11111

COURSE INTRODUCTION AND APPLICATION INFORMATION


umi.fbe.ieu.edu.tr

Course Name
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
Fall/Spring
Prerequisites
None
Course Language
Course Type
Elective
Course Level
-
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s) -
Assistant(s) -
Course Objectives
Learning Outcomes The students who succeeded in this course;
  • will be familiar with boundary uniqueness theorems of analytic functions.
  • will be able to asimilate analytic continuation principle.
  • will be able to apply the spectral theory of nonselfadjoint differential equations.
  • will be able to define some concepts such as spectrum, resolvent set, resolvent operator, Jost solution.
Course Description

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Introduction and Fundamental Concepts. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
2 Fourier Transforms; Properties and Applications. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
3 NonSelfadjoint Differential Equations. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
4 NonSelfadjoint SturmLiouville Differential Operator. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
5 Solutions and Their Asymptotic Behaviours. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
6 Jost Solution and İts Properties. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
7 A Special Integral Representation For Jost Solution. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
8 Integral Equations. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
9 The Resolvent Operator. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
10 Green’s Function and İts Properties. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
11 Boundary Uniqueness Theorems of Analytic Functions. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
12 Beurling and Pavlov Theorems, and Their Applications. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
13 Carleson’s Theorem, and Its Applications. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
14 Quantitative Properties of The Spectrum. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
15 Spectral Expansion. M. A. Naimark, “Linear Differential Equations, Volume II”., Frederick Ungar Publishing Co.
16 Review of the Semester  
Course Notes/Textbooks The extracts above and exercises will be given.
Suggested Readings/Materials B.M. Levitan and I. S. Sargsjan, SturmLiouville and Dirac Operators, Kluwer Academic publishers. Further references and articles related this topic will be delivered in class.

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
5
30
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
30
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
60
Weighting of End-of-Semester Activities on the Final Grade
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
16
5
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
5
4
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
37
Final Exams
1
40
    Total
225

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To develop and deepen his/her knowledge on theories of mathematics and statistics and their applications in level of expertise, and to obtain unique definitions which bring innovations to the area, based on master level competencies,

X
2

To have the ability of original, independent and critical thinking in Mathematics and Statistics and to be able to develop theoretical concepts,

X
3

To have the ability of defining and verifying problems in Mathematics and Statistics,

X
4

With an interdisciplinary approach, to be able to apply theoretical and applied methods of mathematics and statistics in analyzing and solving new problems and to be able to discover his/her own potentials with respect to the application,

X
5

In nearly every fields that mathematics and statistics are used, to be able to execute, conclude and report a research, which requires expertise, independently,

X
6

To be able to evaluate and renew his/her abilities and knowledge acquired in the field of Applied Mathematics and Statistics with critical approach, and to be able to analyze, synthesize and evaluate complex thoughts in a critical way,

X
7

To be able to convey his/her analyses and methods in the field of Applied Mathematics and Statistics to the experts in a scientific way,

X
8

To be able to use national and international academic resources (English) efficiently, to update his/her knowledge, to communicate with his/her native and foreign colleagues easily, to follow the literature periodically, to contribute scientific meetings held in his/her own field and other fields systematically as written, oral and visual.

X
9

To be familiar with computer software commonly used in the fields of Applied Mathematics and Statistics and to be able to use at least two of them efficiently,

X
10

To contribute the transformation process of his/her own society into an information society and the sustainability of this process by introducing scientific, technological, social and cultural advances in the fields of Applied Mathematics and Statistics,

X
11

As having rich cultural background and social sensitivity with a global perspective, to be able to evaluate all processes efficiently, to be able to contribute the solutions of social, scientific, cultural and ethical problems and to support the development of these values,

X
12

As being competent in abstract thinking, to be able to connect abstract events to concrete events and to transfer solutions, to analyze results with scientific methods by designing experiment and collecting data and to interpret them,

X
13

To be able to produce strategies, policies and plans about systems and topics in which mathematics and statistics are used and to be able to interpret and develop results,

X
14

To be able to evaluate, argue and analyze prominent persons, events and phenomena, which play an important role in the development and combination of the fields of Mathematics and Statistics, within the perspective of the development of other fields of science,

X
15

In Applied Mathematics and Statistics, to be able to sustain scientific work as an individual or a group, to be effective in all phases of an independent work, to participate decision-making process and to make and execute necessary planning within an effective time schedule.

X

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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