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      MATH 250 | Course Introduction and Application Information

      Course Name
      Linear Algebra for Engineers
      Code
      Semester
      Theory
      (hour/week)
      Application/Lab
      (hour/week)
      Local Credits
      ECTS
      MATH 250
      Fall
      3
      0
      3
      6

      Prerequisites
        MATH 153 To get a grade of at least FD
      or MATH 109 To get a grade of at least FD
      Course Language
      English
      Course Type
      Required
      Course Level
      First Cycle
      Mode of Delivery -
      Teaching Methods and Techniques of the Course Problem Solving
      Q&A
      Lecture / Presentation
      National Occupation Classification -
      Course Coordinator
      • Doç. Dr. Sevin GÜMGÜM
      • Dr. Öğr. Üyesi Neslişah İMAMOĞLU KARABAŞ
      Course Lecturer(s)
      • Doç. Dr. Halis Can KOYUNCUOĞLU
      • Dr. Öğr. Üyesi Seçkin Günsen
      Assistant(s)
      • Araş. Gör. Merve KAHRAMAN ARİMAN
      • Araş. Gör. Sıla Selenay KOÇ
      Course Objectives The main objective of this course is to establish a basic mathematical background for the students who will receive engineering courses based on linear algebra by providing them with the basic knowledge on linear vector spaces, matrix operations as well as on the methods for solving and analyzing linear systems of algebraic equations.
      Learning Outcomes
      #
      Content
      PC Sub
      * Contribution Level
      1
      2
      3
      4
      5
      1apply the row operations to find (reduced) row echelon forms of matrices.
      2find the inverse of a matrix.
      3apply basic concepts of linear models to various applications.
      4evaluate the determinants of matrices.
      5investigate the linear independence of vectors.
      6identify vector spaces and their subspaces.
      7compute the eigenvalues of a matrix and corresponding eigenvectors.
      8describe the inner product.
      Course Description The main subjects of the course are the vector and matrix operations, linear independence and dependence of vectors, linear vector spaces and subspaces, dimensions and basis vectors for vector spaces, linear transformations, determinants, eigenvalue and eigenvectors.
      Related Sustainable Development Goals

       



      Course Category

      Core Courses
      X
      Major Area Courses
      Supportive Courses
      Media and Management Skills Courses
      Transferable Skill Courses

       

      WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

      Week Subjects Related Preparation Learning Outcome
      1 Systems of linear equations, row reduction and echelon forms, vector equations David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.1, 1.2, D0avid C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.1, 1.2, 1.3
      2 The matrix equation Ax=b, Solution sets of linear systems, applications of linear systems David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.4, 1.5, 1.6
      3 Linear Independence, introduction to linear transformations David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.7, 1.8
      4 The matrix of a linear transformations, linear models in business, science and engineering David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 1.9, 1.10
      5 Matrix operations, The inverse of a matrix David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 2.1, 2.2
      6 Characterization of invertible matrices, Matrix factorizations David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 2.3, 2.5
      7 Introduction to determinants, properties of determinants David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015).Section 3.1, 3.2, 3.3
      8 Cramer’s rule, volume, and linear transformations, Vector spaces and subspaces David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015).Section 3.3, 4.1
      9 Midterm Exam
      10 Null spaces, column spaces, and linear transformations, Linearly independent sets, bases David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 4.2, 4.3
      11 The dimension of a vector space, Rank, Application for Markov chains David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 4.5, 4.6, 4.9
      12 Eigenvalues and eigenvectors, The characteristic equation, Diagonalization David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 5.1, 5.2, 5.3
      13 Diagonalization, Inner product, length, and orthogonality, orthogonal sets David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Sections 5.3, 6.1, 6.2
      14 The Gram-Schmidt process, review David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed.( Pearson, 2015). Section 6.4
      15 Semester review
      16 Final exam

       

      Course Notes/Textbooks

      David C.Lay, Stephan R.Lay and Judi J. McDonald, "Linear Algebra and Its Applications", 5th ed. (Pearson,

      2015). ISBN-13:978-0321982384

      Suggested Readings/Materials

       

      EVALUATION SYSTEM

      Semester Activities Number Weigthing LO 1 LO 2 LO 3 LO 4 LO 5 LO 6 LO 7 LO 8
      Participation
      -
      -
      Laboratory / Application
      -
      -
      Field Work
      -
      -
      Quizzes / Studio Critiques
      4
      20
      Portfolio
      -
      -
      Homework / Assignments
      -
      -
      Presentation / Jury
      -
      -
      Project
      -
      -
      Seminar / Workshop
      -
      -
      Oral Exams
      -
      -
      Midterm
      1
      30
      Final Exam
      1
      50
      Total
      6
      100

      Weighting of Semester Activities on the Final Grade
      5
      50
      Weighting of End-of-Semester Activities on the Final Grade
      1
      50
      Total 6 100

