Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | MAT507 | ADVANCED CALCULUS | Elective | 1 | 2 | 6 |
|
Level of Course Unit |
Second Cycle |
Objectives of the Course |
To inform to student the definition and basic properties of elliptic functions |
Name of Lecturer(s) |
Doç. Dr. Abdullah Sönmezoğlu |
Learning Outcomes |
1 | To define the concepts of the Period, topological group, elliptic function and infinite multiplication | 2 | Learn and apply basic properties of elliptic functions |
|
Mode of Delivery |
Formal Education |
Prerequisites and co-requisities |
None |
Recommended Optional Programme Components |
None |
Course Contents |
periods
Topological groups
A simple periodic function
Cages and fundemental regions
Tor
General properties of elliptic functions
Uniform and normal convergence
infinite products
Weierstrass functions
Body of elliptic functions
Zero the polar areas and the creation of elliptic functions
The main part of the creation of the elliptic functions
Topological properties of elliptic functions
Real elliptic curves
Elliptic integrals, Fourier series, Fourier integrals, Infinite product series, Addition method, Abel convergence, Cesaro convergence, Euler-Maclaurin total formulas, Abel's inequality |
Weekly Detailed Course Contents |
|
1 | periods | | | 2 | Topological groups | | | 3 | A simple periodic function | | | 4 | Cages and fundemental regions | | | 5 | Tor | | | 6 | General properties of elliptic functions | | | 7 | infinite products | | | 8 | Mid-Term Exam | | | 9 | Uniform and normal convergence | | | 10 | Weierstrass functions | | | 11 | Body of elliptic functions | | | 12 | Zero the polar areas and the creation of elliptic functions | | | 13 | The main part of the creation of the elliptic functions | | | 14 | Topological properties of elliptic functions | | | 15 | Real elliptic curves | | | 16 | Final Exam | | |
|
Recommended or Required Reading |
G. A. Jones and D. Singerman, Complex Functions, Cambridge University Press, 1987. |
Planned Learning Activities and Teaching Methods |
|
Assessment Methods and Criteria | |
Midterm Examination | 1 | 100 | SUM | 100 | |
Final Examination | 1 | 100 | SUM | 100 | Term (or Year) Learning Activities | 40 | End Of Term (or Year) Learning Activities | 60 | SUM | 100 |
| Language of Instruction | | Work Placement(s) | None |
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Workload Calculation |
|
Midterm Examination | 1 | 2 | 2 |
Final Examination | 1 | 2 | 2 |
Individual Study for Mid term Examination | 14 | 6 | 84 |
Individual Study for Final Examination | 14 | 6 | 84 |
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Contribution of Learning Outcomes to Programme Outcomes |
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Yozgat Bozok University, Yozgat / TURKEY • Tel (pbx): +90 354 217 86 01 • e-mail: uo@bozok.edu.tr |