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  • Course Information
    • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    Linear Algebra MAT221 FALL-SPRING 3+0 E 6
    Learning Outcomes
    1-Interprets that mathematics is based on numbers and what mathematical systems do.
    2-Defines concepts of matrix and vector space.
    3-Design the geometrically corresponding concepts when reducing the dimensions of these spaces to 2 and 3.
    4-Search Linear Equation Systems and Solution Methods.
  • ECTS / WORKLOAD
    • ActivityPercentage

    (100)

    		NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14342
    Classroom study (Pre-study, practice)14684
    Assignments0000
    Short-Term Exams (exam + preparation) 10155
    Midterm exams (exam + preparation)4012020
    Project0000
    Laboratory 0000
    Final exam (exam + preparation) 5012525
    0000
    Total Workload (hours)   176
    Total Workload (hours) / 30 (s)     5,87 ---- (6)
    ECTS Credit   6
  • Course Content
    • Week Topics Study Metarials
    1 Matrices and Systems of Linear Equations, Row Echelon Form R1-Chapter-1
    2 Elementary matrices, elementary row and column operations in Matrices , separated matrices, triangular decomposition R1-Chapter-1
    3 Definitions of permutation, definition of determinant. R1-Chapter-1
    4 Determinant Expansion, Cramer`s rule R1-Chapter-1
    5 Definition of Vector spaces, Vectors in the plane R1- Chapter -2
    6 Vectors in Space, subspaces R1- Chapter -2
    7 Definition of linear combination and linear independence R1- Chapter -2
    8 Dimension of vector space R1- Chapter -2
    9 Rank of a matrix, Null space of a matrix R1- Chapter -3
    10 Linear transformations, rank and nullity of a linear transformation. R1- Chapter -3
    11 Matrix representation of linear representations R1- Chapter-7
    12 Inner Product R1-Chapter -8
    13 Orthogonal Complement, Vector Product R1-Chapter -8
    14 Eigenvectors of Linear Transform, Diagonalizable Transformations R1- Chapter -10
    Prerequisites -
    Language of Instruction Turkish
    Responsible Dr. Esma BARAN ÖZKAN
    Instructors -
    Assistants -
    Resources R1. Sabuncuoğlu, A. (2012). Mühendislik ve İstatistik Bölümleri için Lineer Cebir(2. Basım). Nobel Akademik Yayıncılık, Ankara.
    Supplementary Book SR1. Leon, S. J. (2015). Linear Algebra with Applications (7th edition). Pearson Prentice Hall, New Jersey. SR2. Kolman, B.(2021). Introductory Linear Algebra with
    Goals To teach the basic concepts of linear algebra and its application to some engineering problems
    Content Matrices and Systems of Equations: Systems of Linear Equations, Row Echelon Form, Matrix algebra, elementary matrices, separated matrices, Determinants: determinant of a matrix, properties of determinant, Cramer`s rule, Vector spaces: definition and examples, subspaces, linear dependence, Base and dimension, base change, row space and column space, Linear transformations: definition and examples, matrix representation of linear representations, similarity, Orthogonality: scalar product in n-dimensional real space, orthogonal subspaces, Least squares method, inner product spaces, orthonormal sets, Gram-Shmidt orthogonalization process, orthogonal polynomials, Eigenvalues and eigenvectors, diagonalization, Hermit matrices, single value decomposition, Quadratic forms, Positive defined matrices
  • Program Learning Outcomes
    • Program Learning Outcomes Level of Contribution
    1 Having advanced theoretical and applied knowledge in the basic areas of mathematics 3
    2 Ability of abstract thinking 3
    3 To be able to use the acquired mathematical knowledge in the process of defining, analyzing and separating the problem encountered into solution stages. 3
    4 Associating mathematical achievements with different disciplines and applying them in real life 3
    5 Ability to work independently in a problem or project that requires knowledge of mathematics -
    6 Ability to work harmoniously and effectively in national or international teams and take responsibility -
    7 Having the skills to critically evaluate and advance the knowledge gained from different areas of mathematics -
    8 To be able to determine what kind of knowledge learning the problem faced and to direct this knowledge learning process. 2
    9 To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time -
    10 Ability to verbally and in writing convey thoughts on mathematical issues, and solution proposals to problems, to experts or non-experts. -
    11 Being able to produce projects and organize events with social responsibility awareness -
    12 Being able to follow publications in the field of mathematics and exchange information with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level -
    13 Ability to use computer software (at least at the Advanced Level of European Computer Use License), information and communication technologies for solving mathematical problems, transferring ideas and results -
    14 Being conscious of acting in accordance with social, scientific, cultural and ethical values -
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