## Course Detail

## Course Description

Course | Code | Semester | T+P (Hour) | Credit | ECTS |
---|---|---|---|---|---|

LINEAR ALGEBRA | COE2219550 | Spring Semester | 3+0 | 3 | 6 |

Course Program | Perşembe 13:30-14:15 Perşembe 14:30-15:15 Perşembe 15:30-16:15 |

Prerequisites Courses | |

Recommended Elective Courses |

Language of Course | English |

Course Level | First Cycle (Bachelor's Degree) |

Course Type | Required |

Course Coordinator | Assist.Prof. Cihan Bilge KAYASANDIK |

Name of Lecturer(s) | Lect. Seçil TUNALI ÇIRAK |

Assistant(s) | Teaching assistant |

Aim | 1. To provide the methods of solution of systems of linear equations and the applications of matrix and determinant. 2. To introduce the basic concepts of vector space, basis, dimension, linear dependency required to understand, construct, solve and interpret data spaces. 3. To give an ability to apply knowledge of mathematics on engineering problems |

Course Content | This course contains; Preliminaries: Matrices and Systems of Linear Algebraic Equations: Definitions and Notation,Matrix Algebra and Terminology and Notation for Systems of Linear Equations ,Elementary Row Operations, Row Echelon Matrices, Reduced Row Echelon Matrices and Solving Systems of Linear Algebraic Equations,Gaussian Elimination and Gauss Jordan Elimination Methods, and The Inverse of a Square Matrix ,Gauss Jordan Method, Determinants and Adjoint Method ,Elementary Matrices, LU Factorization, Cramer Rule ,Vector Spaces: Definition of a Vector Space, Subspaces and Spanning Sets ,Linear Dependency and Independency, Bases and Dimension ,Row and Column Spaces and The Rank-Nullity Theorem ,Inner Product Spaces and Orthogonality ,Eigenvalue/Eigenvector Problem: Eigenvalues and Eigenvectors and Eigenspaces ,Application of Eigenvalues and Eigenvectors Factorization ,Diagonalization and Singular Value Decomposition, Pseudo-inverse Calculation ,Linear Transformations, The Kernel and Range of a Linear Transformation and Further Properties of Linear Transformations . |

Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |

1. Recognize arithmetic operations with matrices, properties of matrices, elementary row operations on matrices and determine row echelon form (REF) and reduced row echelon form (RREF) for matrices and rank of a matrix. | 12, 14, 9 | A, E |

2. Calculate the solutions to the systems of linear equations from: Gaussian and Gauss-Jordan elimination method, the inverse of a matrix, Gauss-Jordan method, and find the value of determinant of a matrix. | 12, 14, 9 | A, E |

4. Recognize the importance of the concepts of a vector space such as subspace, spanning set, linear dependency and independency, basis and dimension, row and column spaces, the Rank-Nullity theorem, inner product spaces and orthogonality. | 12, 14, 9 | A, E |

5. Analyze eigenvalues and the corresponding eigenvectors and eigenspaces of the matrix, diagonalization and singular value decomposition, and pseudo-inverse of a matrix, and linear transformations and apply on engineering problems. | 12, 14, 9 | A, E |

3. Analyze Adjoint Method to find the inverse matrix, elementary matrices, LU factorization and Cramer rule. | 12, 14, 9 | A, E |

Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method |

Assessment Methods: | A: Traditional Written Exam, E: Homework |

## Course Outline

Order | Subjects | Preliminary Work |
---|---|---|

1 | Preliminaries: Matrices and Systems of Linear Algebraic Equations: Definitions and Notation | Book Chapter 3.1 |

2 | Matrix Algebra and Terminology and Notation for Systems of Linear Equations | Book Chapters 3.2, 3.3 |

3 | Elementary Row Operations, Row Echelon Matrices, Reduced Row Echelon Matrices and Solving Systems of Linear Algebraic Equations | Book Chapter 3.4 |

4 | Gaussian Elimination and Gauss Jordan Elimination Methods, and The Inverse of a Square Matrix | Book Chapters 3.5, 3.6 |

5 | Gauss Jordan Method, Determinants and Adjoint Method | Book Chapters 3.6, 4 |

6 | Elementary Matrices, LU Factorization, Cramer Rule | Book Chapters 3.7, 4.3 |

7 | Vector Spaces: Definition of a Vector Space, Subspaces and Spanning Sets | Book Chapters 5.1, 5.2, 5.3, 5.4 |

8 | Linear Dependency and Independency, Bases and Dimension | Book Chapters 5.5, 5.6 |

9 | Row and Column Spaces and The Rank-Nullity Theorem | Book Chapters 5.7, 5.8 |

