Difference Equations and Applications provides unique coverage of high-level topics in the application of difference equations and dynamical systems. The book begins with extensive coverage of the calculus of difference equations, including contemporary topics on l_p stability, exponential stability, and parameters that can be used to qualitatively study solutions to non-linear difference equations, including variations of parameters and equations with constant coefficients, before moving on to the Z-Transform and its various functions, scalings, and applications. It covers systems, Lyapunov functions, and stability, a subject rarely covered in competitor titles, before concluding with a comprehensive section on new variations of parameters. Exercises are provided after each section, ranging from an easy to medium level of difficulty. When finished, students are set up to conduct meaningful research in discrete dynamical systems. In summary, this book is a comprehensive resource that delves into the mathematical theory of difference equations while highlighting their practical applications in various dynamic systems. It is highly likely to be of interest to students, researchers, and professionals in fields where discrete modeling and analysis are essential.
1. Difference Equations and Applications - p. Page i 2. Cover - p. Page i 3. Front Matter - p. Page ii 4. Table of Contents - p. Page iii 5. Copyright - p. Page iii 6. Dedication - p. Page iv 7. Contents - p. Page vi 8. Preface - p. Page vi 9. List of Illustrations - p. Page xi 10. List of Tables - p. Page xii 11. Chapter 1 : The calculus of difference equations - p. Page xii 12. Chapter 2 : Linear difference equations - p. Page 25 13. Chapter 3 : Z-transform - p. Page 81 14. Chapter 4 : Systems - p. Page 136 15. Chapter 5 : Stability - p. Page 164 16. Chapter 6 : Lyapunov functions - p. Page 233 17. Chapter 7 : New variation of parameters - p. Page 284 18. Appendix A : Banach spaces - p. Page 307 19. Bibliography - p. Page 317 20. Index - p. Page 317
Difference Equations and Applications provides unique coverage of high-level topics in the application of difference equations and dynamical systems. The book begins with extensive coverage of the calculus of difference equations, including contemporary topics on l_p stability, exponential stability, and parameters that can be used to qualitatively study solutions to non-linear difference equations, including variations of parameters and equations with constant coefficients, before moving on to the Z-Transform and its various functions, scalings, and applications. It covers systems, Lyapunov functions, and stability, a subject rarely covered in competitor titles, before concluding with a comprehensive section on new variations of parameters. Exercises are provided after each section, ranging from an easy to medium level of difficulty. When finished, students are set up to conduct meaningful research in discrete dynamical systems. In summary, this book is a comprehensive resource that delves into the mathematical theory of difference equations while highlighting their practical applications in various dynamic systems. It is highly likely to be of interest to students, researchers, and professionals in fields where discrete modeling and analysis are essential.
1. Difference Equations and Applications - p. Page i 2. Cover - p. Page i 3. Front Matter - p. Page ii 4. Table of Contents - p. Page iii 5. Copyright - p. Page iii 6. Dedication - p. Page iv 7. Contents - p. Page vi 8. Preface - p. Page vi 9. List of Illustrations - p. Page xi 10. List of Tables - p. Page xii 11. Chapter 1 : The calculus of difference equations - p. Page xii 12. Chapter 2 : Linear difference equations - p. Page 25 13. Chapter 3 : Z-transform - p. Page 81 14. Chapter 4 : Systems - p. Page 136 15. Chapter 5 : Stability - p. Page 164 16. Chapter 6 : Lyapunov functions - p. Page 233 17. Chapter 7 : New variation of parameters - p. Page 284 18. Appendix A : Banach spaces - p. Page 307 19. Bibliography - p. Page 317 20. Index - p. Page 317
