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Intro; Preface; Contents; 1 Calculus on Time Scales; 1.1 Forward and Backward Jump Operators, Graininess Function; 1.2 Differentiation; 1.3 Integration; 1.4 The Exponential Function; 1.5 Hyperbolic and Trigonometric Functions; 1.6 Power Series; 1.7 Advanced Practical Problems; 2 Dynamic Systems; 2.1 Structure of Dynamic Systems on Time Scales; 2.2 Constant Coefficients; 2.3 Examples; 2.3.1 The Logistic Model; 2.3.2 Tumor Growth Models; 2.3.3 The Predator-Prey Model of Lotka-Volterra; 2.3.4 The Ricker Model; 2.3.5 The Beverton-Holt Model; 2.3.6 Competition Models
2.3.7 Single Species Population Growth Models2.4 Advanced Practical Problems; 3 Functional Dynamic Equations. Basic Concepts, Existence, and Uniqueness Theorems; 3.1 Classification of Functional Dynamic Equations; 3.2 The Method of Steps; 3.3 The Picard-Lindelöf Theorem; 3.4 Existence and Uniqueness Theorems; 3.5 Continuous Dependence on Initial Data; 3.6 Advanced Practical Problems; 4 Linear Functional Dynamic Equations; 4.1 Some Properties of Linear Functional Dynamic Equations; 4.2 First-Order Linear Functional Dynamic Equations; 4.3 Second-Order Linear Functional Dynamic Equations
4.4 Advanced Practical Problems5 Stability for First-Order Functional Dynamic Equations; 5.1 Uniform Stability; 5.2 Uniformly Asymptotical Stability; 5.3 Global Stability; 5.4 Asymptotic Stability; 5.5 Exponential Stability I; 5.6 Exponential Stability II; 5.7 Advanced Practical Problems; 6 Oscillations of First-Order Functional Dynamic Equations; 6.1 Positive Solutions; 6.2 Iterated Oscillation Criteria for First-Order Functional Dynamic Equations; 6.3 Oscillations of the Solutions of First-Order Functional Dynamic Equations with Several Delays
6.4 Nonoscillations of First-Order Functional Dynamic Equations with Several Delays6.5 Advanced Practical Problems; 7 Oscillations of Second-Order Linear Functional Dynamic Equations with a Single Delay; 7.1 Reduction to First-Order Linear Functional Dynamic Equations; 7.2 An Oscillation Criteria; 7.3 The Riccati Transformation Technique; 7.4 The Kamenev-Type Oscillation Criteria; 7.5 Advanced Practical Problems; 8 Nonoscillations of Second-Order Functional Dynamic Equations with Several Delays; 8.1 Representation of the Solutions; 8.2 A Nonoscillation Criteria; 8.3 Comparison Theorems
8.4 Explicit Nonoscillation and Oscillation Results8.5 Positive Solutions; 8.6 Advanced Practical Problems; 9 Oscillations of Second-Order Nonlinear Functional Dynamic Equations; 9.1 Oscillation Equivalence of a Class of Second-Order Nonlinear Delay Dynamic Equations and a Class of Second-Order Nonlinear Dynamic Equations; 9.2 Oscillation Criteria for a Class Second-Order Nonlinear Delay Dynamic Equations I; 9.3 Oscillation Criteria for a Class Second-Order Nonlinear Delay Dynamic Equations II; 9.4 Oscillation Criteria for a Class Second-Order Half-Linear Delay Dynamic Equations
2.3.7 Single Species Population Growth Models2.4 Advanced Practical Problems; 3 Functional Dynamic Equations. Basic Concepts, Existence, and Uniqueness Theorems; 3.1 Classification of Functional Dynamic Equations; 3.2 The Method of Steps; 3.3 The Picard-Lindelöf Theorem; 3.4 Existence and Uniqueness Theorems; 3.5 Continuous Dependence on Initial Data; 3.6 Advanced Practical Problems; 4 Linear Functional Dynamic Equations; 4.1 Some Properties of Linear Functional Dynamic Equations; 4.2 First-Order Linear Functional Dynamic Equations; 4.3 Second-Order Linear Functional Dynamic Equations
4.4 Advanced Practical Problems5 Stability for First-Order Functional Dynamic Equations; 5.1 Uniform Stability; 5.2 Uniformly Asymptotical Stability; 5.3 Global Stability; 5.4 Asymptotic Stability; 5.5 Exponential Stability I; 5.6 Exponential Stability II; 5.7 Advanced Practical Problems; 6 Oscillations of First-Order Functional Dynamic Equations; 6.1 Positive Solutions; 6.2 Iterated Oscillation Criteria for First-Order Functional Dynamic Equations; 6.3 Oscillations of the Solutions of First-Order Functional Dynamic Equations with Several Delays
6.4 Nonoscillations of First-Order Functional Dynamic Equations with Several Delays6.5 Advanced Practical Problems; 7 Oscillations of Second-Order Linear Functional Dynamic Equations with a Single Delay; 7.1 Reduction to First-Order Linear Functional Dynamic Equations; 7.2 An Oscillation Criteria; 7.3 The Riccati Transformation Technique; 7.4 The Kamenev-Type Oscillation Criteria; 7.5 Advanced Practical Problems; 8 Nonoscillations of Second-Order Functional Dynamic Equations with Several Delays; 8.1 Representation of the Solutions; 8.2 A Nonoscillation Criteria; 8.3 Comparison Theorems
8.4 Explicit Nonoscillation and Oscillation Results8.5 Positive Solutions; 8.6 Advanced Practical Problems; 9 Oscillations of Second-Order Nonlinear Functional Dynamic Equations; 9.1 Oscillation Equivalence of a Class of Second-Order Nonlinear Delay Dynamic Equations and a Class of Second-Order Nonlinear Dynamic Equations; 9.2 Oscillation Criteria for a Class Second-Order Nonlinear Delay Dynamic Equations I; 9.3 Oscillation Criteria for a Class Second-Order Nonlinear Delay Dynamic Equations II; 9.4 Oscillation Criteria for a Class Second-Order Half-Linear Delay Dynamic Equations