Nevşehir Hacı Bektaş Veli University Course Catalogue
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| Year/Semester of Study | 2 / Fall Semester | ||||
| Level of Course | 1st Cycle Degree Programme | ||||
| Type of Course | Compulsory | ||||
| Department | DEPARTMENT OF COMPUTER ENGINEERING | ||||
| Pre-requisities and Co-requisites | None | ||||
| Mode of Delivery | Face to Face | ||||
| Teaching Period | 14 Weeks | ||||
| Name of Lecturer | CAHİT KÖME (cahit@nevsehir.edu.tr) | ||||
| Name of Lecturer(s) | EBUBEKİR KAYA, | ||||
| Language of Instruction | Turkish | ||||
| Work Placement(s) | None | ||||
| Objectives of the Course | |||||
| Create the necessary information for more advanced mathematics topics | |||||
| Learning Outcomes | PO | MME | |
| The students who succeeded in this course: | |||
| LO-1 | On successful completion of this course unit students will be capable of gained the ability to; perform matrix operations (addition, subtraction,multiplication). Compute the determinant of a given matrix, |
PO-4 Students gain the ability to apply knowledge of mathematics, science and engineering. PO-5 Students gain the ability to define, model, formulate and solve general engineering problems. PO-15 Students will be able to design a system or process to meet the desired needs. PO-19 Students develop self-renewal and researcher skills in order to adapt to innovations and developing technology. |
Examination |
| LO-2 | Solve systems of linear equations by using Gaussian elimination; and apply the basic techniques of matrix algebra, including finding the inverse of an invertible matrix using Gauss-Jordan elimination, |
PO-4 Students gain the ability to apply knowledge of mathematics, science and engineering. PO-5 Students gain the ability to define, model, formulate and solve general engineering problems. PO-15 Students will be able to design a system or process to meet the desired needs. PO-19 Students develop self-renewal and researcher skills in order to adapt to innovations and developing technology. |
Examination |
| LO-3 | Understand the basic ideas of vector algebra: linear dependence and independence; comprehend vector spaces and subspaces, |
PO-4 Students gain the ability to apply knowledge of mathematics, science and engineering. PO-5 Students gain the ability to define, model, formulate and solve general engineering problems. PO-15 Students will be able to design a system or process to meet the desired needs. PO-19 Students develop self-renewal and researcher skills in order to adapt to innovations and developing technology. |
Examination |
| LO-4 | Find the eigenvalues and eigenvectors of a square matrix using the characteristic polynomial, |
PO-4 Students gain the ability to apply knowledge of mathematics, science and engineering. PO-5 Students gain the ability to define, model, formulate and solve general engineering problems. PO-15 Students will be able to design a system or process to meet the desired needs. PO-19 Students develop self-renewal and researcher skills in order to adapt to innovations and developing technology. |
Examination |
| LO-5 | Calculate the inverse and n-th power of a square matrix by using Cayley-Hamilton theorem. |
PO-4 Students gain the ability to apply knowledge of mathematics, science and engineering. PO-5 Students gain the ability to define, model, formulate and solve general engineering problems. PO-15 Students will be able to design a system or process to meet the desired needs. PO-19 Students develop self-renewal and researcher skills in order to adapt to innovations and developing technology. |
Examination |
| PO: Programme Outcomes MME:Method of measurement & Evaluation |
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| Course Contents | ||
| -Matrices: Definition of matrix, Types of matrices, matrix equality, Sum and difference of matrices, The product of scaler and matrix and their properties , Transpose of matrix and its properties - Some Special Matrices and Matrix Applications - Elementary row and column operations in matrices, Reduced row–echelon form, Rank of a matrix, The inverse of a square matrix, - Determinants: The determinant of a square matrix, Laplace's expansion, Properties of determinants -Sarrus rule, Additional matrix, Calculation of the inverse of a matrix with the aid of additional matrix - Systems of Linear Equations: Solving systems of linear equations with the aid of equivalent matrices, Linear homogeneous equations, -Cramer's method, The solution with the help of coefficients matrix -Vectors: Vector definition, the sum of vectors, the difference, the analytical expression vectors, scalar product of vectors, properties of the scalar multiplication Scalar product and its features, the mixed multiplication and properties, and properties of double vector product, -Vector spaces: Definition of vector spaces and theorems. Subspaces. Span concept and fundamental theorems. Linear dependence and linear independence of vectors and some theorems about linear dependence and linear independence. -Bases and dimension concepts and fundamental theorems. Definition of coordinates and transition matrices and some theorems. -Eigenvalues and Eigenvectors: The Calculation of Eigenvalues and Eigenvectors of a square matrix, - The calculation of Inverse and power of a square matrix with the help of the Cayley-Hamilton theorem. | ||
