GAZI UNIVERSITY INFORMATION PACKAGE - 2019 ACADEMIC YEAR

COURSE DESCRIPTION
SPECIAL FUNCTIONS IN APPLIED MATHEMATICS/MAT- 434
Course Title: SPECIAL FUNCTIONS IN APPLIED MATHEMATICS
Credits 3 ECTS 5
Semester 8 Compulsory/Elective Elective
COURSE INFO
 -- LANGUAGE OF INSTRUCTION
  Turkish
 -- NAME OF LECTURER(S)
  Assoc. Prof. Esra ERKUŞ DUMAN
 -- WEB SITE(S) OF LECTURER(S)
  http://websitem.gazi.edu.tr/site/eduman
 -- EMAIL(S) OF LECTURER(S)
  eduman@gazi.edu.tr
 -- LEARNING OUTCOMES OF THE COURSE UNIT
The concept of Gamma and Beta functions and to get their applications
The concept of Pochammer symbol and hypergeometric function
To solve the Gauss differential equation and to get their applications
To solve the Kummer differential equation and the concept of confluent hypergeometric function
The concept of orthogonal polynomials and generating functions
To solve some known differential equations and to get some special functions which their solutions
The concept of Legendre polynomials, to get their Rodrigues formula
To get generating function and recurrence relation of Legendre polynomials
To prove orthogonality of Legendre polynomials and to get their norm
Via methods which is used for Legendre polynomials, to get same properties of other special functions
 -- MODE OF DELIVERY
  The mode of delivery of this course is Face to face
 -- PREREQUISITES AND CO-REQUISITES
  The mode of delivery of this course is Face to face
 -- RECOMMENDED OPTIONAL PROGRAMME COMPONENTS
  Differential equations, Applied mathematics
 --COURSE CONTENT
1. Week  Basic concepts and definitions
2. Week  Gamma and Beta functions
3. Week  Pochammer symbol, Hypergeometric function and Gauss Differential equation
4. Week  Kummer equation and Konfluent hypergeometric functions
5. Week  Generating function, Bilateral and Bilinear generating functions
6. Week  Orthogonal functions system, examples of orthogonal polynomials
7. Week  Differential equations yield by orthogonal functions
8. Week  Mid-Term Exam
9. Week  Rodrigues formula for Legendre polynomials
10. Week  Generating functions for Legendre polynomials
11. Week  Recurrence relations for Legendre polynomials
12. Week  Orthogonality and norm of Legendre polynomials
13. Week  Series representations by Legendre polynomials
14. Week  Via methods which is used for Legendre polynomials, to get same properties of other special functions
15. Week  Applications corresponding to special functions
16. Week  Final Exam
 -- RECOMMENDED OR REQUIRED READING
  Earl D. Rainville, Special Functions. Macmillan, 1960. Andrews, G.E., Askey, R. and Roy, R. ,Special Functions. Cambridge University Pres, 1999.
 -- PLANNED LEARNING ACTIVITIES AND TEACHING METHODS
  Lecture, Question & Answer, Demonstration, Drill - Practise
 -- WORK PLACEMENT(S)
  None
 -- ASSESSMENT METHODS AND CRITERIA
 
Quantity
Percentage
 Mid-terms
1
30
 Assignment
1
10
 Exercises
0
0
 Projects
0
0
 Practice
0
0
 Quiz
0
0
 Contribution of In-term Studies to Overall Grade  
40
 Contribution of Final Examination to Overall Grade  
60
 -- WORKLOAD
 Efficiency  Total Week Count  Weekly Duration (in hour)  Total Workload in Semester
 Theoretical Study Hours of Course Per Week
14
3
42
 Practising Hours of Course Per Week
0
0
0
 Reading
9
3
27
 Searching in Internet and Library
10
2
20
 Designing and Applying Materials
0
0
0
 Preparing Reports
0
0
0
 Preparing Presentation
0
0
0
 Presentation
0
0
0
 Mid-Term and Studying for Mid-Term
1
12
12
 Final and Studying for Final
1
20
20
 Other
10
1
10
 TOTAL WORKLOAD: 
131
 TOTAL WORKLOAD / 25: 
5.24
 ECTS: 
5
 -- COURSE'S CONTRIBUTION TO PROGRAM
NO
 PROGRAM LEARNING OUTCOMES
1
2
3
4
5
1To train individuals who are contemporary, entrepreneur and have unique and aesthetic values, self-confidence and capable of independent decision-making.X
2To give good education in the program fields as algebra, geometry, applied mathematics, topology and analysis in order to be equipped with enough mathematics.X
3To teach mathematical thinking methods in order to improve the ability to express mathematics both orally and in writing.X
4To train individuals who are knowledgeable about the history of mathematics and the production of scientific knowledge and can follow developments in these disciplines.X
5To provide necessary equipments to take positions such areas as banking, finance, econometrics, and actuarial.
6To acquire ability to solve problems encountered in real life by means of mathematical modeling using mathematical methods.X
7To provide ability to do necessary resource researches in the areas of mathematics and to use accessed information.X
8To give appropriate training in such areas as in computer programming and creating algorithms in order to take parts in developing IT sector.
9To gain substructure to be able to study at graduate level.X
10To enable the student to gain the ability of relating mathematics with the other sciences.X