Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
1EEE501LINEAR SYSTEMS3+0+03616.06.2026

 
Course Details
Language of Instruction English
Level of Course Unit Master's Degree
Department / Program ELECTRICAL AND ELECTRONICS ENGINEERING
Type of Program Formal Education
Type of Course Unit Elective
Course Delivery Method Face To Face
Objectives of the Course The aim of this course is to provide students with the advanced mathematical and algebraic foundations necessary to analyze, model, and study the behavior of dynamic and linear systems.
Course Content Function. Vector spaces. Linear transformations on vector spaces. Normal vector spaces. Convergence, existence and uniqueness result on nonlinear differential equations. Dynamical system model; equivalence, linearity, time invariance. Linear time varying differential system representation; state transition matrix and state transition function. Variational and adjoint equations.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator Associate Prof.Dr. Serkan ÖZBAY
Name of Lecturers Associate Prof.Dr. SERKAN ÖZBAY
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Lecture notes
Course Notes Linear Systems Theory
Joao P. Hespanha

Course Category
Mathematics and Basic Sciences %50
Engineering %40
Engineering Design %10

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Mid-terms 2 % 60
Final examination 1 % 40
Total
3
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly lecture hours 14 3 42
Reading Activities 14 3 42
Internet browsing, library work 14 2 28
Midterm and midterm exam preparation 2 20 40
Final exam and preparation for the final exam 1 20 20
Total Work Load   Number of ECTS Credits 6 172

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 To be able to use vector and normed function spaces and linear transformation concepts to analyze dynamical systems
2 To be able to theoretically determine when and under what conditions nonlinear differential equations have a unique solution
3 To be able to analyze and model a dynamic system according to the criteria of linearity, time invariance, and equivalence
4 To be able to find the state transition matrix of systems whose parameters change over time and to calculate their temporal behavior
5 To linearize nonlinear systems around a trajectory and to establish their variational and adjoint equations

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Function
2 Vector spaces
3 Vector spaces
4 Linear transformations on vector spaces
5 Normal vector spaces
6 Convergence, existence and uniqueness result on nonlinear differential equations
7 Convergence, existence and uniqueness result on nonlinear differential equations
8 Dynamical system model; equivalence, linearity, time invariance
9 Dynamical system model; equivalence, linearity, time invariance
10 Linear time varying differential system representation; state transition matrix and state transition function
11 Linear time varying differential system representation; state transition matrix and state transition function
12 Variational and adjoint equations
13 Variational and adjoint equations
14 Variational and adjoint equations

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4
All 5 4 4 4
C1 5 4 4 4
C2 5 4 4 4
C3 5 4 4 4
C4 5 4 4 4
C5 5 4 4 4

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  https://obs.gantep.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=147937&lang=en