Faculty of Engineering and Natural Sciences · Software Engineering (English 30%) · Undergraduate
ECTS: 4 T+P+L: 3+0+0 Compulsory
Coordinator: Dr. Öğr. Üyesi Sümeyra BEDİR
Prerequisites: MAT 115 - Mathematics I
Course Objective
Learning of the linear system, determinants, matrices, eigenvalues and eigenvectors, vector spaces and linear operators theory.
Course Content
Covers systems of linear equation, algebra of matrices, linear transformations, determinants, vector spaces, inner product spaces, eigenvalues and eigenvectors, diagonalization and orthogonality, special matrices and applications.
Course Learning Outcomes
- Understand the structure of systems of linear equations and classify them.
- Find solutions of systems of linear equations using Gauss and Gauss-Jordan elimination methods.
- Identify algebraic properties of matrices.
- Classify matrices with respect to echelon forms.
- Apply matrix operations (addition, scalar multiplication, multiplication)
- Check invertibility of a matrix and find its inverse using different methods such as elementary matrices and adjoints.
- Relate properties of systems of linear equations with properties of their coefficient matrices
- Use elementary matrices and elementary row operations in identifying matrices and solving systems of linear equations.
- Express possible factorizations of square matrices.
- Understand the concept of determinants, know the properties of determinants, and apply them in problem-solving.
- Solve n-dimensional linear systems using the determinant (Cramer’s) method
- Demonstrate a thorough knowledge of vector spaces and subspaces.
- Examine linear independence and spanning properties of a set of vectors in a vector space.
- Find bases for vector spaces and subspaces.
- Find bases for column, row and null spaces of a given matrix, find the rank and nullity.
- Define linear transformations and examine their properties.
- Find eigenvalues and eigenvectors of a square matrix.
- Check diagonalizability of a square matrix and apply diagonalization when it is possible.
- Apply vector operations in Real Vector Spaces
- Use Gram-Schmidt orthogonalization process to orthogonalize/orthonormalize any given basis.
Core Area Distribution
(46) Mathematics and Statistics%80 (52) Engineering and Engineering Trades%20
Teaching Methods
ExpressionQuestion-AnswerDiscussionSelf studyProblem Solving
Assessment & Evaluation
HomeworkTesting (Essay / Tests: True-Falls, multiple-choice, short answer, matching)
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 16 | 3 | 48 |
| Out of Class Study Period | 16 | 1 | 16 |
| Midterm | 2 | 3 | 6 |
| Quiz | 9 | 1 | 9 |
| Assignment | 5 | 3 | 15 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 3 | 3 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | Matrix Notion and Matrix algebra | Basic algebra operations |
| 2 | The transpose of a matrix, augmented matrix and inversion | Previous lecture |
| 3 | Determinant of a matrix and properties of determinant | Previous lectures |
| 4 | Linear systems and properties. Solution techniques to solve system of linear equations | Previous lectures |
| 5 | A vector notion, properties and vector algebra. Vectors in plane and space. | Previous lectures |
| 6 | Düzlemde, uzayda doğru denklemi ve uzayda düzlem denklemi. Vektör uzayı kavramı ve özellikleri. | |
| 7 | Standart vektör uzayları .Alt vektör uzayları, alt uzayların boyutları | |
| 8 | Ara Sınav | Ara Sınav |
| 9 | Vektörlerin Lineer bağımlılığı ve bağımsızlığı. | |
| 10 | Bazların değişimi .Alt vektör uzaylarının doğrudan toplamı. | |
| 11 | İç çarpım, iç çarpım uzayı. | |
| 12 | Ortogonallik , Gram-Schmidt ortogonalleme işlemi. | |
| 13 | Vektör uzaylarında Lineer dönüşümler. | |
| 14 | Vektör uzaylarında lineer dönüşümlerin sınıflandırılması. | |
| 15 | Lineer dönüşümlerin matrislerle gösterilmesi. | |
| 16 | Final Sınavı | Final Sınavı |