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 | X |
|---|---|
| Major Area Courses | |
| 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 | Acquiring the skills of understanding, explaining, and using the fundamental concepts and methods of economics | |||||
| 2 | Acquiring the skills of macro level economic analysis | |||||
| 3 | Acquiring the skills of micro level economic analysis | |||||
| 4 | Understanding the formulation and implementation of economic policies at the local, national, regional, and/or global level | |||||
| 5 | Learning different approaches on economic and related issues | |||||
| 6 | Acquiring the quantitative and/or qualitative techniques in economic analysis | X | ||||
| 7 | Improving the ability to use the modern software, hardware and/or technological devices | |||||
| 8 | Developing intra-disciplinary and inter-disciplinary team work skills | X | ||||
| 9 | Acquiring an open-minded behavior through encouraging critical analysis, discussions, and/or life-long learning | |||||
| 10 | Adopting work ethic and social responsibility | |||||
| 11 | Developing the skills of communication. | |||||
| 12 | Improving the ability to effectively implement the knowledge and skills in at least one of the following areas: economic policy, public policy, international economic relations, industrial relations, monetary and financial affairs. | 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 | ||