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Information
| Code | AA024 |
| Name | Mathematical Methods in Astronomy II |
| Term | 2024-2025 Academic Year |
| Term | Spring |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. METİN ÖZDEMİR |
| Course Instructor |
1 |
Course Goal / Objective
Solution of some dynamical systems using equations that are obtained using variational techniques.
Course Content
Variation analysis, Euler's equation, Lagrange's undetermined coefficients, Hamilton principle, Lagrange and Hamilton dynamics; generalized coordinates, small vibrations, dynamics of rigid bodies.
Course Precondition
none
Resources
Parçacıklar ve Sistemler için Klasik Mekanik, Marion, Thornton, Arkadaş Kitabevi, 2011
Notes
Lecture notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | understands variational analysis |
| LO02 | Understands how to solve using the variational technique. |
| LO03 | Understands how to obtain Euler's equation using variational analysis. |
| LO04 | Understands how to write the Lagrange and Hamilton functions for various dynamical systems. |
| LO05 | Understands how to write Euler-Lagrange equations for various systems. |
| LO06 | Understands how to write Hamilton's equations for various systems. |
| LO07 | Understands what a rigid body is. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | To know and apply the branches of science and observational methods used in their fields. | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | To critically evaluate the knowledge gained in Physics, Mathematics, and Space Sciences and Technologies, to determine needs, to pursue life-long learning, to monitor developments and to use technology effectively to reach up-to-date information. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | To carry out thesis studies in the fields related to Astronomy and Space Sciences, to support their thoughts on the subjects and the solutions to the problems with quantitative and qualitative data. | 3 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Communicate verbally and in writing; develop communication skills in the field of ICT using at least one foreign language and develop communication skills with colleagues. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | To design and develop scientific and technological materials for the skills acquired in the field of Astronomy and Space Sciences. | 2 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Organizing projects and activities for the social environment in which they live with social responsibility awareness and implementing them. | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | To be able to access information from written, permanent, reliable and accurate sources and use information resources. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | To be able to make interdisciplinary and interdisciplinary group studies, to work effectively and to use time effectively | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | To be able to take responsibility, to act independently and to gain the ability of creativity. | 3 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Develop professional responsibility and ethical awareness. | 3 |
| PLO11 | Bilgi - Kuramsal, Olgusal | To be able to derive information about the properties and evolution of the source from the photons recorded by linking the basic physical interactions with the radiation processes. | |
| PLO12 | Bilgi - Kuramsal, Olgusal | To be able to evaluate the structure, formation and evolution of the universe as a whole with scientific methods. | 4 |
| PLO13 | Beceriler - Bilişsel, Uygulamalı | To be able to comprehend and apply the processes related to data collection, analysis and interpretation. | 3 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Variational analysis | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 2 | Variational analysis and Euler's equation, Undetermined coefficients | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 3 | Solution of some problems using variational analysis | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Problem Çözme |
| 4 | Hamilton's principle, Lagrange and Hamilton dynamics | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Problem Çözme |
| 5 | Generalized coordinates and Lagrange equations | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Problem Çözme |
| 6 | Canonical equations of motion, Hamilton dynamics | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Problem Çözme |
| 7 | Phase space, Liouville's theorem, Virial theorem | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Problem Çözme |
| 8 | Mid-Term Exam | Ölçme Yöntemleri: Yazılı Sınav, Ödev |
|
| 9 | Rigid bodies | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Problem Çözme |
| 10 | Moment of inertia tensor | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Problem Çözme |
| 11 | Euler angels | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Problem Çözme |
| 12 | Coopled oscillations | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Problem Çözme |
| 13 | Normal coordinates | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Problem Çözme |
| 14 | Continuous systems, waves | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Problem Çözme |
| 15 | Continuous systems (cont'd) | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 16 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||