CANKIRI KARATEKIN UNIVERSITY
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  • Course Information
  • Course Title Code Semester Laboratory+Practice (Hour) Pool Type ECTS
    PARTIAL DIFFERENTIAL EQUATIONS MAT206 SPRING 4+0 C 6
    Learning Outcomes
    1-To solve initial value problems of quasilinear equations.
    2-To classify second order equations with two variables and reduce to canonical form.
    3-To reduce second order equations with two variables to canonical form.
    4-To compute fourier series of piecewise continuous functions.
    5-To solve initial value and initial-boundary value problems for one-dimensional wave equation.
    6-To apply separation of variables method to boundary value problems.
    7-To solve initial-boundary value problems for one-dimensional heat equation.
    8-To solve different boundary value problems of laplace equation.
  • 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) 5011616
    Other 0000
    Total Workload (hours)   180
    Total Workload (hours) / 30 (s)     6 ---- (6)
    ECTS Credit   6
  • Course Content
  • Week Topics Study Metarials
    1 Basic equations and concepts, classification of partial differential equations, integral curves of vector fields
    2 Constructing integral curves of a vector field
    3 Constructing integral surfaces of a vector field containing a given curve
    4 First order quasilinear equations
    5 Classification of second order equations with two variables, canonical forms, equations of mathematical physics, well-posed problems
    6 Cauchy-Kowalewskaya theorem, initial value problem for one dimensional wave equation, d`Alembert formula, domain of dependence
    7 Initial-boundary value problems for one dimensional wave equation
    8 Fourier series and their convergence, Fourier sine and cosine series
    9 Separation of variables, initial-boundary value problem for one-dimensional wave equation, existence and uniqueness of the solution
    10 Initial-boundary value problem for one-dimensional heat equation, existence and uniqueness of the solution
    11 Nonhomogeneous problems
    12 Boundary value problems, Laplace equation, harmonic functions, maximum and minimum principles, uniqueness and continuity of Dirichlet problem
    13 Dirichlet problem for a circle, mean value theorem, Dirichlet problem for a circular annulus
    14 Neumann problem for a circle, Dirichlet and Neumann problems for a rectangle
    Prerequisites ANALYSIS I, ANALYSIS II, ADVANCED ANALYSIS I, ORDINARY DIFFERENTIAL EQUATIONS
    Language of Instruction Turkish
    Course Coordinator Assist. Prof. Dr. Müfit ŞAN
    Instructors -
    Assistants -
    Resources Kısmi Diferansiyel Denklemler, İbrahim Ethem Anar, Palme Yayınevi, 2005.
    Supplementary Book [1] Linear Partial Differential Equations for Scientists and Engineers, 4th Ed., Tyn Myint-U, Lokenath Debnath, 2007. [2] Kısmi Türevli Denklemler, Alemdar Hasanoğlu (Hasanov), Literatür Yayıncılık, 2010. [3] Kısmi Diferensiyel Denklemler, Mehmet Çağlıyan, Okay Çelebi, Dora Basım Yayın, 2010. [4] Kısmi Türevli Denklemler ve Çözümlü Problemler, A. Neşe Dernek, Nobel Yayın Dağıtım, 2009. [5] Kısmi Diferensiyel Denklemler, David W. Zachmann, Paul DuChateau, Çeviri: H. Hilmi Hacısalihoğlu, Nobel Yayın Dağıtım [6] Kısmi Türevli Denklemler, Kerim Koca, Gündüz Eğitim ve Yayıncılık, 2001.
    Document Lecture notes.
    Goals To teach basic theory and solution techniques of partial 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 4
    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 4
    9 To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time 2
    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 -
    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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