction to measure chain (time scale) theory with emphasis on
its usefulness in allowing for the simultaneous development of
differential equations and difference equations. Motivating the
subject is the notion that dynamic equations on measure chains can
build bridges between continuous and discrete mathematics. The study
of measure chain theory has also led to applications in the study of
insect population models, neural networks, heat transfer, epidemic
models. This book may stimulate the development of new kinds of
equations with potentially new applications. Includes examples,
exercises, solutions.

1. The Time Scales Calculus.- 1.1. Basic Definitions.- 1.2. Differentiation.- 1.3. Examples and Applications.- 1.4. Integration.- 1.5. Chain Rules.- 1.6. Polynomials.- 1.7. Further Basic Results.- 1.8. Notes and References.- 2. First Order Linear Equations.- 2.1. Hilger's Complex Plane.- 2.2. The Exponential Function.- 2.3. Examples of Exponential Functions.- 2.4. Initial Value Problems.- 2.5. Notes and References.- 3. Second Order Linear Equations.- 3.1. Wronskians.- 3.2. Hyperbolic and Trigonometric Functions.- 3.3. Reduction of Order.- 3.4. Method of Factoring.- 3.5. Nonconstant Coefficients.- 3.6. Hyperbolic and Trigonometric Functions II.- 3.7. Euler-Cauchy Equations.- 3.8. Variation of Parameters.- 3.9. Annihilator Method.- 3.10. Laplace Transform.- 3.11. Notes and References.- 4. Self-Adjoint Equations.- 4.1. Preliminaries and Examples.- 4.2. The Riccati Equation.- 4.3. Disconjugacy.- 4.4. Boundary Value Problems and Green's Function.- 4.5. Eigenvalue Problems.- 4.6. Notes and References.- 5. Linear Systems and Higher Order Equations.- 5.1. Regressive Matrices.- 5.2. Constant Coefficients.- 5.3. Self-Adjoint Matrix Equations.- 5.4. Asymptotic Behavior of Solutions.- 5.5. Higher Order Linear Dynamic Equations.- 5.6. Notes and References.- 6. Dynamic Inequalities.- 6.1. Gronwall's Inequality.- 6.2. Holder's and Minkowski's Inequalities.- 6.3. Jensen's Inequality.- 6.4. Opial Inequalities.- 6.5. Lyapunov Inequalities.- 6.6. Upper and Lower Solutions.- 6.7. Notes and References.- 7. Linear Symplectic Dynamic Systems.- 7.1. Symplectic Systems and Special Cases.- 7.2. Conjoined Bases.- 7.3. Transformation Theory and Trigonometric Systems.- 7.4. Notes and References.- 8. Extensions.- 8.1. Measure Chains.- 8.2. Nonlinear Theory.- 8.3. Alpha Derivatives.- 8.4. Nabla Derivatives.- 8.5. Notes and References.- Solutions to Selected Problems.