# Difference between revisions of "Book:Martin Bohner/Dynamic Equations on Time Scales"

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::1.1. Basic Definitions | ::1.1. Basic Definitions | ||

:::[[Time scale|page 1]] | :::[[Time scale|page 1]] | ||

− | :::[[Forward jump|Definition 1.1]] | + | :::[[Forward jump|Definition $1.1$]] |

− | :::[[Induction on time scales|Theorem 1.7]] | + | :::[[Induction on time scales|Theorem $1.7$]] |

::1.2. Differentiation | ::1.2. Differentiation | ||

− | :::[[Delta derivative|Definition 1.10]] | + | :::[[Delta derivative|Definition $1.10$]] |

− | :::[[Delta differentiable implies continuous|Theorem 1.16 (i)]] | + | :::[[Delta differentiable implies continuous|Theorem $1.16 (i)$]] |

− | :::[[Delta derivative at right-scattered|Theorem 1.16 (ii)]] | + | :::[[Delta derivative at right-scattered|Theorem $1.16 (ii)$]] |

− | :::[[Delta derivative at right-dense|Theorem 1.16 (iii)]] | + | :::[[Delta derivative at right-dense|Theorem $1.16 (iii)$]] |

− | :::[[Delta simple useful formula|Theorem 1.16 (iv)]] | + | :::[[Delta simple useful formula|Theorem $1.16 (iv)$]] |

− | :::[[Delta derivative of sum|Theorem 1.20 (i)]] | + | :::[[Delta derivative of sum|Theorem $1.20 (i)$]] |

− | :::[[Delta derivative of constant multiple|Theorem 1.20 (ii)]] | + | :::[[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 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 reciprocal|Theorem $1.20 (iv)$]] |

− | :::[[Delta derivative of quotient|Theorem 1.20 (v)]] | + | :::[[Delta derivative of quotient|Theorem $1.20 (v)$]] |

− | :::[[Delta derivative of classical polynomial|Theorem 1.24 (i)]] | + | :::[[Delta derivative of classical polynomial|Theorem $1.24 (i)$]] |

− | :::[[Delta derivative of reciprocal of classical polynomial|Theorem 1.24 (ii)]] | + | :::[[Delta derivative of reciprocal of classical polynomial|Theorem $1.24 (ii)$]] |

::1.3. Examples and Applications | ::1.3. Examples and Applications | ||

::1.4. Integration | ::1.4. Integration |

## Revision as of 15:07, 25 September 2016

## Martin Bohner and Allan Peterson: *Dynamic Equations on Time Scales*

### Online versions

Chapters 1-3 hosted by Martin Bohner

### Contents

- Preface
- Chapter 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

- 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