Time Scales Analysis

by Svetlin G. Georgiev

Time scale theory was first initiated by Stefan Hilger in 1988 in his PhD thesis to unify both approaches of dynamic modelling: difference and differential equations. Similar ideas have been used before and go back in the introduction of the Riemann-Stieltjes integral which unifies sums and integrals. Many results to differential equations carry over easily to corresponding results for difference equations, while other results seem to be totally different in nature. Because of these reasons, tim

Description from LibreTexts.

Publisher
Sorbonne University
Subjects
Mathematics
Licence
CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read
Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. Chapter 1: Time Scales Analysis PDF
  7. Chapter 2: Definition. Examples
  8. Chapter 3: Forward Jump Operators, Backward Jump Operators and Graininess Functions
  9. Chapter 4: A Classification of Points
  10. Chapter 5: The Topology of Time Scales
  11. Chapter 6: Functions and Jump Operators
  12. Chapter 7: The Induction Principle
  13. Chapter 8: Differentiable Functions of One Variable
  14. Chapter 9: Higher Order Delta Differentiation
  15. Chapter 10: Nabla Derivatives
  16. Chapter 11: Regulated, rd-Continuous, and Pre-Differentiable Functions
  17. Chapter 12: The Delta Integral
  18. Chapter 13: Improper Integrals of the First Kind
  19. Chapter 14: Improper Integrals of the Second Kind
  20. Chapter 15: Sequences of Functions
  21. Chapter 16: Series of Functions
  22. Chapter 17: Exam
  23. Chapter 18: Homeworks
  24. Chapter 19: A Project
  25. Chapter 20: A Supplementary Material- Matrix Exponential Functions on Time Scales
  26. Page 20.1: Regressive Matrix-Valued Functions
  27. Page 20.2: Definition for a Matrix Exponential Function. Properties
  28. Page 20.3: The Putzer Algorithm on Time Scales
  29. Chapter 21: A Supplementary Material- Generalized Zeros
  30. Page 21.1: Definition. Properties
  31. Page 21.2: The Rolle Theorem
  32. Page 21.3: The Knesser Theorem
  33. Chapter 22: A Supplementary Material- Linear Integral Inequalities
  34. Page 22.1: Gronwall-Type Integral Inequalities
  35. Page 22.2: Pachpatte Integral Inequalities
  36. Page 22.3: Dragomir-Type Integral Inequalities
  37. Chapter 23: A Supplementary Material- Diamond Alpha Calculus on Time Scales
  38. Page 23.1: Diamond Alpha Differential Calculus
  39. Page 23.2: Diamond Alpha Integral Calculus
  40. Page 23.3: Some Steffensen Inequalities
  41. Chapter 24: A Supplementary Material- Inequalities for Convex Functions
  42. Page 24.1: Inequalities for Exponentially Convex Functions
  43. Page 24.2: Inequalities for Strongly r-Convex Functions
  44. Page 24.3: Inequalities for Exponentially s-Convex Functions
  45. Back Matter
  46. Index
  47. Glossary
  48. Detailed Licensing
  49. Detailed Licensing