| Course Name | Code | Semester | T+U Hours | Credit | ECTS |
|---|---|---|---|---|---|
| Advanced Mathematical In Physics II | FIZ 603 | 0 | 3 + 0 | 3 | 6 |
| Precondition Courses | |
| Recommended Optional Courses | |
| Course Language | Turkish |
| Course Level | Doctorate Degree |
| Course Type | Optional |
| Course Coordinator | Dr.Öğr.Üyesi NAGİHAN DELİBAŞ |
| Course Lecturers | |
| Course Assistants | |
| Course Category | Field Proper Education |
| Course Objective | To gain the ability solving problems related with complex analysis and to inform students about some special topics such as group theory and chaos |
| Course Content | Complex Numbers, Residue Theorem, Integral Theorem, Variational Principle, Tensor Analysis, Fundamental Concepts in Group Theory, Chaos |
| # | Course Learning Outcomes | Teaching Methods | Assessment Methods |
|---|---|---|---|
| 1 | Defines Riemann surfaces for a given function | Lecture, Question-Answer, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, |
| 2 | Expresses the Residue theorem and solves integrals by using this theorem | Lecture, Question-Answer, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, |
| 3 | Solves differential equations by using the technique of Fourier transform | Lecture, Question-Answer, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, |
| 4 | Expresses the properties of multivalent functions | Lecture, Question-Answer, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, |
| 5 | Writes Euler-Lagrange equations and solves physics problems by using these equations | Lecture, Question-Answer, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, |
| 6 | Defines the concept of group by giving examples | Lecture, Question-Answer, Drilland Practice, Self Study, Problem Solving, | Testing, Homework, |
| Week | Course Topics | Preliminary Preparation |
|---|---|---|
| 1 | Complex Numbers, Cauchy-Riemann Equations | [1] pp 111-141 |
| 2 | Complex Functions, Critical Points, Complex Integration | [1] pp 141-163 |
| 3 | Cauchy´s Integral Formula | [1] pp 163-188 |
| 4 | Residue Theorem | [1] pp 191-214 |
| 5 | Multivalent Functions, Riemann Surfaces | [1] pp 215-232 |
| 6 | Periodic Functions, Fourier Series | [1] pp 385-406 |
| 7 | Fourier Transforms | [1] pp 407-428 |
| 8 | Laplace Transforms | [1] pp 429-444 |
| 9 | Midterm Exam | |
| 10 | Calculus of Variations, Euler-Lagrange Equations | [2] pp 355-375 |
| 11 | Applications of Variational Calculus | [2] pp 375-386 |
| 12 | Tensor Analysis | [2] pp 146-175 |
| 13 | Introduction to Group Theory | [3] pp 241-261 |
| 14 | Nonlinear Methods and Chaos | [3] pp 1079-1107 |
| Resources | |
|---|---|
| Course Notes | [1] Öztürk E., Fizik ve Mühendislikte Matematik Yöntemler, Seçkin Yayıncılık, 2011<br>[2] Önem C., Mühendislik ve Fizikte Matematik Metodlar, Birsen Yayınevi, 1998<br>[3] Arfken G.B., Weber H.J., Mathematical Methods for Physicists, Elsevier Academic, 2005 |
| Course Resources | |
| Order | Program Outcomes | Level of Contribution | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Using the knowledge of graduate and postgraduate education in postgraduate level. | X | |||||
| 2 | To be able to make literature search, presentation, experimental setup preparation, application and explication of results. | X | |||||
| 3 | To be able to join interdisciplinary and multidisciplinary team works. | X | |||||
| 4 | Sharing their concepts in seminar, symposium, conference etc. by using the skills of self-study. | ||||||
| 5 | To be able to prepare a scientific publication with the knowledges obtained from graduate and postgraduate studies. | ||||||
| 6 | Design and apply theoretical, experimental and model-based research; the ability to analyze and resolve complex problems that arise during this | ||||||
| Evaluation System | |
|---|---|
| Semester Studies | Contribution Rate |
| 1. Ara Sınav | 50 |
| 1. Kısa Sınav | 10 |
| 2. Kısa Sınav | 10 |
| 1. Ödev | 30 |
| Total | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Total | 100 |
| ECTS - Workload Activity | Quantity | Time (Hours) | Total Workload (Hours) |
|---|---|---|---|
| Course Duration (Including the exam week: 16x Total course hours) | 16 | 3 | 48 |
| Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
| Mid-terms | 1 | 15 | 15 |
| Quiz | 2 | 5 | 10 |
| Assignment | 1 | 10 | 10 |
| Final examination | 1 | 20 | 20 |
| Total Workload | 151 | ||
| Total Workload / 25 (Hours) | 6.04 | ||
| dersAKTSKredisi | 6 | ||