COURSE UNIT TITLE

: TIME SCALE CALCULUS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5075 TIME SCALE CALCULUS ELECTIVE 3 0 0 7

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR DOCTOR BAŞAK KARPUZ

Offered to

Mathematics (English)
Mathematics (English)

Course Objective

The aim of this course is to introduce the notion of time scale, which builds a connection between the continuous and the discrete mathematics.

Learning Outcomes of the Course Unit

1   Understanding the mathematical analysis on more general sets than reals such as the set of integers and the quantum set.
2   Unifying the usual and the discrete calculus.
3   Extending mathematical results to more general sets.
4   Understanding the effect of varying step-size in mathematical analysis proccess.
5   Defining and examining the classical special functions on general sets.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Basic Definitions, Delta-Derivative
2 Some Examples and Applications
3 Delta-Integral
4 Chain Rules
5 Monomials I
6 Miscellaneous Results
7 Hilger's Complex Plane
8 Monomials II
9 The Exponential Function
10 First-Order Dynamic Equations
11 Second-Order Dynamic Equations I
12 Second-Order Dynamic Equations II
13 The Laplace Transform
14 Some Dynamic Inequalities

Recomended or Required Reading

Textbook:
M. Bohner and A. Peterson, Dynamic equations on time scales: An introduction with applications, Birkhäuser Boston, Inc., Boston, MA, 2001.

Supplementary Books:
M. Bohner and A. Peterson, Advances in dynamic equations on time scales, Birkhäuser Boston, Inc., Boston, MA, 2003.
V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan, Dynamic systems on measure chains, Mathematics and its Applications, 370. Kluwer Academic Publishers Group, Dordrecht, 1996.

References:

Materials:
Instructor's Notes and Presentations

Planned Learning Activities and Teaching Methods

Lecture Notes
Presentation
Problem Solving

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 ASG ASSIGNMENT
2 MTE MIDTERM EXAM
3 FIN FINAL EXAM
4 FCG FINAL COURSE GRADE ASG * 0.30 + MTE * 0.30 + FIN * 0.40
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) ASG * 0.30 + MTE * 0.30 + RST * 0.40


Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

Attendance to at least 70% for the lectures is an essential requirement of this course and is the responsibility of the student. It is necessary that attendance to the lecture and homework delivery must be on time. Any unethical behavior that occurs either in presentations or in exams will be dealt with as outlined in school policy. You can find the graduate policy at http://web.fbe.deu.edu.tr

Contact Details for the Lecturer(s)

e-mail: basak.karpuz@deu.edu.tr
Office: 0 (232) 301 85 76

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 14 4 56
Preparation for midterm exam 1 31 31
Preparation for final exam 1 37 37
Midterm 1 3 3
Final 1 4 4
TOTAL WORKLOAD (hours) 173

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11
LO.144322443
LO.244222333
LO.333322433
LO.433222432
LO.533222332

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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