Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| LINEAR SYSTEM THEORY | EECD1114254 | Fall Semester | 3+0 | 3 | 8 |
| Course Program | Salı 13:30-14:15 Salı 14:30-15:15 Salı 15:30-16:15 |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | Third Cycle (Doctorate Degree) |
| Course Type | Elective |
| Course Coordinator | Prof.Dr. Mehmet Kemal ÖZDEMİR |
| Name of Lecturer(s) | Prof.Dr. Mehmet Kemal ÖZDEMİR |
| Assistant(s) | |
| Aim | The system concept, a key idea in engineering, can be used to assess and solve a wide range of engineering problems. Systems can be divided into two broad categories—linear and nonlinear—even though they may have a variety of different traits. Despite the fact that most systems are nonlinear, under specific circumstances, systems might be presumed to be linear. In this way, it is possible to analyze nonlinear systems using the perspective of linear systems. The purpose of this course is to give students the background they need to comprehend and solve engineering problems using the theory and techniques created for linear systems. |
| Course Content | This course contains; Determinants and their Properties, Matrix Arithmetic. ,The Inverse of a Matrix and Cramer’s rule, Derivatives of Determinants.,Theory of Linear Equations, Vector Spaces, Subspaces , Span, Basis, Dimension, Rank. ,General Linear Systems, Least-squares Solutions. ,Elementary Row Operations, LU Decomposition.,Eigenvalues, Eigenvectors and Canonical Forms, Unitary Matrices. ,The Gram-Schmidt Process, Principal Axes of Ellipsoids, Hermitian Matrices.,Midterm Exam Study,Positive Definiteness, Unitary Triangularization, Normal Matrices.,The Jordan Canonical Form, Principal Vectors, Jordan’s Theorem.,Application of Matrix Analysis to Differential Equations, Exponential of a Matrix.,Solution of Differential Equations by Eigenvalues and Eigenvectors.,Variational Principles and Perturbation Theory, the Rayleigh Principle, the Courant Minimax Theorem,The Inclusion Principle, Criteria for Positive Definiteness, Hadamard’s Inequality, Weyl’s Inequality, Gershgorin’s Theorem.,Numerical Linear Algebra. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| 1. Solves a system of n equations in m variables. | 16, 6, 9 | A, E, G |
| 2. Determines the dimension of a vector space, rank of a matrix and basis for a vector space. | 16, 6, 9 | A, E, G |
| 3. Applies the concepts of linear independence, linear transformation and determinants. | 16, 6, 9 | A, E, G |
| 4. Reduces a matrix using Gauss-Jordan reduction. | 16, 6, 9 | A, E, G |
| 5. Finds the inverse of a matrix, eigen-values and eigenvectors of a matrix. | 16, 6, 9 | A, E, G |
| 6. Applies theories learnt above to solve engineering problems. | 16, 6, 9 | A, E, G |
| Teaching Methods: | 16: Question - Answer Technique, 6: Experiential Learning, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, E: Homework, G: Quiz |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Determinants and their Properties, Matrix Arithmetic. | The Textbook |
| 2 | The Inverse of a Matrix and Cramer’s rule, Derivatives of Determinants. | The Textbook |
| 3 | Theory of Linear Equations, Vector Spaces, Subspaces , Span, Basis, Dimension, Rank. | The Textbook |
| 4 | General Linear Systems, Least-squares Solutions. | The Textbook |
| 5 | Elementary Row Operations, LU Decomposition. | The Textbook |
| 6 | Eigenvalues, Eigenvectors and Canonical Forms, Unitary Matrices. | The Textbook |
| 7 | The Gram-Schmidt Process, Principal Axes of Ellipsoids, Hermitian Matrices. | The Textbook |
| 8 | Midterm Exam Study | The Textbook |
| 9 | Positive Definiteness, Unitary Triangularization, Normal Matrices. | The Textbook |
| 10 | The Jordan Canonical Form, Principal Vectors, Jordan’s Theorem. | The Textbook |
| 11 | Application of Matrix Analysis to Differential Equations, Exponential of a Matrix. | The Textbook |
| 12 | Solution of Differential Equations by Eigenvalues and Eigenvectors. | The Textbook |
| 13 | Variational Principles and Perturbation Theory, the Rayleigh Principle, the Courant Minimax Theorem | The Textbook |
| 14 | The Inclusion Principle, Criteria for Positive Definiteness, Hadamard’s Inequality, Weyl’s Inequality, Gershgorin’s Theorem. | The Textbook |
| 15 | Numerical Linear Algebra | The Textbook |
| Resources |
| Applied Linear Algebra, Ben Noble and James W. Daniel |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Develop and deepen the current and advanced knowledge in the field with original thought and/or research and come up with innovative definitions based on Master's degree qualifications. | X | |||||
