Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
5MATH385SPECIAL FUNCTIONS OF APPLIED MATHEMATICS3+036

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course This course is intended primarily for the student of mathematics, physics or engineering who wishes to study special functions. After successful completion of this course, students will be able to develop key concepts in special functions.
Course Content Gamma and Beta functions. Pochhammer s symbol. Hypergeometric series. Hypergeometric differential equation. Ordinary and confluent hypergeometric functions. Generalized hypergeometric functions. The contiguous function relations. Orthogonal polynomials. Bessel function. The functional relationships. Bessel s differential equation. Orthogonality of Bessel functions.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Prof.Dr. Oğuz Yılmaz
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Temme, N.M., “Special Functions”, Wiley, 1996
Rainville, E.D., “Special Functions”, Macmillan, 1960
Andrews, G.E et.al., “Special Functions”, Cambridge University Press, 1999

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 50
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 50
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 36 36
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 27 27
Exams and Exam Preparations 1 81 81
Total Work Load   Number of ECTS Credits 5 144

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 have basic knowledge in special functions
2 solve problems associated with special functions
3 analyze advanced problems arising in physics and engineering
4 use special functions to solve differential and integral equations


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Gamma and Beta functions Rainville, E.D., “Special Functions”, Macmillan, 1960
2 Pochhammer s symbol Rainville, E.D., “Special Functions”, Macmillan, 1960
3 Hypergeometric series Rainville, E.D., “Special Functions”, Macmillan, 1960
4 Hypergeometric differential equation Rainville, E.D., “Special Functions”, Macmillan, 1960
5 Ordinary and confluent hypergeometric functions Rainville, E.D., “Special Functions”, Macmillan, 1960
6 Hypergeometric functions Rainville, E.D., “Special Functions”, Macmillan, 1960
7 Generalized hypergeometric functions Rainville, E.D., “Special Functions”, Macmillan, 1960
8 Contiguous function relations Rainville, E.D., “Special Functions”, Macmillan, 1960
9 Orthogonal polynomials Rainville, E.D., “Special Functions”, Macmillan, 1960
10 Bessel functions Rainville, E.D., “Special Functions”, Macmillan, 1960
11 Functional relationships Rainville, E.D., “Special Functions”, Macmillan, 1960
12 Bessel functions Rainville, E.D., “Special Functions”, Macmillan, 1960
13 Bessel s differential equation Rainville, E.D., “Special Functions”, Macmillan, 1960
14 Orthogonality of Bessel functions Rainville, E.D., “Special Functions”, Macmillan, 1960


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 3 4 3
C2 4 3 4 3
C3 4 3 4 3
C4 4 3 4 3

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=163251&lang=en