View source for Book:Martin Bohner/Dynamic Equations on Time Scales

{{Book|Dynamic Equations on Time Scales||||Martin Bohner|author2=Allan Peterson}}

===Online versions===
[http://web.mst.edu/~bohner/sample.pdf Chapters 1-3 hosted by Martin Bohner]<br />

===Contents===
:Preface
:Chapter 1. The Time Scales Calculus
::1.1. Basic Definitions
:::[[Time scale|page 1]]
:::[[Forward jump|Definition 1.1]]
:::[[Induction on time scales|Theorem 1.7]]
::1.2. Differentiation
:::[[Delta derivative|Definition 1.10]]
:::[[Delta differentiable implies continuous|Theorem 1.16 (i)]]
:::[[Delta derivative at right-scattered|Theorem 1.16 (ii)]]
:::[[Delta derivative at right-dense|Theorem 1.16 (iii)]]
:::[[Delta simple useful formula|Theorem 1.16 (iv)]]
:::[[Delta derivative of sum|Theorem 1.20 (i)]]
:::[[Delta derivative of constant multiple|Theorem 1.20 (ii)]]
:::[[Delta derivative of product (1)|Theorem 1.20 (iii)]] (and [[Delta derivative of product (2)|Theorem 1.20 (iii)]])
:::[[Delta derivative of reciprocal|Theorem 1.20 (iv)]]
:::[[Delta derivative of quotient|Theorem 1.20 (v)]]
:::[[Delta derivative of classical polynomial|Theorem 1.24 (i)]]
:::[[Delta derivative of reciprocal of classical polynomial|Theorem 1.24 (ii)]]
::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
:Chapter 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
:Chapter 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
:Chapter 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
:Chapter 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
:Chapter 6. Dynamic Inequalities
::6.1. Gronwall's Inequality
::6.2. Hölder'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
:Chapter 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
:Chapter 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
:Bibliography
:Index

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