10 | Inner Product Spaces and Orthogonality | Book Chapters 5.9, 5.10 |

11 | Eigenvalue/Eigenvector Problem: Eigenvalues and Eigenvectors and Eigenspaces | Book Chapters 6.5, 6.6 |

12 | Application of Eigenvalues and Eigenvectors Factorization | Book Chapters 6.7, other sources |

13 | Diagonalization and Singular Value Decomposition, Pseudo-inverse Calculation | Book Chapters 6.7, other sources |

14 | Linear Transformations, The Kernel and Range of a Linear Transformation and Further Properties of Linear Transformations | Book Chapters 6.1, 6.2, 6.3, 6.4 |

Resources |

Differential Equations & Linear Algebra Second Edition, Stephen W. Goode. Prentice-Hall, Inc. 2000,1991. |

## Course Contribution to Program Qualifications

Course Contribution to Program Qualifications | |||||||

No | Program Qualification | Contribution Level | |||||

1 | 2 | 3 | 4 | 5 | |||

1 | 1. An ability to apply knowledge of mathematics, science, and engineering | X | |||||

2 | 2. An ability to identify, formulate, and solve engineering problems | X | |||||

3 | 3. An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability | ||||||

4 | 4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | ||||||

5 | 5. An ability to design and conduct experiments, as well as to analyze and interpret data | ||||||

6 | 6. An ability to function on multidisciplinary teams | X | |||||

7 | 7. An ability to communicate effectively | X | |||||

8 | 8. A recognition of the need for, and an ability to engage in life-long learning | ||||||

9 | 9. An understanding of professional and ethical responsibility | ||||||

10 | 10. A knowledge of contemporary issues | ||||||

11 | 11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context |

## Assessment Methods

Contribution Level | Absolute Evaluation | |

Rate of Midterm Exam to Success | 30 | |

Rate of Final Exam to Success | 70 | |

Total | 100 |

ECTS / Workload Table | ||||||

Activities | Number of | Duration(Hour) | Total Workload(Hour) | |||

Course Hours | 13 | 3 | 39 | |||

Guided Problem Solving | 0 | 0 | 0 | |||

Resolution of Homework Problems and Submission as a Report | 14 | 6 | 84 | |||

Term Project | 0 | 0 | 0 | |||

Presentation of Project / Seminar | 0 | 0 | 0 | |||

Quiz | 0 | 0 | 0 | |||

Midterm Exam | 1 | 22 | 22 | |||

General Exam | 1 | 22 | 22 | |||

Performance Task, Maintenance Plan | 0 | 0 | 0 | |||

Total Workload(Hour) | 167 | |||||

Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(167/30) | 6 | |||||

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 ALGEBRA | COE2219550 | Spring Semester | 3+0 | 3 | 6 |

Course Program | Perşembe 13:30-14:15 Perşembe 14:30-15:15 Perşembe 15:30-16:15 |

Prerequisites Courses | |

Recommended Elective Courses |

Language of Course | English |

Course Level | First Cycle (Bachelor's Degree) |

Course Type | Required |

Course Coordinator | Assist.Prof. Cihan Bilge KAYASANDIK |

Name of Lecturer(s) | Lect. Seçil TUNALI ÇIRAK |

Assistant(s) | Teaching assistant |

Aim | 1. To provide the methods of solution of systems of linear equations and the applications of matrix and determinant. 2. To introduce the basic concepts of vector space, basis, dimension, linear dependency required to understand, construct, solve and interpret data spaces. 3. To give an ability to apply knowledge of mathematics on engineering problems |

Course Content | This course contains; Preliminaries: Matrices and Systems of Linear Algebraic Equations: Definitions and Notation,Matrix Algebra and Terminology and Notation for Systems of Linear Equations ,Elementary Row Operations, Row Echelon Matrices, Reduced Row Echelon Matrices and Solving Systems of Linear Algebraic Equations,Gaussian Elimination and Gauss Jordan Elimination Methods, and The Inverse of a Square Matrix ,Gauss Jordan Method, Determinants and Adjoint Method ,Elementary Matrices, LU Factorization, Cramer Rule ,Vector Spaces: Definition of a Vector Space, Subspaces and Spanning Sets ,Linear Dependency and Independency, Bases and Dimension ,Row and Column Spaces and The Rank-Nullity Theorem ,Inner Product Spaces and Orthogonality ,Eigenvalue/Eigenvector Problem: Eigenvalues and Eigenvectors and Eigenspaces ,Application of Eigenvalues and Eigenvectors Factorization ,Diagonalization and Singular Value Decomposition, Pseudo-inverse Calculation ,Linear Transformations, The Kernel and Range of a Linear Transformation and Further Properties of Linear Transformations . |

