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İzmir Ekonomi Üniversitesi

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    GRADUATE SCHOOL

    M.SC. in Computer Engineering (Without Thesis)

    MATH 601 | Course Introduction and Application Information

    Course Name
    Differential Equations
    Code
    Semester
    Theory
    (hour/week)
    Application/Lab
    (hour/week)
    Local Credits
    ECTS
    MATH 601
    Fall/Spring
    3
    0
    3
    7.5

    Prerequisites
    None
    Course Language
    English
    Course Type
    Elective
    Course Level
    Third Cycle
    Mode of Delivery -
    Teaching Methods and Techniques of the Course Problem Solving
    Case Study
    Q&A
    National Occupation Classification -
    Course Coordinator
    Course Lecturer(s)
    Assistant(s)
    Course Objectives This course aims to give the analysis of linear and nonlinear systems, existence and uniqueness of solutions and stability theory.
    Learning Outcomes
    #
    Content
    		 PC Sub
    * Contribution Level
    1
    2
    3
    4
    5
    1will be able to analyze, transform, use in the models and solve the second order differential equations
    2will be able to solve Systems of Linear differential equations.
    3will be able to analyze the methods of nonlinear differential equations.
    4will be able to solve Hamiltonian Systems.
    5will be able to determine Stability of linear and nonlinear systems.
    Course Description This course contains the results of linear equations and systems, perturbations of linear systems, the existence and uniqueness of nonlinear initial value problems and the stability theory of linear and nonlinear equations. It also includes the boundary value problems.

     



    Course Category

    		Core Courses
    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 Initial-value problems, Picard existence theorem. John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 1.2, 1.3
    2 Peano existence theorem. John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section: 1.4
    3 Continiuity of solutions. John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 2.1, 2.3, 2.4
    4 Continuous dependance of solutions on initial conditions, Continuity of solutions wrt Parameter John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 2.3, 2.4
    5 Linear systems of differential equations John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 5.1
    6 Stability Theory: First order systems John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 7.1
    7 Stability Theory: Lyapunov’s method R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 12.5
    8 Stability Theory: Higher order systems R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section: 12.7
    9 Perturbated Linear Systems John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 8.1
    10 Comparison theorems John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 4.1
    11 Diffrential inequalities John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 4.1
    12 Diffrential inequalities: Applications John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), Section 4.1
    13 Boundary value problems R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section. 11.3
    14 Boundary value problems R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section. 11.4,11.7
    15 Semester Review Nonlinear Ordinary Differential Equations, D.W.Jordan & P.Smith,Oxford, Fourth Edition
    16 Final Exam

     

    Course Notes/Textbooks

    John R Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, ‘’ Ordinary Differential Equations and Boundary Value Problems: Volume I: Advanced Ordinary Differential Equations’’, (World Scientific, 2018), ISBN: 9811221359,9789811221354,9813236450,9789813236455.
    Suggested Readings/Materials

    Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), ISBN-13: 978-0321747747.

     

    EVALUATION SYSTEM

    Semester Activities Number Weighting LO 1 LO 2 LO 3 LO 4 LO 5
    Participation
    Laboratory / Application
    Field Work
    Quizzes / Studio Critiques
    Portfolio
    Homework / Assignments
    Presentation / Jury
    Project
    Seminar / Workshop
    Oral Exams
    Midterm
    2
    60
    Final Exam
    1
    40
    Total

    Weighting of Semester Activities on the Final Grade
    2
    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
    3
    48
    Laboratory / Application Hours
    (Including exam week: '.16.' x total hours)
    16
    0
    Study Hours Out of Class
    15
    6
    90
    Field Work
    0
    Quizzes / Studio Critiques
    0
    Portfolio
    0
    Homework / Assignments
    0
    Presentation / Jury
    0
    Project
    0
    Seminar / Workshop
    0
    Oral Exam
    0
    Midterms
    2
    25
    50
    Final Exam
    1
    37
    37
        Total
    225

     

    COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

    #
    		 PC Sub Program Competencies/Outcomes
    * Contribution Level
    1
    2
    3
    4
    5
    1 Accesses information in breadth and depth by conducting scientific research in Computer Engineering, evaluates, interprets and applies information.
    -
    -
    -
    X
    -
    2 Is well-informed about contemporary techniques and methods used in Computer Engineering and their limitations.
    -
    -
    X
    -
    -
    3 Uses scientific methods to complete and apply information from uncertain, limited or incomplete data, can combine and use information from different disciplines.
    -
    -
    -
    X
    -
    4 Is informed about new and upcoming applications in the field and learns them whenever necessary.
    -
    -
    -
    -
    X
    5 Defines and formulates problems related to Computer Engineering, develops methods to solve them and uses progressive methods in solutions.
    -
    -
    -
    -
    X
    6 Develops novel and/or original methods, designs complex systems or processes and develops progressive/alternative solutions in designs.
    -
    -
    -
    X
    -
    7 Designs and implements studies based on theory, experiments and modelling, analyses and resolves the complex problems that arise in this process.
    -
    -
    -
    X
    -
    8 Can work effectively in interdisciplinary teams as well as teams of the same discipline, can lead such teams and can develop approaches for resolving complex situations, can work independently and takes responsibility.
    -
    -
    X
    -
    -
    9 Engages in written and oral communication at least in Level B2 of the European Language Portfolio Global Scale.
    -
    -
    X
    -
    -
    10 Communicates the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.
    -
    -
    X
    -
    -
    11 Is knowledgeable about the social, environmental, health, security and law implications of Computer Engineering applications, knows their project management and business applications, and is aware of their limitations in Computer Engineering applications.
    -
    -
    X
    -
    -
    12 Highly regards scientific and ethical values in data collection, interpretation, communication and in every professional activity.
    -
    X
    -
    -
    -

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

     

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