| Weekly Course Content | ||
| Week | Subject | Learning Activities and Teaching Methods |
| 1 | Definition of matrix, types of matrix, Equality of Matrices, Addition and subtraction of matrices, matrix multiplication by a scalar, Some properties about them. Multiplying matrices and Some properties about it. Transposes of matrices and properties of the transpose. | Explaining, Question-answer, Problem Solving, Practice |
| 2 | Some Special Matrices and matrix applications.(Symmetric Matrix,Anti symmetric matrix, periodic matrix, idempotent matrix, Nilpotent matrix, orthogonal matrix, A conjugate of a matrix and its properties, hermitian matrix,Anti hermitian matrix, regular matrix, singuler matrix, and their applications. | Explaining, Question-answer, Problem Solving, Practice |
| 3 | Elementary row and column operations in the Matrices. Row-Echelon form and reduced row-echelon form. Rank of a matrix. Inverses of matrices and some applications about this. | Explaining, Question-answer, Problem Solving, Practice |
| 4 | Definition of a determinant. Laplace expansion of a matrix. Properties of a determinant. | Explaining, Question-answer, Problem Solving, Practice |
| 5 | Rule of Sarrus. The adjoint of a matrix, Using the adjoint matrix to find an inverse matrix and some applications about this. | Explaining, Question-answer, Problem Solving, Practice |
| 6 | System of linear equations: solving systems of linear equations with aid of equaivalent matrices, linear homogeneous equations and some applications about this. | Explaining, Question-answer, Problem Solving, Practice |
| 7 | Cramer’s rule. Using the inverse of a coefficient matrix to solve a linear systems and some applications about this. | Explaining, Question-answer, Problem Solving, Practice |
| 8 | mid-term exam | |
| 9 | Vectors: Definition of Vectors,The sum of vectors and Subtraction of vectors and Multiplication of vectors, Dot product of two vectors and their properties, Vector product of two vectors(Cross product of vectors ) and their properties, Mixed product of three vectors(Triple product) and their properties, Double vector product(double cross) and their properties and some applications about this. | Explaining, Question-answer, Problem Solving, Practice |
| 10 | Vector Spaces: Definition of vector spaces and theorems. Subspaces and their applications. | Explaining, Question-answer, Problem Solving, Practice |
| 11 | Span concept and fundamental theorems. Linear dependence and linear independence of vectors and some theorems about linear dependence and linear independence. Some applications about this. | Explaining, Question-answer, Problem Solving, Practice |
| 12 | Quiz, Bases and dimension concepts and fundamental theorems. Some applications about this. | Explaining, Question-answer, Problem Solving, Practice |
| 13 | Definition of coordinates and transition matrices and some theorems.Some applications about this. | Explaining, Question-answer, Problem Solving, Practice |
| 14 | Eigenvalues and eigenvectors: The eigenvalues of a square matrix.Cayley Hamilton Theorem and their applications. | Explaining, Question-answer, Problem Solving, Practice |
| 15 | Application | Explaining, Question-answer, Problem Solving, Practice |
| 16 | final exam | |
| Recommend Course Book / Supplementary Book/Reading | ||
| 1 | Gilbert Strang - Introduction of Lineer Algebra | |
| 2 | Arif Sabuncuoğlu - Lineer Cebir | |
| Required Course instruments and materials | ||
| Anton Howard, “Elementary Linear Algebra”, 2000 | ||
| Assessment Methods | |||
| Type of Assessment | Week | Hours | Weight(%) |
| mid-term exam | 8 | 1 | 40 |
| Other assessment methods | |||
| 1.Oral Examination | |||
| 2.Quiz | |||
| 3.Laboratory exam | |||
| 4.Presentation | |||
| 5.Report | |||
| 6.Workshop | |||
| 7.Performance Project | |||
| 8.Term Paper | |||
| 9.Project | |||
| final exam | 16 | 1 | 60 |
| Student Work Load | |||
| Type of Work | Weekly Hours | Number of Weeks | Work Load |
| Weekly Course Hours (Theoretical+Practice) | 3 | 14 | 42 |
| Outside Class | |||
| a) Reading | 13 | 4 | 52 |
| b) Search in internet/Library | 0 | ||
| c) Performance Project | 0 | ||
| d) Prepare a workshop/Presentation/Report | 0 | ||
| e) Term paper/Project | 0 | ||
| Oral Examination | 0 | ||
| Quiz | 0 | ||
| Laboratory exam | 0 | ||
| Own study for mid-term exam | 1 | 12 | 12 |
| mid-term exam | 1 | 1 | 1 |
| Own study for final exam | 1 | 12 | 12 |
| final exam | 1 | 1 | 1 |
| 0 | |||
| 0 | |||
| Total work load; | 120 | ||