Information Of Programmes

INSTITUTE OF SCIENCE / MAT587 - MATHEMATICS

Code: MAT587

Course Title: Q-ANALYSIS I

Theoretical+Practice: 3+0

ECTS: 6

Year/Semester of Study

1 / Fall Semester

Level of Course

2nd Cycle Degree Programme

Type of Course

Optional

Department

MATHEMATICS

Pre-requisities and Co-requisites

None

Mode of Delivery

Face to Face

Teaching Period

14 Weeks

Name of Lecturer

SURE KÖME (sure.kome@nevsehir.edu.tr)

Name of Lecturer(s)

Language of Instruction

Turkish

Work Placement(s)

None

Objectives of the Course

The purpose of this course having detailed knowledge Quantum Calculus which are important during graduate and doctorate education

Learning Outcomes		PO	MME
The students who succeeded in this course:
LO-1	Recognize the q-derivetive and h-derivative concepts.	PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other.	Examination Term Paper
LO-2	Learns to q-derivative of binomials.	PO-1 Fundamental theorems of about some sub-theories of Analysis, Applied Mathematics, Geometry, and Algebra can apply to new problems. PO-2 Ability to assimilate mathematic related concepts and associate these concepts with each other.	Examination Term Paper
PO: Programme Outcomes MME:Method of measurement & Evaluation

Course Contents
q-Derivative, h-Derivative, q-derivatives of binomials, q-binomial coefficients, q-Trigonometrik functions
Weekly Course Content
Week	Subject	Learning Activities and Teaching Methods
1	Introduction to quantum calculus	Oral expression, discussion, question-answer
2	q-derivative and h- derivative	Oral expression, discussion, question-answer
3	Generalized Taylor’s formula for Polynomials	Oral expression, discussion, question-answer
4	q-analogue of 〖(x-a)〗^n and q-derivatives of binomials	Oral expression, discussion, question-answer
5	q-Taylor’s formula for Polynomials	Oral expression, discussion, question-answer
6	Gauss’s binomial formula	Oral expression, discussion, question-answer
7	Properties of q-Binomial coefficients	Oral expression, discussion, question-answer
8	mid-term exam
9	q-Binomial coefficients	Oral expression, discussion, question-answer
10	q-Taylor’s formula for formal power series and Heine’s binomial formula	Oral expression, discussion, question-answer
11	Two Euler’s identities	Oral expression, discussion, question-answer
12	Two q-exponential functions	Oral expression, discussion, question-answer
13	q-Trigonometric functions	Oral expression, discussion, question-answer
14	Jacobi’s triple product identity	Oral expression, discussion, question-answer
15	Classical partition function and Euler’s product formula	Oral expression, discussion, question-answer
16	final exam
Recommend Course Book / Supplementary Book/Reading
1	Kac, Victor, and Pokman Cheung. Quantum calculus. Springer Science & Business Media, 2001.
Required Course instruments and materials
Course book, Laptop computer

Assessment Methods
Type of Assessment	Week	Hours	Weight(%)
mid-term exam	8	2	40
Other assessment methods
1.Oral Examination
2.Quiz
3.Laboratory exam
4.Presentation
5.Report
6.Workshop
7.Performance Project
8.Term Paper
9.Project
final exam	16	2	60

Student Work Load
Type of Work	Weekly Hours	Number of Weeks	Work Load
Weekly Course Hours (Theoretical+Practice)	3	14	42
Outside Class
a) Reading	5	14	70
b) Search in internet/Library	2	14	28
c) Performance Project			0
d) Prepare a workshop/Presentation/Report			0
e) Term paper/Project			0
Oral Examination			0
Quiz			0
Laboratory exam			0
Own study for mid-term exam	4	4	16
mid-term exam	2	1	2
Own study for final exam	5	4	20
final exam	2	1	2
			0
			0
Total work load;			180