Time Scales Analysis (28/28)

Course title: Time Scales Analysis

Contact hours: 3h per week

Week 1

• 10 Sept – Introduction to Time Scales: Motivation, examples (ℝ, ℤ, qℤ, mixed sets)

• 12 Sept – Definition and Examples

Week 2

• 17 Sept – Forward/Backward Jump Operators and Graininess Functions

• 19 Sept – Classification of Points – The Topology of Time Scales

Week 3

• 24 Sept – Functions and Jump Operators – The Induction Principle

• 26 Sept – Delta Derivative: Definition, Examples, and Basic Rules

Week 4

• 1 Oct – Higher Order Delta Differentiation – Nabla Derivatives

• 3 Oct – Delta Mean Value Theorems – Delta Increasing/Decreasing Functions

Week 5

• 8 Oct – Delta Convex and Concave Functions – Extreme Values

• 10 Oct – Completely Delta Differentiable Functions

Week 6

• 15 Oct – One-Sided Delta Derivatives

• 17 Oct – Delta Chain Rules – Delta L’Hôpital’s Rule

Week 7

• 22 Oct – Regulated, Rd-Continuous, and Delta Pre-Differentiable Functions

• 24 Oct – Delta Indefinite Integral – The Darboux Delta Integral

Week 8

• 29 Oct – The Riemann Delta Integral

• 31 Oct – Alternative Definitions of the Riemann Delta Integral

Week 9

• 5 Nov – Properties of the Riemann Integral

• 7 Nov – Improper Delta Integrals of the First Kind

Week 10

• 12 Nov – Improper Integrals of the Second Kind

• 14 Nov – Delta Monomials – The Taylor Formula

Week 11

• 19 Nov – Survey on Nabla Integrals – Hilger’s Complex Plane

• 21 Nov – Delta Regressive Functions

Week 12

• 26 Nov – The Delta Exponential Functions

• 28 Nov – Delta Regressive Functions (cont.)

Week 13

• 3 Dec – The Delta Exponential Functions (advanced)

• 5 Dec – Delta Hyperbolic Functions

Week 14

• 10 Dec – Delta Trigonometric Functions

• 12 Dec – Review & Final Course Presentations

Main reference:

1. Svetlin G. Georgiev and Khaled Zennir, Differential Equations: Projector Analysis on Time
   Scales, Walter de Gruyter GmbH, 2024.
2. Svetlin G. Georgiev and Khaled Zennir, Advances on Fractional Dynamic Inequalities on Time
   Scales, World Scientific, 2023.
3. Svetlin G. Georgiev and Khaled Zennir, Boundary Value Problems on Time Scales, Volume I, Volume II, Chapman and Hall/CRC, 2021.