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      Department of Electrical and Electronics Engineering

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      EEE 281 | Course Introduction and Application Information

      Course Name
      Engineering Mathematics I
      Code
      Semester
      Theory
      (hour/week)
      Application/Lab
      (hour/week)
      Local Credits
      ECTS
      EEE 281
      Fall
      2
      2
      3
      6

      Prerequisites
        MATH 153 To succeed (To get a grade of at least DD)
      Course Language
      English
      Course Type
      Required
      Course Level
      First Cycle
      Mode of Delivery -
      Teaching Methods and Techniques of the Course Problem Solving
      National Occupation Classification -
      Course Coordinator
      • Prof. Dr. Murat AŞKAR
      Course Lecturer(s)
      • Prof. Dr. Murat AŞKAR
      Assistant(s) -
      Course Objectives Vector spaces, bases, GramSchmidt, linear maps and matrices, linear functionals, the transposed matrix and duality, kernel, image and rank, invertibility, triangularization, determinants and multilinear forms, powers of matrices, the exponential of a matrix, eigenvalues, eigenspaces, singular value decomposition, Jordan normal form. Symmetric hermitian and positive definite matrices, diagonalizability, unitary matrices. Solution of firstorder ODEs by analytical, graphical, and numerical methods. Linear ODEs, primarily second order with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Laplace transform methods; convolution and delta function. Matrix methods for the solution of ODEs: eigenvalues and eigenvectors, matrix exponentials, variation of parameters. MATLAB is introduced for problem sets.
      Learning Outcomes
      #
      Content
      PC Sub
      * Contribution Level
      1
      2
      3
      4
      5
      1Explain the foundations of Vector spaces, bases, Gram-Schmidt, linear maps and matrices, linear functionals, the transposed matrix and duality, kernel, image and rank, invertibility, triangularization, determinants and multilinear forms, powers of matrices, the exponential of a matrix, eigenvalues, eigenspaces, singular value decomposition, Jordan normal form,
      2Analyse first-order differential equations; seperable differential equations, linear differential equations and higher order linear differential equations,
      3Apply the methods of undetermined coefficients, and the method of variation of parameters for the solution of ordinary differential equations,
      4Apply the techniques of reduction of order for the numerical solutions of ordinary differential equations,
      5Use Laplace Transform to solve initial value problems,
      6Analyse the problems of differential equations with many unknowns through linear algebra and applied matrix theory.
      Course Description Vector spaces, bases, GramSchmidt, linear maps and matrices, linear functionals, the transposed matrix and duality, kernel, image and rank, invertibility, triangularization, determinants and multilinear forms, powers of matrices, the exponential of a matrix, eigenvalues, eigenspaces, singular value decomposition, Jordan normal form. Symmetric hermitian and positive definite matrices, diagonalizability, unitary matrices. Solution of firstorder ODEs by analytical, graphical, and numerical methods. Linear ODEs, primarily second order with constant coefficients. Complex numbers and exponentials. Inhomogeneous equations: polynomial, sinusoidal, and exponential inputs. Laplace transform methods; convolution and delta function. Matrix methods for the solution of ODEs: eigenvalues and eigenvectors, matrix exponentials, variation of parameters. MATLAB is introduced for problem sets.
      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 Matrices and Determinants / Dizey ve Belirteçler Systems of Linear Equations. Matrices and Matrix Operations. Inverses of Matrices. Kısım 1. / Chapter 1 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      2 Special Matrices and Additional Properties of Matrices. Determinants. Further Properties of Determinants. Proofs of Theorems on Determinants. Kısım 1. / Chapter 1 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      3 Vector Spaces / Vektör Uzayları Vector Spaces. Subspaces and Spanning Sets. Linear Independence and Bases. Dimension; Nullspace, Rowspace, and Column Space. Wronskians Kısım 2. / Chapter 2 . • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      4 First Order Ordinary Differential Equations / Birinci Mertebeden Türevli Denklemler Introduction to Differential Equations. Separable Differential Equations. Exact Differential Equations. Linear Differential Equations. Kısım 3. / Chapter 3 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      5 More Techniques for Solving First Order Differential Equations. Modeling With Differential Equations. Reduction of Order. The Theory of First Order Differential Equations. Numerical Solutions of Ordinary Differential Equations. Kısım 3. / Chapter 3 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      6 Linear Differential Equations / Doğrusal Türevli Denklemler The Theory of Higher Order Linear Differential Equations. Homogenous Constant Coefficient Linear Differential Equations. The Method of Undetermined Coefficients. The Method of Variation of Parameters. Some Applications of Higher Order Differential Equations Kısım 4. / Chapter 4 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      7 Linear Transformations, Eigenvalues, and Eigenvectors / Doğrusal Dönüşümler, Özdeğerler, ve Özvektörler Linear Transformations. The Algebra of Linear Transformations; Differential Operators and Differential Equations. Matrices for Linear Transformations. Kısım 5. / Chapter 5 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      8 Eigenvectors and Eigenvalues of Matrices. Similar Matrices, Diagonalization, and Jordan Canonical Form.Eigenvectors and Eigenvalues of Linear Transformations Kısım 5. / Chapter 5 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      9 Systems of Differential Equations / Türevli Denklem Sistemleri The Theory of Systems of Linear Differential Equations. Homogenous Systems with Constant Coefficients: The Diagonalizable Case. Kısım 6. / Chapter 6 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      10 Homogenous Systems with Constant Coefficients: The Nondiagonalizable Case. Nonhomogenous Linear Systems. Nonhomogenous Linear Systems Kısım 6. / Chapter 6 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      11 Converting Differential Equations to First Order Systems. Applications Involving Systems of Linear Differential Equations. 2x2 Systems of Nonlinear Differential Equations. Kısım 6. / Chapter 6 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      12 Laplace Transform / Laplace Dönüşümü Definition and Properties of the Laplace Transform. Solving Constant Coefficient Linear Initial Value Problems with Laplace Transforms Kısım 7. / Chapter 7 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      13 The Step Functions, Impulse Functions and the Delta Function. Convolution Integrals. Systems of Linear Differential Equations. Kısım 7. / Chapter 7 . • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      14 Power Series Solutions to Linear Differential Equations / Doğrusal Türevli Denklemlerin Serilerle Çözümü Introduction to Power Series Solutions. Series Solutions for Second Order Linear Differential equations. Kısım 8. / Chapter 8 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      15 Euler Type Equations. Series Solutions Near a Regular Singular Point.. Kısım 8. / Chapter 8 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      16 Inner Product Spaces / Dahili Çarpım Uzayları Inner Product Spaces. Orthonormal Bases Schur's Theorem and Symmetric Matrices. Kısım 9. / Chapter 9 • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122

