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  • > THEORY OF DIFFERENTIAL EQUATIONS- II
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About the Course

Department Profile
Course unit title Level of course unit Course unit code Type of course unit Semester of course unit Local credit ECTS credit Syllabus
THEORY OF DIFFERENTIAL EQUATIONS- II Second cycle MAT 532 2 7.50 7.50 Print
   
Description of course unit
Prerequisites and course requisities No
Language of instruction Turkish
Coordinator Assoc. Prof. Pakize TEMTEK
Lecturer(s) Assoc. Prof. Pakize TEMTEK
Teaching assitant(s) No
Mode of delivery Face to face
Course objective The objective of this course is to teach the student theoretical and practical aspects of ordinary differential equations and their applications.
Course description First order ordinary differential equations. Proof of the existence - unequeness theorem. differential inequalities, integral inequalities and Gronwall’s Lemma. Picard Method, preparation for the existence theorem and proof of the existence theorem. Systems and higher order ordinary differential equations. Second order linear equations and the Wronskian identity. Boundary value problems and eigenvalue problems.

Course contents
1 First Order Ordinary Differential Equations.
2 Tangent Line Approximation, Cauchy – Euler Method , The Graph Method.
3 Preliminary Discussion of Existence and Uniqueness of Solutions of Initial Value Problem’s.
4 Differential Inequalities, Integral Inequalities and Gronwall’s Lemma.
5 Integral Equations, The Uniqueness Theorem.
6 Picard Method, Preparation for the Existence Theorem and Proof of the Existence Theorem.
7 Continuation of the Solution, Dependence on the Initial Value.
8 MID-TERM EXAM
9 Systems and Higher Order Ordinary Differential Equations.
10 Complex Valued Equations.
11 Second Order Linear Equations and the Wronskian Identity
12 Boundary Value Problems, Examples.
13 The Number of Solutions of a Boundary Value Problem.
14 Eigenvalue Problems and examples.
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Learning outcomes of the course unit
1 First order ordinary differential equations, Proof of the existence - unequeness theorem
2 Differential inequalities,integral inequalities and Gronwall’s Lemma.
3 Picard Method, preparation for the existence theorem and proof of the existence theorem.
4 Systems and higher order ordinary differential equations.
5 Second order linear equations and the Wronskian identity.
6 Boundary value problems and eigenvalue problems.
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8
9
10

*Contribution level of the course unit to the key learning outcomes
1 Students are not only high self-confident about their subjects, but also active and competent at academic spheres, so they have practical and theoritical knowledge about Russian language and literature, its history and culture.
2 Students have theoritical and practical knowledge in order to qualify the categories of Russian literature with their characteristical features. So, they are able to explain and analyse the texts, which represent these categories, with their historical, social, cultural, economical and political backgrounds.
3 Students have current theoritical and practical knowledge in order to make translations from Russian to Turkish or from Turkish to Russian in different types of texts.
4 Student practically analyses literary and cultural texts related to their theories as part of interdisciplinary approach.
5 The students gain the ability of researching methods as an expert and to make academic publications in the field of literature and linguistics.
6 The students gain expert skills in a positive sense from intercultural differences and have the ability to compare Turkish and Russian cultures with extensive knowledge about the Russian culture as having.
7 The student is able to collect information and data individually and/or in groups about Russian language, literature and culture through up-to-date information technologies and research methods and techniques, and shares these in national and international educational and other professional environments.
8 Students have knowledge about Russian language, literature, history and culture to work in public-private sectors.
9 The students organise social, cultural and artistic activities which are necessary to be done in the fields of Russian culture, literature, language and history.
10 The student develops an unbiased, respectful and open attitude towards different languages, races, sexes, religions, and social classes.
11 Students are able to prepare and make visual or written presentations about Russian language and literature.
12 Students have theoritical and practical knowledge in order to qualify the categories of Russian literature with their characteristical features. So, they are able to explain and analyse the texts, which represent these categories, with their historical, social, cultural, economical and political backgrounds.
13 Students have current theoritical and practical knowledge in order to make translations from Russian to Turkish or from Turkish to Russian in different types of texts.
14 Student practically analyses literary and cultural texts related to their theories as part of interdisciplinary approach.
15 The student is able to do researches, becomes an expert in own field, solve problems with his/her critical, creative and analytical thinking skills and he can express himself at each subject. - The students gain expert skills in a positive sense from intercultural differences and have the ability to compare Turkish and Russian cultures with extensive knowledge about the Russian culture as having.
16 The student is able to collect information and data individually and/or in groups about Russian language, literature and culture through up-to-date information technologies and research methods and techniques, and shares these in national and international educational and other professional environments.
17 Students have knowledge about Russian language, literature, history and culture to work in public-private sectors.
18 The students organise social, cultural and artistic activities which are necessary to be done in the fields of Russian culture, literature, language and history.
19 The student develops an unbiased, respectful and open attitude towards different languages, races, sexes, religions, and social classes.
20 Students are able to prepare and make visual or written presentations about Russian language and literature.
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Number of stars refer to level of contribution from 1 (the least) to 5 (the most)

Planned learning activities, teaching methods and ECTS work load
  Quantity Time (hour) Quantity*Time (hour)
Lectures (face to face teaching) 14 3 42
Study hours out of classroom (study before and after the class) 14 5 70
Homework 5 4 20
Presentation / seminar 3 3 9
Quiz 0 0 0
Preparation for midterm exams 7 2 14
Midterm exams 1 2 2
Project (term paper) 0 0 0
Laboratuar 0 0 0
Field study 0 0 0
Preparation for final exam 6 3 18
Final exam 1 2 2
Research 3 3 9
Total work load     186
ECTS     7.50

Assessment methods and criteria
Evaluation during semester Quantity Percentage
Midterm exam 1 70
Quiz 0 0
Homework 3 30
Semester total   100
Contribution ratio of evaluation during semester to success   40
Contribution ratio of final exam to success   60
General total   100

Recommended and required reading
Textbook • Introduction to Theoretical Aspects of Ordinary Differential Equations, Erkip A.
Additional references • Theory and Numerics of Ordinary Differential Equations, Ainsworth .M.,Levesley J.,Light W.A. and Marletta M., Oxford Science Publications,1995. • Lectures on Ordinary Differential Equations, Hurewicz, W., Technology Press and Wiley, New York,1958. • Theory of Ordinary Differential Equations, Coddington, Earl.A. and Levinson N., New York, Mc Graw Hill ,1955.

Files related to the course unit