EE508 Integral Equations

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code EE508
Name Integral Equations
Term 2022-2023 Academic Year
Semester . Semester
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 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

Update Time: 19.11.2022 06:49