TÜRKÇE
ENGLISH
Information
| Code | FZK202 |
| Name | Mathematics for Physics |
| Term | 2024-2025 Academic Year |
| Semester | 4. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. AYSEL KAYIŞ TOPAKSU |
| Course Instructor |
1 2 Prof. Dr. AYŞE POLATÖZ (A Group) (Asst. Ins.) |
Course Goal / Objective
The purpose of this class is to build a bridge between courses that require the use of mathematics at a high level in physics.
Course Content
Complex numbers, operations and rules with complex numbers; Polar representation of complex numbers, De Moivre formula, Euler formula, regions in the complex plane; basic functions of complex numbers; representation of complex variable functions (mapping); Analytic Functions: Derivative, limit and continuity concepts, Cauchy-Riemann equations, Harmonic functions; integrals and series in complex plane; Cauchy Theorem, series expansion of analytic functions: Taylor and Laurent series; Residue theorem, Real integral solution with the help of Residue theorem are processed in this lecture.
Course Precondition
None
Resources
Fizikte ve Mühendislikte Matematiksel Yöntemler, Bekir Karaoğlu
Notes
Complex Variables, Murray Spiegel, Seymour Lipschutz, John J. Schiller, Dennis Spellman
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Defines complex numbers. |
| LO02 | Defines the regions in the complex plane. |
| LO03 | Define analytic function. |
| LO04 | Calculate the harmonic match. |
| LO05 | Calculate the complex integrals |
| LO06 | Solves real integrals by residual method. |
| LO07 | Establishes the relationship between integrals and series in complex planes. |
| LO08 | Presents complex numbers in the polar plane. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the basic concepts and principles in the field of physics. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Follows the developments in the field of Physics and uses scientific methods and techniques. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Combine the knowledge gained in the field of Physics with the knowledge in other scientific fields and explains the method of producing scientific knowledge. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Identify problems in the field of physics and for the solutions apply the analytical and simulative methods. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use the advanced theoretical and practical knowledge he has acquired in the field of Physics and designs experiments related to his field. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Take responsibility as a team or alone to overcome the problems encountered in the field of physics . | 3 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Classify, use and critically evaluate the knowledg taken by his/her efforts. | |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Improves himself by knowing that the learning process is lifelong. | 3 |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Knowing the importance of individual development, she/he implements what is necessary. | 2 |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Evaluates the developments in the field of physics in terms of social ethics by watching and learning them. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Complex numbers, operations with complex numbers and rules. | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Polar representation of complex numbers. | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | De Moivre formula, Euler formula. | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Areas in the complex plane, the basic functions of complex numbers, the representation of complex variable functions. | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Analytic Functions: Derivative, limit and continuity concepts. | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Cauchy-Riemann equations, Harmonic functions. | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Integrals and series in complex plane. | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Independent Study | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Cauchy Theory | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | The baic formulas of Integralion and Cauchy integral formulas. | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Taylor series | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Series expansion of analytic functions: Taylor and Laurent series. | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Residue Theory and Residue calculation techniques. | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Solution of real integrals with the help of residue theorem. | The related chapter in the book should be read. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Solution of trigonometric real integrals with the help of residue theorem. | The related chapter in the book should be read. | Öğretim Yöntemleri: Soru-Cevap, Tartışma, Problem Çözme |
| 16 | Term Exams | Independent Study | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Independent study | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 8 | 8 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 122 | ||
| Total Workload / 25 (h) | 4,88 | ||
| ECTS | 5 ECTS | ||