       

      Course Notes/Textbooks • Linear Algebra and Differential Equations, 1/E, Peterson & Sochacki ©2002 AddisonWesley Published:07/24/2001, ISBN10: 0201662124, ISBN13: 9780201662122
      Suggested Readings/Materials • Differential Equations and Linear Algebra, 3/E, Edwards & Penney, ©2010, PrenticeHall, Published:10/10/2008, ISBN10: 0136054250, ISBN13: 9780136054252 • Differential Equations and Linear Algebra, 3/E, Goode & Annin, ©2008 PrenticeHall, Published:03/13/2007, ISBN10: 0130457949, ISBN13: 9780130457943 • Elementary Differential Equations, 6/E, Edwards & Penney ©2008, Pearson, ISBN10: 0132397307, ISBN13: 9780132397308• Differential Equations and Linear Algebra, 3/E, Edwards & Penney, ©2010 , PrenticeHall, Published:10/10/2008ISBN10: 36054250, ISBN13: 9780136054252 • Advanced Modern Engineering Mathematics, 3/E, James & James, ©2004 , PrenticeHall, Published:07/21/2005, ISBN10: 0130454257, ISBN13: 9780130454256 • Advanced Engineering Mathematics, 2/E, Greenberg ©1998 , PrenticeHall, Published: 01/08/1998, ISBN10: 0133214311, ISBN13: 9780133214314

       

      EVALUATION SYSTEM

      Semester Activities Number Weigthing LO 1 LO 2 LO 3 LO 4 LO 5 LO 6
      Participation
      Laboratory / Application
      Field Work
      Quizzes / Studio Critiques
      3
      20
      Portfolio
      Homework / Assignments
      1
      5
      Presentation / Jury
      Project
      Seminar / Workshop
      Oral Exams
      Midterm
      1
      35
      Final Exam
      1
      40
      Total

      Weighting of Semester Activities on the Final Grade
      3
      60
      Weighting of End-of-Semester Activities on the Final Grade
      1
      40
      Total

      ECTS / WORKLOAD TABLE

      Semester Activities Number Duration (Hours) Workload
      Theoretical Course Hours
      (Including exam week: 16 x total hours)
      16
      4
      64
      Laboratory / Application Hours
      (Including exam week: '.16.' x total hours)
      16
      0
      Study Hours Out of Class
      16
      4
      64
      Field Work
      0
      Quizzes / Studio Critiques
      3
      0
      Portfolio
      0
      Homework / Assignments
      0
      Presentation / Jury
      0
      Project
      0
      Seminar / Workshop
      0
      Oral Exam
      0
      Midterms
      1
      10
      10
      Final Exam
      1
      30
      30
          Total
      168

       

      COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

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

      To have adequate knowledge in Mathematics, Science and Electrical and Electronics Engineering; to be able to use theoretical and applied information in these areas on complex engineering problems.

      -
      -
      -
      -
      X
      2

      To be able to identify, define, formulate, and solve complex Electrical and Electronics Engineering problems; to be able to select and apply proper analysis and modeling methods for this purpose.

      -
      -
      -
      -
      X
      3

      To be able to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the requirements; to be able to apply modern design methods for this purpose.

      -
      -
      -
      -
      X
      4

      To be able to devise, select, and use modern techniques and tools needed for analysis and solution of complex problems in Electrical and Electronics Engineering applications; uses computer and information technologies effectively.

      -
      -
      -
      -
      X
      5

      To be able to design and conduct experiments, gather data, analyze and interpret results for investigating complex engineering problems or Electrical and Electronics Engineering research topics.

      -
      -
      -
      X
      -
      6

      To be able to work efficiently in Electrical and Electronics Engineering disciplinary and multi-disciplinary teams; to be able to work individually.

      -
      -
      X
      -
      -
      7

      To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively, to be able to give and receive clear and comprehensible instructions.

      -
      -
      -
      -
      -
      8

      To have knowledge about global and social impact of engineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to Electrical and Electronics Engineering; to be aware of the legal ramifications of Electrical and Electronics Engineering solutions.

      -
      X
      -
      -
      -
      9

      To be aware of ethical behavior, professional and ethical responsibility; to have knowledge about standards utilized in engineering applications

      -
      -
      X
      -
      -
      10

      To have knowledge about industrial practices such as project management, risk management, and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development.

      -
      -
      -
      X
      -
      11

      To be able to collect data in the area of Electrical and Electronics Engineering, and to be able to communicate with colleagues in a foreign language. ("European Language Portfolio Global Scale", Level B1)

      -
      X
      -
      -
      -
      12

      To be able to speak a second foreign language at a medium level of fluency efficiently.

      -
      -
      -
      -
      -
      13

      To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Electrical and Electronics Engineering.

      -
      -
      -
      X
      -

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


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