GRADUATE SCHOOL
M.SC. in Bioengineering (With Thesis)
EEE 551 | Course Introduction and Application Information
| Course Name |
Linear Systems Theory
|
|
Code
|
Semester
|
Theory
(hour/week) |
Application/Lab
(hour/week) |
Local Credits
|
ECTS
|
|
EEE 551
|
Fall/Spring
|
3
|
0
|
3
|
7.5
|
| Prerequisites |
None
|
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| Course Language |
English
|
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| Course Type |
Elective
|
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| Course Level |
Second Cycle
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| Mode of Delivery | - | |||||
| Teaching Methods and Techniques of the Course | - | |||||
| Course Coordinator | ||||||
| Course Lecturer(s) | ||||||
| Assistant(s) | - | |||||
| Course Objectives | The course aims the students: i) to get a solid mathematical background on real analysis, normed linear spaces and linear differential equations in the state form. ii) to gain basic skills in analyzing a given linear time-invariant dynamical system; determining whether or not the system has a well-defined solution, so analyzing qualitative properties of solutions, and analyzing the stability, controllability and observability of linear dynamical systems, and iii) to have a dynamical system view. |
| Learning Outcomes |
The students who succeeded in this course;
|
| Course Description | Real analysis. Algebraic structures. Linear spaces and transformations. State equations. Existence and uniqueness of solutions. Properties of dynamical systems. State transition matrix for linear time-invariant systems. Zero-state solutions. Zero-input solutions. Minimal polynomial and Cayley-Hamilton theorem. Eigenvalues and eigenvectors. Jordan form. Stability in the sense of Liapunov.Bounded-Input Bounded-Output Stability. Controllablity and observability. Minimal realization. |
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Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Management Skills Courses | ||
| Transferable Skill Courses |
WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES
| Week | Subjects | Related Preparation |
| 1 | Set theory overview. Ordering relation. Greatest and least elements | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 2 | Algebraic structures: Group, ring, field and linear space. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 3 | Normed, metric and inner-product spaces. Vector and matrix norms. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 4 | Derivation of state equations from systems. Existence and uniqueness of solutions. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 5 | Fundamental matrix and state transition matrix of linear state equations. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 6 | Zero-input, zero-state and complete solutions. Impulse response matrix. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 7 | Benzerlik dönüşümü ile köşegenleştirme. Rezidü matrisleri. Karakteristik ve minimal polinaomlar. Cayley-Hamilton Teoremi. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 8 | Generalized eigenvalues and Jordan form for state matrix. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 9 | 1. Midterm | |
| 10 | Liapunov stability of linear time-invariant and time-varying systems. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 11 | Liapunov stability of linear time-invariant and time-varying systems. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 12 | Controllability of linear time-invariant and time-varying systems. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 13 | 2. Midterm | |
| 14 | Controllability of linear time-invariant and time-varying systems. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 15 | Minimal realization of linear time-invariant dynamical systems. | Deseor, C. A. (1970) Notes for a Second Course on Linear Systems, Van Nostrand Reinhold. |
| 16 | Review of the Semester |
| Course Notes/Textbooks | The textbook referenced above and lecture notes |
| Suggested Readings/Materials | Related Books |
EVALUATION SYSTEM
| Semester Activities | Number | Weigthing |
| Participation |
1
|
10
|
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | ||
| Portfolio | ||
| Homework / Assignments | ||
| Presentation / Jury | ||
| Project | ||
| Seminar / Workshop | ||
| Oral Exams | ||
| Midterm |
2
|
40
|
| Final Exam |
1
|
50
|
| Total |
| Weighting of Semester Activities on the Final Grade |
3
|
50
|
| Weighting of End-of-Semester Activities on the Final Grade |
1
|
50
|
| Total |
ECTS / WORKLOAD TABLE
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Theoretical Course Hours (Including exam week: 16 x total hours) |
16
|
3
|
48
|
| Laboratory / Application Hours (Including exam week: '.16.' x total hours) |
16
|
0
|
|
| Study Hours Out of Class |
15
|
4
|
60
|
| Field Work |
0
|
||
| Quizzes / Studio Critiques |
0
|
||
| Portfolio |
0
|
||
| Homework / Assignments |
10
|
0
|
|
| Presentation / Jury |
5
|
0
|
|
| Project |
0
|
||
| Seminar / Workshop |
0
|
||
| Oral Exam |
0
|
||
| Midterms |
2
|
40
|
80
|
| Final Exam |
1
|
37
|
37
|
| Total |
225
|
COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP
|
#
|
Program Competencies/Outcomes |
* Contribution Level
|
||||
|
1
|
2
|
3
|
4
|
5
|
||
| 1 | To be able to have adequate knowledge in Mathematics, Life Sciences and Bioengineering; to be able to use theoretical and applied information in these areas to model and solve Bioengineering problems. |
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| 2 | To be able to use scientific methods to complete and apply information from uncertain, limited or incomplete data; to be able to combine and use information from related disciplines. |
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| 3 | To be able to design and apply theoretical, experimental and model-based research; to be able to solve complex problems in such processes. |
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| 4 | Being able to utilize Natural Sciences and Bioengineering principles to design systems, devices and processes. |
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| 5 | To be able to follow and apply new developments and technologies in the field of Bioengineering. |
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| 6 | To be able to work effectively in multi-disciplinary teams within the discipline of Bioengineering; to be able to exhibit individual work. |
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| 7 | To be able to have the knowledge about the social, environmental, health, security and law implications of Bioengineering applications, to be able to have the knowledge to manage projects and business applications, and to be able to be aware of their limitations in professional life. |
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| 8 | To be able to have the social, scientific and ethical values in the stages of collection, interpretation, dissemination and application of data related to the field of Bioengineering. |
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| 9 | To be able to prepare an original thesis/term project in accordance with the criteria related to the field of Bioengineering. |
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| 10 | To be able to follow information about Bioengineering in a foreign language and to be able to participate in discussions in academic environments. |
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| 11 | To be able to improve the acquired knowledge, skills and qualifications for social and universal purposes regarding the studied area. |
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| 12 | To be able to recognize regional and global issues/problems, and to be able to develop solutions based on research and scientific evidence related to Bioengineering. |
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*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest