TÜRKÇE
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Information
| Code | EE508 |
| Name | Integral Equations |
| 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 | İngilizce |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. TURGUT İKİZ |
| Course Instructor |
1 |
Course Goal / Objective
Comprehending the solution methods of kernel integral equations with some special forms.
Course Content
Classification of integral equations, Fredholm's Theory, Equations with symmetric kernels, Volterra's equation of the first kind, Fredholm's equation with symetric kernels of the first kind, Singular integral equations, İnversion formulas, Nonlinear integral equations.
Course Precondition
None
Resources
Advanced Mathematics for Engineers, , A. D. Myskis
Notes
Lecture notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Basic classes of integral equations. Fredholm Theory. Equations with degenerate kernels. Equations with small kernels. Perturbed kernels. Equations with symmetric kernels. Special classes of integral equations. Nonlinear integral equations. |
| LO02 | To be able to work on the thesis topic in a programmatic way, in accordance with the logical integrity required by the subject, within the framework determined by the advisor. |
| LO03 | To be able to search for literature in scientific databases; in particular, the ability to properly and accurately scan databases and evaluate and categorize listed items. |
| LO04 | To get the relation between the integral equations and differential equations |
| LO05 | To reduce some kind of integro-diferential equations into a differential equations |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Being able to specialize in at least one of the branches that form the foundations of Electrical and Electronics Engineering by increasing the level of knowledge beyond the master's level | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | To comprehend the integrity of all the subjects included in the field of specialization. | 3 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Having knowledge of the current scientific literature in the field of specialization to analyze the literature critically | |
| PLO04 | Bilgi - Kuramsal, Olgusal | To comprehend the interdisciplinary interaction of the field with other related branches, to suggest similar interactions. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Ability to do theoretical and experimental work | |
| PLO06 | Bilgi - Kuramsal, Olgusal | To create a complete scientific text by compiling the information obtained from the research | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | To work on the thesis topic programmatically, following the logical integrity required by the subject within the framework determined by the advisor. | 5 |
| PLO08 | Bilgi - Kuramsal, Olgusal | To search for literature in scientific databases, particularly the ability to correctly and accurately scan databases and evaluate and categorize listed items. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Having a command of English and related English jargon at a level that can easily read and understand a scientific text written in English in the field of specialization and write a similar text | 3 |
| PLO10 | Bilgi - Kuramsal, Olgusal | Ability to write a computer program in a familiar programming language, generally for a specific purpose, specifically related to the field of expertise. | |
| PLO11 | Bilgi - Kuramsal, Olgusal | Ability to plan and teach lessons related to the field of specialization or related fields | |
| PLO12 | Bilgi - Kuramsal, Olgusal | Being able to guide and take the initiative in environments that require solving problems related to the field | 3 |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Ability to communicate with people in an appropriate language | 3 |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Adopting the ethical values required by both education and research aspects of academician | 4 |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | To be able to produce projects, policies, and processes in the field of expertise and to evaluate these elements | |
| PLO16 | Yetkinlikler - Öğrenme Yetkinliği | Ability to research new topics based on existing research experience | 2 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Classification of integral equations | Classification of the differential equations | Öğretim Yöntemleri: Soru-Cevap, Anlatım |
| 2 | Fredholm's Theory, Equation with degenerate kernels, Equation with small kernels | Review of the previous lecture | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Volterra's integral equations of the second kind, çözümlerin özellikleri | Review of the previous lecture | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Equations with symmetric kernels, expanding kernels with respect to eigenfnctions | Review of the previous lecture | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | Some special classes of integral equations, Voltarres equation of the first kind | Review of the previous lecture | Öğretim Yöntemleri: Anlatım, Tartışma |
| 6 | Some special classes of integral equations, Freholm's equation of the first kind with symmetric kernels | Review of the previous lecture | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Some special classes of integral equations, Volterra's equation with difference kernels | Review of the previous lectures | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Mid-Term Exam | Review | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | singular integrals and inversion formulas | Review | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Direct applications of inversion formulas | Review of the previous lecture | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Reduction to an infinite system of algebraic equations | Reviev of the previous lecture | Öğretim Yöntemleri: Anlatım, Tartışma |
| 12 | Nonlinear integral equations | Review of the previous lecture | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | reduction of nonlinear integral equations to finite equations | Review of the previous lecture | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Iteration methods and small parameter method | Review of the previous lecture | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | A general discussion on integral equations | Review of the previous lectures | Öğretim Yöntemleri: Tartışma |
| 16 | Term Exams | Review | Ölçme Yöntemleri: Ödev |
| 17 | Term Exams | Review | Ölçme Yöntemleri: Ödev |
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 | ||