COURSE UNIT TITLE

: LINEAR ALGEBRA

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 3001 LINEAR ALGEBRA COMPULSORY 2 2 0 7

Offered By

Physics

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ENGIN MERMUT

Offered to

Physics
Physics(Evening)

Course Objective

The aim of this course is to investigate the basic concepts and methods of linear algebra such as solutions of linear systems of equations, the concepts of matrices, determinants, vectors in n dimension and vector spaces, linear transformations and operators, inner product spaces, orthogonality, self-adjoint, unitary, normal and orthogonal operators, Spectral theorem, bilinear and quadratic forms, Jordan form and rational canonical form.

Learning Outcomes of the Course Unit

1   be able to analyse linear systems of equations using matrices, elementary matrices and inverse of matrices.
2   be able to use linear operators and their matrix representations for computations.
3   be able to apply the determinant and its properties.
4   be able to analyse vector spaces, subspaces, linear dependence and linear independence of vectors and bases for vector spaces.
5   be able to identify eigenvalues and related eigenvectors, and to operate diagonalization.
6   be able to use properties of inner product spaces and the properties of the normal, self-adjoint, unitary and orthogonal operators.
7   be able to use Gram Schmidt orthogonalization process to find an orthonormal basis for a subspace of an inner product space and determine the formula for the orthogonal projection map onto this subspace using that orthonormal basis.
8   be able to find the Jordan form of a matrix.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Systems of Linear Equations.
2 Matrix Algebra. Elementary Matrix Operations and Elementary Matrices. The Rank of a Matrix and Matrix Inverses.
3 Vector Spaces. Subspaces.
4 Linear Dependence and Independence. Bases and dimension. Dual spaces.
5 Linear Transformations, Nullspace, Range. Matrix Representation of Linear Transformations and the Change-of-basis formula.
6 Determinants of Matrices. The Geometric Meaning of the Determinant: Volumes and Orientation.
7 Eigenvalues and Eigenvectors. Diagonalizability. Invariant Subspaces.
8 Real and Complex Inner Product Spaces. The Gram-Schmidt Orthogonalization Process and Orthogonal Complements. The Orthogonal Projection onto a Subspace.
9 Midterm Exam
10 Normal, Self-adjoint, Unitary and Orthogonal operators. The Spectral Theorem. Positive operators.
11 The Singular Value Decomposition and the Pseudoinverse.
12 Bilinear and Quadratic Forms. Slyvester s Law of Inertia. The Geometry of Orthogonal Operators.
13 Nilpotent linear operators. Jordan Canonical Form.
14 Cayley Hamilton Theorem and the Minimal Polynomial. Rational Canonical Form.

Recomended or Required Reading

Textbook(s)/References/Materials:
Textbook(s):
[1] Friedberg,S. H., Insel, A. J., Spence, L. E. Linear Algebra, 4th Edition, Pearson, 2003.
[2] Koç, C. Basic Linear Algebra, Matematik Vakfı Yayınları, 2009 (Turkish translation Doğrusal Cebir , 2014).

Supplementary Book(s):
[1] Shifrin, T. and Adams, M. R. Linear Algebra: A Geometric Approach, 2nd edition, W. H. Freeman and Company, 2011.
[2] Koç, C. Topics in Linear Algebra, Matematik Vakfı Yayınları, 1996.
[3] Strang, G. Linear Algebra and Its Applications. 4th edition. Thomson Brooks/Cole, 2006.

References:
[1] Lay, D. C. Linear Algebra and Its Applications. 4th edition. Pearson, 2012.
[2] Hoffman, K. M. and Kunze, R. Linear Algebra. 2nd edition. Pearson, 1971.

Materials: Lecture Notes.

Planned Learning Activities and Teaching Methods

Lecture notes.
Problem solving.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 QUZ QUIZ
3 ASG ASSIGNMENT
4 FIN FINAL EXAM
5 FCG FINAL COURSE GRADE MTE * 0.40 + QUZ * 0.10 + ASG * 0.10 + FIN * 0.40
6 RST RESIT
7 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + QUZ * 0.10 + ASG * 0.10 + RST * 0.40


Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

Office: B251/1 (Math. Dept.)
Phone: +90 (232) 301 85 82

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 4 52
Preparations before/after weekly lectures 12 2 24
Preparation for midterm exam 1 20 20
Preparation for final exam 1 30 30
Preparing assignments 4 5 20
Preparation for quiz etc. 4 2,5 10
Final 1 2 2
Midterm 1 2 2
Quiz etc. 4 1 4
TOTAL WORKLOAD (hours) 164

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12
LO.1555344
LO.2555344
LO.3555344
LO.4555344
LO.5555344
LO.6555344
LO.7555344
LO.8555344

CONTACT INFORMATION
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Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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