      ECTS / WORKLOAD TABLE

      Semester Activities Number Duration (Hours) Workload
      Theoretical Course Hours
      (Including exam week: 16 x total hours)
      16
      3
      48
      Laboratory / Application Hours
      (Including exam week: '.16.' x total hours)
      -
      -
      -
      Study Hours Out of Class
      14
      3
      42
      Field Work
      -
      -
      -
      Quizzes / Studio Critiques
      4
      5
      20
      Portfolio
      -
      -
      -
      Homework / Assignments
      -
      -
      -
      Presentation / Jury
      -
      -
      -
      Project
      -
      -
      -
      Seminar / Workshop
      -
      -
      -
      Oral Exam
      -
      -
      -
      Midterms
      1
      30
      30
      Final Exam
      1
      40
      40
          Total
      180

       

      COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

      #
      PC Sub Program Competencies/Outcomes
      * Contribution Level
      1
      2
      3
      4
      5
      1

      Engineering Knowledge: Knowledge of mathematics, science, basic engineering, computer computation, and topics specific to related engineering disciplines; the ability to use this knowledge in solving complex engineering problems

      -
      -
      X
      -
      -
      1

      Mathematics

      -
      -
      -
      -
      -
      2

      Science

      -
      -
      -
      -
      -
      3

      Basic engineering

      -
      -
      -
      -
      -
      4

      Computer computation

      -
      -
      -
      -
      -
      5

      Topics specific to related engineering disciplines

      -
      -
      -
      -
      -
      6

      The ability to use this knowledge in solving complex engineering problems

      -
      -
      -
      -
      -
      2

      Problem Analysis: The ability to define, formulate, and analyze complex engineering problems by using fundamental science, mathematics, and engineering knowledge, while considering the relevant UN Sustainable Development Goals (SDGs) related to the problem.

      -
      -
      -
      -
      -
      3

      Engineering Design: The ability to design creative solutions to complex engineering problems; the ability to design complex systems, processes, devices, or products that meet present and future requirements, considering realistic constraints and conditions.

      -
      -
      -
      -
      -
      1

      The ability to design creative solutions to complex engineering problems

      -
      -
      -
      -
      -
      2

      Considering realistic constraints and conditions in designing complex systems, processes, devices, or products

      -
      -
      -
      -
      -
      3

      The ability to design in a way that meets current and future requirements

      -
      -
      -
      -
      -
      4

      Use of Techniques and Tools: The ability to select and use appropriate techniques, resources, and modern engineering and information technology tools, including prediction and modeling, for the analysis and solution of complex engineering problems, while being aware of their limitations

      -
      -
      X
      -
      -
      5

      Research and Investigation: The ability to use research methods, including literature review, designing experiments, conducting experiments, collecting data, analyzing and interpreting results, for the investigation of complex engineering problems.

      -
      -
      -
      -
      -
      1

      The ability to use research methods, including literature review

      -
      -
      -
      -
      -
      2

      Designing experiments

      -
      -
      -
      -
      -
      3

      Conducting experiments, collecting data, analyzing and interpreting results, for the investigation of complex engineering problems

      -
      -
      -
      -
      -
      6

      Global Impact of Engineering Practices: Knowledge of the impacts of engineering practices on society, health and safety, the economy, sustainability, and the environment within the scope of the UN Sustainable Development Goals (SDGs); awareness of the legal consequences of engineering solutions

      -
      -
      -
      -
      -
      1

      Global Impact of Engineering Practices: Knowledge of the impacts of engineering practices on society, health and safety, the economy, sustainability, and the environment within the scope of the UN Sustainable Development Goals (SDGs)

      -
      -
      -
      -
      -
      2

      Awareness of the legal consequences of engineering solutions

      -
      -
      -
      -
      -
      7

      Ethical Behavior: Acting in accordance with the principles of the engineering profession; knowledge of ethical responsibility; awareness of acting impartially and inclusively, without discrimination in any matter. (FENG101)

      -
      -
      -
      -
      -
      1

      Acting in accordance with the principles of the engineering profession; knowledge of ethical responsibility

      -
      -
      -
      -
      -
      2

      Awareness of acting impartially and inclusively, without discrimination in any matter.

      -
      -
      -
      -
      -
      8

      Individual and Team Work: The ability to work effectively as an individual and as a member or leader of both intra-disciplinary and interdisciplinary teams (whether face-to-face, remote, or hybrid).

      -
      -
      -
      -
      -
      9

      Verbal and Written Communication: Taking into account the various differences of the target audience (such as education, language, profession), particularly in technical matters.

      -
      -
      -
      -
      -
      1

      Verbal (ENGxxx)

      -
      -
      -
      -
      -
      2

      Written effective communication skills. (ENGxxx)

      -
      -
      -
      -
      -
      10

      Project Management: Knowledge of business practices such as project management and economic feasibility analysis; awareness of entrepreneurship and innovation.

      -
      -
      -
      -
      -
      1

      Knowledge of business practices such as project management and economic feasibility analysis; (FENG497-FENG498)

      -
      -
      -
      -
      -
      2

      Awareness of entrepreneurship and innovation. (FENG101)

      -
      -
      -
      -
      -
      11

      Lifelong Learning: The ability to learn independently and continuously, adapt to new and emerging technologies, and think critically about technological changes.

      -
      -
      -
      -
      -

      *1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest


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