ECTS - Classical Orthogonal Polynomials
Classical Orthogonal Polynomials (MATH484) Course Detail
| Course Name | Course Code | Season | Lecture Hours | Application Hours | Lab Hours | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| Classical Orthogonal Polynomials | MATH484 | Elective Courses | 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 use the “orthogonal” polynomials associated with the names of Legendre, Hermite and Languerre. It aims at providing in a compact form most of the properties of these polynomials in the simplest possible way. |
| Course Learning Outcomes |
The students who succeeded in this course;
|
| Course Content | Generating functions; orthogonal polynomials; Legendre polynomials; Hermite polynomials; Laguerre polynomials; Tchebicheff polynomials; Gegenbauer polynomials. |
Weekly Subjects and Releated Preparation Studies
| Week | Subjects | Preparation |
|---|---|---|
| 1 | Generating Functions: The generating function concept, Generating functions of the form G(2xt-t^2), Sets generated by exp(t)f(xt), The generating functions A(t)exp[-xt/(1-t)] | pp. 129-137 |
| 2 | Orthogonal Polynomials: Simple sets of polynomials, Orthogonality, An equivalent condition for orthogonality, Zeros of orthogonal polynomials | pp. 147-150 |
| 3 | Expansion of polynomials, The three-term recurrence relation, The Cristoffel-Darboux formula, Normalization; Bessel's inequality | pp. 150-155 |
| 4 | Legendre Polynomials: A generating function, Differential recurrence relation, the pure recurrence relation, Legendre's differential equation | pp. 157-161 |
| 5 | The Rodrigues formula, Hypergeometric forms of P_n(x), Special properties of P_n(x), Laplace's first integral form, Some bounds on P_n(x) | pp. 165-181 |
| 6 | Orthogonality, An expansion theorem, Expansion of analytic functions | pp. 187-190 |
| 7 | Midterm | |
| 8 | Hermite Polynomials: Definition, Recurrence relations, The Rodrigues formula, Other generating functions | pp. 191-196 |
| 9 | Integrals, The Hermite polynomials as a 2_F_0, Differential equation, Orthogonality, Expansion of polynomials, More generating functions | pp. 200-203 |
| 10 | Laguerre Polynomials: The Laguerre polynomials, Generating functions, Recurrence relations, The Rodrigues formula | pp. 204-213 |
| 11 | Christffel-Darboux Formula, The differential equation, Orthogonality, Expansion of polynomials, Special properties, Other generating functions, The simple Laguerre polynomials | pp.254-260 |
| 12 | Chebyshev polynomials: A generating function relation, Recurrence relation, Some other representations, Differential equation, Orthogonality | pp. 261-269 |
| 13 | Gegenbauer Polynomials: A generating function relation, Recurrence relation, Some other representations | s. 276-283 |
| 14 | Differential equation, Orthogonality, Expansion of polynomials, Rodrigues formula | p. 285, pp. 299-301 |
| 15 | Review | |
| 16 | Final Exam |
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 Applications, 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 | |
| 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 | ||