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 | Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area | |||||
| 2 | Can apply gained knowledge and problem solving abilities in inter-disciplinary research | |||||
| 3 | Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary | |||||
| 4 | Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study | |||||
| 5 | Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework | |||||
| 6 | Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility | |||||
| 7 | Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation | |||||
| 8 | To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) | |||||
| 9 | Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge | |||||
| 10 | Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. | |||||
| 11 | Has professional 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. | |||||
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 | ||