ECTS - Special Functions of Applied Mathematics
Special Functions of Applied Mathematics (MATH483) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Special Functions of Applied Mathematics | MATH483 | Area Elective | 3 | 0 | 0 | 3 | 6 |
| Pre-requisite Course(s) |
|---|
| MATH262 |
| Course Language | English |
|---|---|
| Course Type | Elective Courses |
| Course Level | Bachelor’s Degree (First Cycle) |
| Mode of Delivery | Face To Face |
| Learning and Teaching Strategies | Lecture, Question and Answer, Team/Group. |
| Course Lecturer(s) |
|
| Course Objectives | This course is intended primarily for the student of mathematics, physics or engineering who wishes to study the “special” functions in connection with the use of “hypergeometric functions”. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Gamma and Beta functions; Pochhammer`s symbol; hypergeometric series; hypergeometric differential equation; generalized hypergeometric functions; Bessel function; the functional relationships, Bessel`s differential equation; orthogonality of Bessel functions. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Infinite Products: Introduction, Definition, Necessary condition for convergence, Absolute Convergence, Uniform Convergence | pp. 1-5 |
| 2 | The Gamma and Beta Functions: The Euler Constant, The Gamma function, The order symbols, Evaluation of certain infinite products, Euler's integral for the Gamma function | pp. 8-15 |
| 3 | The Beta Function, The factorial function (Pochhammer's symbol), Legendre's duplication formula, A summation formula due to Euler | pp. 16-29 |
| 4 | Asymptotic Series: Definition of an asymptotic expansion, Asymptotic expansions about infinity, Algebraic properties, Term-by-term integration, Uniqueness, Watson's Lemma | pp. 33-41 |
| 5 | The Hypergeometric Function (HGF) : The Function F(a, b; c; z), A simple integral form, Evaluation of F(a, b; c; 1), The contiguous function relations, The HG differential equation, Logarithmic solutions of the HG equation, | pp. 45-65 |
| 6 | F(a, b; c; z) as a function of its parameters, Elementary series manipulations, Simple transformations, Relation between functions of z and 1-z, A quadratic transformation, A theorem due to Kummer, Additional properties | pp. 55-68 |
| 7 | Midterm | |
| 8 | Generalized HGF | pp. 73. 83 |
| 9 | Generalized HGF (continued) | pp. 83-93 |
| 10 | Generalized HGF (continued) | pp. 93-102 |
| 11 | Bessel Functions: Remarks, Definition, Bessel's differential equation, Differential recurrence relations | pp. 108-111 |
| 12 | A pure recurrence relation, A generating function, Bessel's Integral, Index Half an odd integer | pp. 111-114 |
| 13 | Modified Bessel functions, Neumann polynomials, Neumann series | pp. 116-119 |
| 14 | The Confluent HGF: Basic properties, Kummer's first formula, Kummer's second formula. | pp. 123-125 |
| 15 | Review | |
| 16 | Final |
Sources
| Course Book | 1. Earl D. Rainville, Special Functions, MacMillan, New York, 1960. |
|---|---|
| Other Sources | 2. Z. X. Wang, D. R. Guo, Special Functions, World Scientific, 1989 |
| 3. N. N. Lebedev, Special Functions and Their Aslications, Prentice-Hall, 1965 |
Evaluation System
| Requirements | Number | Percentage of Grade |
|---|---|---|
| Attendance/Participation | - | - |
| Laboratory | - | - |
| Application | - | - |
| Field Work | - | - |
| Special Course Internship | - | - |
| Quizzes/Studio Critics | - | - |
| Homework Assignments | 5 | 10 |
| Presentation | - | - |
| Project | - | - |
| Report | - | - |
| Seminar | - | - |
| Midterms Exams/Midterms Jury | 2 | 50 |
| Final Exam/Final Jury | 1 | 40 |
| Toplam | 8 | 100 |
| Percentage of Semester Work | 60 |
|---|---|
| Percentage of Final Work | 40 |
| Total | 100 |
Course Category
| Core Courses | |
|---|---|
| Major Area Courses | X |
| Supportive Courses | |
| Media and Managment Skills Courses | |
| Transferable Skill Courses |
The Relation Between Course Learning Competencies and Program Qualifications
| # | Program Qualifications / Competencies | Level of Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Acquires skills to use the advanced theoretical and applied knowledge obtained at the mathematics bachelors program to do further academic and scientific research in both mathematics-based graduate programs and public or private sectors. | X | ||||
| 2 | Transplants and applies the theoretical and applicable knowledge gained in their field to the secondary education by using suitable tools and devices. | X | ||||
| 3 | Acquires the skill of choosing, using and improving problem solving techniques which are needed for modeling and solving current problems in mathematics or related fields by using the obtained knowledge and skills. | X | ||||
| 4 | Acquires analytical thinking and uses time effectively in the process of deduction. | X | ||||
| 5 | Acquires basic software knowledge necessary to work in the computer science related fields and together with the skills to use information technologies effectively. | X | ||||
| 6 | Obtains the ability to collect data, to analyze, interpret and use statistical methods necessary in decision making processes. | X | ||||
| 7 | Acquires the level of knowledge to be able to work in the mathematics and related fields and keeps professional knowledge and skills up-to-date with awareness in the importance of lifelong learning. | X | ||||
| 8 | Takes responsibility in mathematics related areas and has the ability to work affectively either individually or as a member of a team. | X | ||||
| 9 | Has proficiency in English language and has the ability to communicate with colleagues and to follow the innovations in mathematics and related fields. | X | ||||
| 10 | Has the ability to communicate ideas with peers supported by qualitative and quantitative data. | X | ||||
| 11 | Has professional and ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. | X | ||||
ECTS/Workload Table
| Activities | Number | Duration (Hours) | Total Workload |
|---|---|---|---|
| Course Hours (Including Exam Week: 16 x Total Hours) | |||
| Laboratory | |||
| Application | |||
| Special Course Internship | |||
| Field Work | |||
| Study Hours Out of Class | 16 | 3 | 48 |
| Presentation/Seminar Prepration | |||
| Project | |||
| Report | |||
| Homework Assignments | 5 | 8 | 40 |
| Quizzes/Studio Critics | |||
| Prepration of Midterm Exams/Midterm Jury | 2 | 12 | 24 |
| Prepration of Final Exams/Final Jury | 1 | 18 | 18 |
| Total Workload | 130 | ||