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Dynamic Equations on Time Scales An Introduction with Applications

On becoming familiar with difference equations and their close re­ lation to differential equations, I was in hopes that the theory of difference equations could be brought completely abreast with that for ordinary differential equations. [HUGH L. TURRITTIN, My Mathematical Expectations, Springer Le...

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Bibliographic Details
Main Authors: Bohner, Martin, Peterson, Allan (Author)
Format: eBook
Language:English
Published: Boston, MA Birkhäuser 2001, 2001
Edition:1st ed. 2001
Subjects:
Mathematical Analysis
Computational Mathematics And Numerical Analysis
Mathematics / Data Processing
Control Theory
Systems Theory, Control
Analysis
System Theory
Applications Of Mathematics
Mathematics
Differential Equations
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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

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