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    Department of Mechanical Engineering

    MATH 207 | Course Introduction and Application Information

    Course Name
    Introduction to Differential Equations I
    Code
    Semester
    Theory
    (hour/week)
    Application/Lab
    (hour/week)
    Local Credits
    ECTS
    MATH 207
    SPRING
    2
    2
    3
    5

    Prerequisites MATH 154 To get a grade of at least FD or MATH 110 To get a grade of at least FD
    Course Language English
    Course Type Required (Core Course)
    Course Level First Cycle
    Mode of Delivery face to face
    Teaching Methods and Techniques of the Course Problem Solving Case Study Q&A
    National Occupational Classification Code -
    Course Coordinator
    • Doç. Dr. Sevin Gümgüm
    Course Lecturer(s)
    • Dr. Öğr. Üyesi Ayşe Beler
    • Dr. Öğr. Üyesi Neslişah İmamoğlu Karabaş
    Assistant(s) -
    Course Objectives This course is an introduction to the basic concepts, theory, methods and applications of ordinary differential equations. The aim of this course is to solve differential equations and to develop the basics of modeling of real life problems.
    Learning Outcomes The students who succeeded in this course;
    Name Description PC Sub * Contribution Level
    1 2 3 4 5
    LO1 Will be able to apply mathematical modelling in areas such as physics, engineering, biology or economics and interpret their solutions. X
    LO2 will be able to define and classify differential equations, and establish the relationship between the initial value and the existence interval of the solution. X
    LO3 will be able to solve first order ordinary differential equations and interpret their qualitative behaviour. X
    LO4 will be able to find solutions of homogeneous and nonhomogeneous second order linear differential equations. X
    LO5 Will be able to find solutions of systems of linear diffrential equations X
    LO6 Will be able to use the Laplace transform method to solve linear ordinary differential equations. X
    Course Description In this course basic concepts of differential equations will be discussed.The types of first order ordinary differential equations will be given and the solution methods will be taught. Also, solution methods for higherorder ordinary differential equations will be analyzed.
    Related Sustainable Development Goals
    -

     



    Course Category

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

     

    WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

    Week Subjects Required Materials Learning Outcome
    1 Introduction, classification of differential equations, mathematical modeling, and the fundamentals of ecological mathematical models. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 1.1 -
    2 Separable Differential Equations. First Order Linear Differential Equations. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section: 2.2, 2.3 -
    3 R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section: 2.2, 2.3 R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 2.4, 2.5. -
    4 Bernoulli Differential Equations. Existence and uniqueness theorem. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 2.6, 13.2 -
    5 Homogeneous, Non-homogeneous Constant Coefficient Second Order Differential Equations. The Method of Undetermined Coefficients. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.2, 4.4 -
    6 Non-homogeneous Constant Coefficient Second Order Differential Equations. The Method of Undetermined Coefficients. Variation of parameters. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.4, 4.6 -
    7 Homogeneous, Non-homogeneous Variable Coefficient Second Order Differential Equations. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 4.7 -
    8 Higher order linear equations: General theory, systems of linear differential equations, and distinct eigenvalues, with applications in ecosystem modeling and biodiversity dynamics. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5-9.6 -
    9 Midterm Exam -
    10 Systems of Linear Differential Equations, Distinct eigenvalues and Complex eigenvalues. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5-9.6 -
    11 Systems of Linear Differential Equations, Complex and repeated eigenvalues. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'’, (Pearson, 2011), Section 9.5-9.6 -
    12 Laplace Transforms: Definition of the Laplace Transform, Inverse Laplace Transforms R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'ʼ, (Pearson, 2011), Section 7.2, 7.3, 7.4 -
    13 Solving Initial Value Problems by Laplace Transforms. Laplace transforms of discontinuous functions: Unit step functions, pulse functions and impulse functions. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'ʼ, (Pearson, 2011), Section 7.5, 7.9 -
    14 Laplace transforms of discontinuous functions: Unit step functions, pulse functions and impulse functions. Convolution Integral, Convolution theorem. Solutions of integro differential equations. R. Kent Nagle, Edward B. Saff and Arthur David Snider, ''Fundamentals of Differential Equations and Boundary Value Problems'ʼ, (Pearson, 2011), Section 7.6, 7.8 7.9 -
    15 Semester review -
    16 Final exam -

     

    Course Notes/Textbooks 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.
    Suggested Readings/Materials Shepley L. Ross
    ''Introduction to Ordinary Differential Equations''
    Fourth Edition
    (John Wiley and Sons
    1989)
    ISBN-13: 978-0471032953.

     

    EVALUATION SYSTEM

    Semester Activities Number Weighting LO1 LO2 LO3 LO4 LO5 LO6
    Quizzes / Studio Critiques 2 20 X X X X X X
    Midterm 1 30 X X X X X X
    Final Exam 1 50 X X X X X X
    Total 4 100

     

    ECTS / WORKLOAD TABLE

    Semester Activities Number Duration (Hours) Workload
    Participation - - -
    Theoretical Course Hours 16 2 32
    Laboratory / Application Hours 16 2 32
    Study Hours Out of Class 14 3 42
    Field Work - - -
    Quizzes / Studio Critiques 2 4 8
    Portfolio - - -
    Homework / Assignments - - -
    Presentation / Jury - - -
    Project - - -
    Seminar / Workshop - - -
    Oral Exams - - -
    Midterms 1 16 16
    Final Exam 1 20 20
        Total 150

     

    COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

    # PC Sub Program Competencies/Outcomes * Contribution Level
    1 2 3 4 5
    No program competency data found.

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

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