TÜRKÇE
ENGLISH
Information
| Code | ECMZ203 |
| Name | Linear Algebra |
| Semester | 3. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | İngilizce |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Dr. Öğr. Üyesi FELA ÖZBEY |
Course Goal
This module aims to provide an accessible review of the linear algebra from the text book to long after the class. Linear algebra is an essential part of the mathematical background required of econometricians. It presents a source for undergraduate students. In general it covers an introduction to linear algebra which will be found helpful to all readers.
Course Content
Matrices, matrix algebra, special types of matrices, elementary row and colomn operations, echelon form, rank of a matrix, inverses, equivalent matrices, determinants, properties of determinants, cofactor and adjoint of a matrix, derivation of inverse matrix, systems of linear equations, solutions of linear equations systems, Cramers method, Gauss elimination method, vector spaces, subspaces, linear independence, bases and dimension, eigen values, eigen vectors.
Course Precondition
None
Resources
Bernard Kolman, David Hill (2008), Elementary Linear Algebra with Applications, Pearson, ISBN: 0-13-229654-3
Notes
Ron Larson, David C. Falvo, (2009), Elementary Linear Algebra, Sixth Edition, ISBN: 978-0-618-78376-2
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes special types of matrices. |
| LO02 | performs elementary row (colomn) operations. |
| LO03 | Obtains the echelon form of a matrix. |
| LO04 | Finds the rank of a matrix. |
| LO05 | Evaluates the inverse of a square matrix. |
| LO06 | Evaluates the determinant of a square matrix. |
| LO07 | Lists the properties of a determinant. |
| LO08 | Evaluates the minor matrix. |
| LO09 | Recognizes equivalent matrices. |
| LO10 | Solves linear equations systems. |
| LO11 | Applies the method of Cramer. |
| LO12 | Applies the method of Gauss. |
| LO13 | Recognizes vector spaces. |
| LO14 | Recognizes subvector spaces. |
| LO15 | Determines whether vectors are linearly independent or not. |
| LO16 | Calculates the eigenvalues of a square matrix. |
| LO17 | Calculates the eigenvectors of a square matrix. |
| LO18 | Performs matrix operations. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the basic concepts and theorems in the fields of Econometrics, Statistics and Operations research | 4 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Acquires basic Mathematics, Statistics and Operation Research concepts | 5 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Describes the necessary concepts of Business | |
| PLO04 | Beceriler - Bilişsel, Uygulamalı | Equipped with the foundations of Economics, and develops Economic models | 2 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Models problems with Mathematics, Statistics, and Econometrics | 5 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Has the ability to analyze/interpret at the conceptual level to develop solutions to problems | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Collects/analyses data | 2 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Interprets the results analyzed with the model | 2 |
| PLO09 | Beceriler - Bilişsel, Uygulamalı | Combines the information obtained from different sources within the framework of academic rules in a field which does not research | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | It develops traditional approaches, practices and methods into new working methods when it deems necessary | 2 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Leads by taking responsibility individually and/or within the team | |
| PLO12 | Yetkinlikler - Öğrenme Yetkinliği | In addition to herself/himself professional development, constantly improves in scientific, cultural, artistic and social fields in line with interests and abilities | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Being aware of the necessity of lifelong learning, it follows the current developments in the field / constantly renews itself | |
| PLO14 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses a package program of Econometrics, Statistics, and Operation Research | |
| PLO15 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses Turkish and at least one other foreign language, academically and in the business context | 4 |
| PLO16 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Interprets the feelings, thoughts and behaviors of the related persons correctly/expresses himself/herself correctly in written and verbal form | |
| PLO17 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets data on current economic and social issues | |
| PLO18 | Yetkinlikler - Alana Özgü Yetkinlik | Applies social, scientific and professional ethical values | 2 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Systems of Linear Equations, Solving a System of Linear Equations | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 2 | Definition of a Matrix, Elementary Row Operations, Using Elementary Row Operations to Solve a System | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 3 | Row-Echelon Form of a Matrix Homogeneous and Nonhomogeneous Systems of Linear Equations | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 4 | Equality of Matrices, Matrix Addition, Scalar Multiplication and Matrix Subtraction | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 5 | Matrix Multiplication, representing a system of linear equations in the form of Matrix Multiplication, Partitioned Matrices | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 6 | Properties of Matrix Operations, The Transpose of a Matrix | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 7 | The Inverse of a Matrix and Properties of Inverses, Solving a System of Equations Using an Inverse Matrix | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 8 | Mid-Term Exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 9 | Solving a System of Equations Using the Inverse Matrix. | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 10 | The Determinant of a Matrix, Definitions of Minors and Cofactors of a Matrix, The Effects of Elementary Row Operations on a Determinant, Properties of Determinants | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 11 | Eigenvalues and Eigenvectors, Finding Eigenvalues and Eigenvectors | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 12 | The Adjoint of a Matrix, The Inverse of a Matrix Given by Its Adjoint | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 13 | Cramer s Rule, Using Cramer s Rule | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 14 | Vector Spaces, Subspaces of Vector Spaces | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 15 | Linear Dependence and Linear Independence | Students will be prepared by studying relevant subjects from source books according to the weekly program | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Problem Çözme |
| 16 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||