Nevşehir Hacı Bektaş Veli University Course Catalogue

Information Of Programmes

INSTITUTE OF SCIENCE / MAT588 - MATHEMATICS

Code: MAT588 Course Title: Q-ANALYSIS II Theoretical+Practice: 3+0 ECTS: 6
Year/Semester of Study 1 / Spring 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 h-derivative and h-integral 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-Gamma and q-Beta functions 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
h-derivative, h-integral, q-Gamma function, q-Beta function
Weekly Course Content
Week Subject Learning Activities and Teaching Methods
1 q-Hypergeometric functions and Heine’s formula Oral expression, discussion, question-answer
2 More information on Heine’s formula Oral expression, discussion, question-answer
3 Ramanujan product formula Oral expression, discussion, question-answer
4 Explicit formulas for Sums of two and four squares Oral expression, discussion, question-answer
5 Explicit formulas for Sums of two and four triangular numbers Oral expression, discussion, question-answer
6 q-antiderivative Oral expression, discussion, question-answer
7 Jackson integral Oral expression, discussion, question-answer
8 mid-term exam
9 Fundamental theorem of q-calculus Oral expression, discussion, question-answer
10 q-Gamma and q-Beta functions Oral expression, discussion, question-answer
11 h-derivative and h-integral Oral expression, discussion, question-answer
12 Bernoulli polynomials and Bernoulli numbers Oral expression, discussion, question-answer
13 Sums of powers Oral expression, discussion, question-answer
14 Euler-Maclaurin formula Oral expression, discussion, question-answer
15 Symmetric quantum calculus 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