Course title: Time Scales Analysis
Contact hours: 3h per week
Week 1
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10 Sept – Introduction to Time Scales: Motivation, examples (ℝ, ℤ, qℤ, mixed sets)
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12 Sept – Definition and Examples
Week 2
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17 Sept – Forward/Backward Jump Operators and Graininess Functions
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19 Sept – Classification of Points – The Topology of Time Scales
Week 3
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24 Sept – Functions and Jump Operators – The Induction Principle
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26 Sept – Delta Derivative: Definition, Examples, and Basic Rules
Week 4
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1 Oct – Higher Order Delta Differentiation – Nabla Derivatives
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3 Oct – Delta Mean Value Theorems – Delta Increasing/Decreasing Functions
Week 5
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8 Oct – Delta Convex and Concave Functions – Extreme Values
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10 Oct – Completely Delta Differentiable Functions
Week 6
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15 Oct – One-Sided Delta Derivatives
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17 Oct – Delta Chain Rules – Delta L’Hôpital’s Rule
Week 7
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22 Oct – Regulated, Rd-Continuous, and Delta Pre-Differentiable Functions
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24 Oct – Delta Indefinite Integral – The Darboux Delta Integral
Week 8
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29 Oct – The Riemann Delta Integral
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31 Oct – Alternative Definitions of the Riemann Delta Integral
Week 9
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5 Nov – Properties of the Riemann Integral
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7 Nov – Improper Delta Integrals of the First Kind
Week 10
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12 Nov – Improper Integrals of the Second Kind
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14 Nov – Delta Monomials – The Taylor Formula
Week 11
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19 Nov – Survey on Nabla Integrals – Hilger’s Complex Plane
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21 Nov – Delta Regressive Functions
Week 12
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26 Nov – The Delta Exponential Functions
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28 Nov – Delta Regressive Functions (cont.)
Week 13
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3 Dec – The Delta Exponential Functions (advanced)
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5 Dec – Delta Hyperbolic Functions
Week 14
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10 Dec – Delta Trigonometric Functions
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12 Dec – Review & Final Course Presentations
Main reference:
- Svetlin G. Georgiev and Khaled Zennir, Differential Equations: Projector Analysis on Time
Scales, Walter de Gruyter GmbH, 2024. - Svetlin G. Georgiev and Khaled Zennir, Advances on Fractional Dynamic Inequalities on Time
Scales, World Scientific, 2023. - Svetlin G. Georgiev and Khaled Zennir, Boundary Value Problems on Time Scales, Volume I, Volume II, Chapman and Hall/CRC, 2021.