Dersin Öğrenme Kazanımları | Teaching Methods | Assessment Methods |

1. Recognize arithmetic operations with matrices, properties of matrices, elementary row operations on matrices and determine row echelon form (REF) and reduced row echelon form (RREF) for matrices and rank of a matrix. | 12, 14, 9 | A, E |

2. Calculate the solutions to the systems of linear equations from: Gaussian and Gauss-Jordan elimination method, the inverse of a matrix, Gauss-Jordan method, and find the value of determinant of a matrix. | 12, 14, 9 | A, E |

4. Recognize the importance of the concepts of a vector space such as subspace, spanning set, linear dependency and independency, basis and dimension, row and column spaces, the Rank-Nullity theorem, inner product spaces and orthogonality. | 12, 14, 9 | A, E |

5. Analyze eigenvalues and the corresponding eigenvectors and eigenspaces of the matrix, diagonalization and singular value decomposition, and pseudo-inverse of a matrix, and linear transformations and apply on engineering problems. | 12, 14, 9 | A, E |

3. Analyze Adjoint Method to find the inverse matrix, elementary matrices, LU factorization and Cramer rule. | 12, 14, 9 | A, E |

Teaching Methods: | 12: Problem Solving Method, 14: Self Study Method, 9: Lecture Method |

Assessment Methods: | A: Traditional Written Exam, E: Homework |

### Course Outline

Order | Subjects | Preliminary Work |
---|---|---|

1 | Preliminaries: Matrices and Systems of Linear Algebraic Equations: Definitions and Notation | Book Chapter 3.1 |

2 | Matrix Algebra and Terminology and Notation for Systems of Linear Equations | Book Chapters 3.2, 3.3 |

3 | Elementary Row Operations, Row Echelon Matrices, Reduced Row Echelon Matrices and Solving Systems of Linear Algebraic Equations | Book Chapter 3.4 |

4 | Gaussian Elimination and Gauss Jordan Elimination Methods, and The Inverse of a Square Matrix | Book Chapters 3.5, 3.6 |

5 | Gauss Jordan Method, Determinants and Adjoint Method | Book Chapters 3.6, 4 |

6 | Elementary Matrices, LU Factorization, Cramer Rule | Book Chapters 3.7, 4.3 |

7 | Vector Spaces: Definition of a Vector Space, Subspaces and Spanning Sets | Book Chapters 5.1, 5.2, 5.3, 5.4 |

8 | Linear Dependency and Independency, Bases and Dimension | Book Chapters 5.5, 5.6 |

9 | Row and Column Spaces and The Rank-Nullity Theorem | Book Chapters 5.7, 5.8 |

10 | Inner Product Spaces and Orthogonality | Book Chapters 5.9, 5.10 |

11 | Eigenvalue/Eigenvector Problem: Eigenvalues and Eigenvectors and Eigenspaces | Book Chapters 6.5, 6.6 |

12 | Application of Eigenvalues and Eigenvectors Factorization | Book Chapters 6.7, other sources |

13 | Diagonalization and Singular Value Decomposition, Pseudo-inverse Calculation | Book Chapters 6.7, other sources |

14 | Linear Transformations, The Kernel and Range of a Linear Transformation and Further Properties of Linear Transformations | Book Chapters 6.1, 6.2, 6.3, 6.4 |

Resources |

Differential Equations & Linear Algebra Second Edition, Stephen W. Goode. Prentice-Hall, Inc. 2000,1991. |

### Course Contribution to Program Qualifications

Course Contribution to Program Qualifications | |||||||

No | Program Qualification | Contribution Level | |||||

1 | 2 | 3 | 4 | 5 | |||

1 | 1. An ability to apply knowledge of mathematics, science, and engineering | X | |||||

2 | 2. An ability to identify, formulate, and solve engineering problems | X | |||||

3 | 3. An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability | ||||||

4 | 4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice | ||||||

5 | 5. An ability to design and conduct experiments, as well as to analyze and interpret data | ||||||

6 | 6. An ability to function on multidisciplinary teams | X | |||||

7 | 7. An ability to communicate effectively | X | |||||

8 | 8. A recognition of the need for, and an ability to engage in life-long learning | ||||||

9 | 9. An understanding of professional and ethical responsibility | ||||||

10 | 10. A knowledge of contemporary issues | ||||||

11 | 11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context |

### Assessment Methods

Contribution Level | Absolute Evaluation | |

Rate of Midterm Exam to Success | 30 | |

Rate of Final Exam to Success | 70 | |

Total | 100 |