## Course Detail

## Course Description

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

LINEAR ALGEBRA | IND2119550 | Fall Semester | 3+0 | 3 | 6 |

Course Program | Pazartesi 13:30-14:15 Pazartesi 14:30-15:15 Pazartesi 15:30-16:15 Pazartesi 16:30-17:15 |

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) | Assist.Prof. Cihan Bilge KAYASANDIK, 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 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||

2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||

3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | ||||||

4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | ||||||

5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | ||||||

6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | X | |||||

7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | X | |||||

8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | ||||||

9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | ||||||

10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||

11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. |

## 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 | IND2119550 | Fall Semester | 3+0 | 3 | 6 |

Course Program | Pazartesi 13:30-14:15 Pazartesi 14:30-15:15 Pazartesi 15:30-16:15 Pazartesi 16:30-17:15 |

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) | Assist.Prof. Cihan Bilge KAYASANDIK, 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 | Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems. | X | |||||

2 | Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose. | X | |||||

3 | Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. | ||||||

4 | Ability to select and use modern techniques and tools needed for analyzing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. | ||||||

5 | Ability to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or discipline specific research questions. | ||||||

6 | Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. | X | |||||

7 | Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. | X | |||||

8 | Awareness of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. | ||||||

9 | Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices. | ||||||

10 | Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. | ||||||

11 | Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions. |

### Assessment Methods

Contribution Level | Absolute Evaluation | |

Rate of Midterm Exam to Success | 30 | |

Rate of Final Exam to Success | 70 | |

Total | 100 |