| 2 | Conceive the interdisciplinary interaction which the field is related with ; come up with original solutions by using knowledge requiring proficiency on analysis, synthesis and assessment of new and complex ideas. | X | |||||
| 3 | Evaluate and use new information within the field in a systematic approach and gain advanced level skills in the use of research methods in the field. | X | |||||
| 4 | Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field. | ||||||
| 5 | Broaden the borders of the knowledge in the field by producing or interpreting an original work or publishing at least one scientific paper in the field in national and/or international refereed journals. | ||||||
| 6 | Contribute to the transition of the community to an information society and its sustainability process by introducing scientific, technological, social or cultural improvements. | ||||||
| 7 | Independently perceive, design, apply, finalize and conduct a novel research process. | X | |||||
| 8 | Ability to communicate and discuss orally, in written and visually with peers by using a foreign language at least at a level of European Language Portfolio C1 General Level. | ||||||
| 9 | Critical analysis, synthesis and evaluation of new and complex ideas in the field. | ||||||
| 10 | Recognizes the scientific, technological, social or cultural improvements of the field and contribute to the solution finding process regarding social, scientific, cultural and ethical problems in the field and support the development of these values. | ||||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 50 | |
| Rate of Final Exam to Success | 50 | |
| Total | 100 | |
| ECTS / Workload Table | ||||||
| Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||
| Course Hours | 14 | 3 | 42 | |||
| Guided Problem Solving | 0 | 0 | 0 | |||
| Resolution of Homework Problems and Submission as a Report | 6 | 24 | 144 | |||
| Term Project | 0 | 0 | 0 | |||
| Presentation of Project / Seminar | 0 | 0 | 0 | |||
| Quiz | 0 | 0 | 0 | |||
| Midterm Exam | 1 | 15 | 15 | |||
| General Exam | 1 | 24 | 24 | |||
| Performance Task, Maintenance Plan | 0 | 0 | 0 | |||
| Total Workload(Hour) | 225 | |||||
| Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(225/30) | 8 | |||||
| ECTS of the course: 30 hours of work is counted as 1 ECTS credit. | ||||||
Detail Informations of the Course
Course Description
| Course | Code | Semester | T+P (Hour) | Credit | ECTS |
|---|---|---|---|---|---|
| LINEAR SYSTEM THEORY | EECD1114254 | Fall Semester | 3+0 | 3 | 8 |
| Course Program | Salı 13:30-14:15 Salı 14:30-15:15 Salı 15:30-16:15 |
| Prerequisites Courses | |
| Recommended Elective Courses |
| Language of Course | English |
| Course Level | Third Cycle (Doctorate Degree) |
| Course Type | Elective |
| Course Coordinator | Prof.Dr. Mehmet Kemal ÖZDEMİR |
| Name of Lecturer(s) | Prof.Dr. Mehmet Kemal ÖZDEMİR |
| Assistant(s) | |
| Aim | The system concept, a key idea in engineering, can be used to assess and solve a wide range of engineering problems. Systems can be divided into two broad categories—linear and nonlinear—even though they may have a variety of different traits. Despite the fact that most systems are nonlinear, under specific circumstances, systems might be presumed to be linear. In this way, it is possible to analyze nonlinear systems using the perspective of linear systems. The purpose of this course is to give students the background they need to comprehend and solve engineering problems using the theory and techniques created for linear systems. |
| Course Content | This course contains; Determinants and their Properties, Matrix Arithmetic. ,The Inverse of a Matrix and Cramer’s rule, Derivatives of Determinants.,Theory of Linear Equations, Vector Spaces, Subspaces , Span, Basis, Dimension, Rank. ,General Linear Systems, Least-squares Solutions. ,Elementary Row Operations, LU Decomposition.,Eigenvalues, Eigenvectors and Canonical Forms, Unitary Matrices. ,The Gram-Schmidt Process, Principal Axes of Ellipsoids, Hermitian Matrices.,Midterm Exam Study,Positive Definiteness, Unitary Triangularization, Normal Matrices.,The Jordan Canonical Form, Principal Vectors, Jordan’s Theorem.,Application of Matrix Analysis to Differential Equations, Exponential of a Matrix.,Solution of Differential Equations by Eigenvalues and Eigenvectors.,Variational Principles and Perturbation Theory, the Rayleigh Principle, the Courant Minimax Theorem,The Inclusion Principle, Criteria for Positive Definiteness, Hadamard’s Inequality, Weyl’s Inequality, Gershgorin’s Theorem.,Numerical Linear Algebra. |
| Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |
| 1. Solves a system of n equations in m variables. | 16, 6, 9 | A, E, G |
| 2. Determines the dimension of a vector space, rank of a matrix and basis for a vector space. | 16, 6, 9 | A, E, G |
| 3. Applies the concepts of linear independence, linear transformation and determinants. | 16, 6, 9 | A, E, G |
| 4. Reduces a matrix using Gauss-Jordan reduction. | 16, 6, 9 | A, E, G |
| 5. Finds the inverse of a matrix, eigen-values and eigenvectors of a matrix. | 16, 6, 9 | A, E, G |
| 6. Applies theories learnt above to solve engineering problems. | 16, 6, 9 | A, E, G |
| Teaching Methods: | 16: Question - Answer Technique, 6: Experiential Learning, 9: Lecture Method |
| Assessment Methods: | A: Traditional Written Exam, E: Homework, G: Quiz |
Course Outline
| Order | Subjects | Preliminary Work |
|---|---|---|
| 1 | Determinants and their Properties, Matrix Arithmetic. | The Textbook |
| 2 | The Inverse of a Matrix and Cramer’s rule, Derivatives of Determinants. | The Textbook |
| 3 | Theory of Linear Equations, Vector Spaces, Subspaces , Span, Basis, Dimension, Rank. | The Textbook |
| 4 | General Linear Systems, Least-squares Solutions. | The Textbook |
| 5 | Elementary Row Operations, LU Decomposition. | The Textbook |
| 6 | Eigenvalues, Eigenvectors and Canonical Forms, Unitary Matrices. | The Textbook |
| 7 | The Gram-Schmidt Process, Principal Axes of Ellipsoids, Hermitian Matrices. | The Textbook |
| 8 | Midterm Exam Study | The Textbook |
| 9 | Positive Definiteness, Unitary Triangularization, Normal Matrices. | The Textbook |
| 10 | The Jordan Canonical Form, Principal Vectors, Jordan’s Theorem. | The Textbook |
| 11 | Application of Matrix Analysis to Differential Equations, Exponential of a Matrix. | The Textbook |
| 12 | Solution of Differential Equations by Eigenvalues and Eigenvectors. | The Textbook |
| 13 | Variational Principles and Perturbation Theory, the Rayleigh Principle, the Courant Minimax Theorem | The Textbook |
| 14 | The Inclusion Principle, Criteria for Positive Definiteness, Hadamard’s Inequality, Weyl’s Inequality, Gershgorin’s Theorem. | The Textbook |
| 15 | Numerical Linear Algebra | The Textbook |
| Resources |
| Applied Linear Algebra, Ben Noble and James W. Daniel |
Course Contribution to Program Qualifications
| Course Contribution to Program Qualifications | |||||||
| No | Program Qualification | Contribution Level | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | Develop and deepen the current and advanced knowledge in the field with original thought and/or research and come up with innovative definitions based on Master's degree qualifications. | X | |||||
| 2 | Conceive the interdisciplinary interaction which the field is related with ; come up with original solutions by using knowledge requiring proficiency on analysis, synthesis and assessment of new and complex ideas. | X | |||||
| 3 | Evaluate and use new information within the field in a systematic approach and gain advanced level skills in the use of research methods in the field. | X | |||||
| 4 | Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field. | ||||||
| 5 | Broaden the borders of the knowledge in the field by producing or interpreting an original work or publishing at least one scientific paper in the field in national and/or international refereed journals. | ||||||
| 6 | Contribute to the transition of the community to an information society and its sustainability process by introducing scientific, technological, social or cultural improvements. | ||||||
| 7 | Independently perceive, design, apply, finalize and conduct a novel research process. | X | |||||
| 8 | Ability to communicate and discuss orally, in written and visually with peers by using a foreign language at least at a level of European Language Portfolio C1 General Level. | ||||||
| 9 | Critical analysis, synthesis and evaluation of new and complex ideas in the field. | ||||||
| 10 | Recognizes the scientific, technological, social or cultural improvements of the field and contribute to the solution finding process regarding social, scientific, cultural and ethical problems in the field and support the development of these values. | ||||||
Assessment Methods
| Contribution Level | Absolute Evaluation | |
| Rate of Midterm Exam to Success | 50 | |
| Rate of Final Exam to Success | 50 | |
| Total | 100 | |