CANKIRI KARATEKIN UNIVERSITY
Bologna Information System


  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    ORDINARY DIFFERENTIAL EQUATIONS MAT205 FALL 4+0 C 6
    Learning Outcomes
    1-To classify differential equations.
    2-To solve differential equations of various orders and systems.
    3-To explain the fundamental theory of differential equations
    4-To apply the laplace transformation to initial value problems for differential equations and systems.
  • ECTS / WORKLOAD
  • ActivityPercentage

    (100)

    NumberTime (Hours)Total Workload (hours)
    Course Duration (Weeks x Course Hours)14456
    Classroom study (Pre-study, practice)14570
    Assignments102612
    Short-Term Exams (exam + preparation) 102612
    Midterm exams (exam + preparation)3011414
    Project0000
    Laboratory 0000
    Final exam (exam + preparation) 5011515
    Other 0000
    Total Workload (hours)   179
    Total Workload (hours) / 30 (s)     5,97 ---- (6)
    ECTS Credit   6
  • Course Content
  • Week Topics Study Metarials
    1 Definition of differential equation and classification of differential equations, first order differential equations, linear equations, separable equations
    2 Exact differential equations and integrating factors, existence and uniqueness theorem Bernoulli equation, special integrating factors and transformations
    3 Higher order linear homogeneous equations with constant coefficients, characteristic equation, fundamental solutions, linear independence and Wronskian
    4 Complex roots and repeated roots, reduction of order
    5 Higher order nonhomogeneous equations, method of undetermined coefficients
    6 The method of variation of parameters, Cauchy-Euler equation
    7 Physical models and applications
    8 Series solutions near an ordinary point
    9 Series solutions near a regular singular point, Frobenius method
    10 Laplace transform
    11 Convolution integral, solution of initial value problems
    12 Systems of first order linear homogeneous differential equations with constant
    13 Coefficients, fundamental matrices, complex and repeated eigenvalues
    14 Nonhomogeneous systems of linear differential equations
    Prerequisites ANALYSIS I, ANALYSIS II
    Language of Instruction Turkish
    Course Coordinator Assist. Prof. Dr. Müfit ŞAN
    Instructors

    1-)Müfit Şan

    Assistants -
    Resources Diferensiyel Denklemler ve Sınır Değer Problemleri, Edwards & Penney (Çeviri Editörü: Prof. Dr. Ömer AKIN), Palme Yayıncılık, 1997
    Supplementary Book [1] Diferensiyel Denklemler, Mustafa BAYRAM, Birsen Yayınevi, 2002. [2] Diferansiyel Denklemler ve Uygulamaları, Mehmet Aydın, Gönül Gündüz, Beno Kuryel, Galip Oturanç, Fakülteler Barış Yayınları, 2007.
    Document Lecture Notes
    Goals To comprehend solution techniques and basic theory of ordinary differential equations.
    Content -
  • Program Learning Outcomes
  • Program Learning Outcomes Level of Contribution
    1 To have a grasp of theoretical and applied knowledge in main fields of mathematics 5
    2 To have the ability of abstract thinking 4
    3 To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps 5
    4 To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life 4
    5 To have the qualification of studying independently in a problem or a project requiring mathematical knowledge 2
    6 To be able to work compatibly and effectively in national and international groups and take responsibility -
    7 To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge 3
    8 To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge 3
    9 To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time -
    10 To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally 3
    11 To be able to produce projects and arrange activities with awareness of social responsibility -
    12 To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level -
    13 To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results -
    14 To have the awareness of acting compatible with social, scientific, cultural and ethical values -
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