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OF FACULTY of TECHNOLOGY / DEPARTMENT of SOFTWARE ENGINEERING

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OF FACULTY of TECHNOLOGY / DEPARTMENT of SOFTWARE ENGINEERING /
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YZM2005Differantial Equations4+0+0ECTS:5
Year / SemesterFall Semester
Level of CourseFirst Cycle
Status Compulsory
DepartmentDEPARTMENT of SOFTWARE ENGINEERING
Prerequisites and co-requisitesNone
Mode of DeliveryFace to face
Contact Hours14 weeks - 4 hours of lectures per week
LecturerDoç. Dr. Esma ULUTAŞ
Co-Lecturer
Language of instructionTurkish
Professional practise ( internship ) None
 
The aim of the course:
This course aims to provide students with general knowledge on formulating problems that arises in applied sciences as mathematical models, solving such models through analytical, qualitative and numerical methods, as well as interpreting solutions within the concept of physical problem at hand.
 
Learning OutcomesCTPOTOA
Upon successful completion of the course, the students will be able to :
LO - 1 : formulate mathematical models for a variety of problems1,21,
LO - 2 : solve the model using analytical, qualitative and partically some numerical methods, solve the model using analytical, qualitative and partically some numerical methods1,21,
LO - 3 : interprate the solution within the concept of the phenomenon being modelled1,21,
LO - 4 : obtain solution for models studied within the scope of the course1,21,
CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome

 
Contents of the Course
Differential equations and basic concepts. Differential equations as mathematical model (Ordinary differential equations, order and degree of differential equations. Derivation of differential equations.) General, particular and singular solutions of the differential equations. Existence and uniqueness theorems. Direction fields and solution curves. Separable, homogenous, exact differential equations and transforming to exact differential equation by using integrating factor. Linear differential equations, Bernoulli differential equation and applications of the first order differential equations(Population model, acceleration-velocity model, temperature problems). Change of variables. Reducible differential equations (single variable and non-linear differential equations). General solution of nth order linear differential equations (linearly independent solutions, super position principle for the homogeneous equations, particular and general solutions). General solution of nth order constant coefficient homogenous differential equations. Solutions of the constant coefficient non-homogenous equations. (Undetermined coefficients, change of parameters). Initial Value Problems (IVP) and Boundary Value Problems (BVP) (Eigenvalues and eigenfunctions for boundary value problems. Physical applications, mechanical vibrations, electrical circuits). Variable coefficient homogenous and non-homogenous differential equations (Cauchy-Euler, Legendre differential equations). Reduction of order. Power series solutions of differential equations around ordinary points. Laplace and inverse Laplace transformations. Solutions of constant and variable coefficient boundary value problems and differential equations containing Dirac-Delta function and transformation functions by using Laplace transformations. System of differential equations. Transformation of higher order differential equation to the system of first order differential equations. Solutions of the homogenous differential equations using eigenvalues and eigenvectors. Solutions of non-homogeneous constant coefficient system of differential equations. Application of the Laplace transformation to system of differential equations. Numerical solutions of differential equations (Euler and Runge-Kutta methods).
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Differential equations and basic concepts. Differential equations as mathematical model (Ordinary differential equations, order and degree of differential equations. Derivation of differential equations.)
 Week 2General, particular and singular solutions of the differential equations. Existence and uniqueness theorem.
 Week 3Separable, homogenous differential equations.
 Week 4Exact differential equations and transforming to exact differential equation by using integrating factor.
 Week 5 Linear Differential Equations, Bernoulli Differential Equation.
 Week 6Applications (population model, acceleration-velocity model, heat problems, electrical circuits)
 Week 7General solution of nth order linear differential equations (linearly independent solutions, super position principle for the homogeneous equations, particular and general solutions).
 Week 8 General solution of nth order constant coefficient homogenous differential equations.
 Week 9mid-term exam
 Week 10Solutions of the constant coefficient non-homogenous equations. (Undetermined coefficients, change of parameters)
 Week 11Cauchy Euler Equations.
 Week 12Power series solutions of differential equations around ordinary points.
 Week 13Laplace and inverse Laplace transformations.
 Week 14Solutions of differential equations by using Laplace transformations.
 Week 15System of differential equations. Solutions of the homogenous differential equations using eigenvalues and eigenvectors.
 Week 16final exam
 
Textbook / Material
1Edwards, C.H., Penney, D.E. (Çeviri Ed. AKIN, Ö). 2006; Diferensiyel Denklemler ve Sınır Değer Problemleri (Bölüm 1-7), Palme Yayıncılık, Ankara.
 
Recommended Reading
1COŞKUN, H. 2002; Diferansiyel Denklemler, KTÜ Yayınları, Trabzon.
2BAŞARIR, M., TUNCER, E.S. 2003; Çözümlü Problemlerle Diferansiyel Denklemler, Değişim Yayınları, İstanbul.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 30.11.2023 50
End-of-term exam 16 15.01.2024 50
 
Student Work Load and its Distribution
Type of workDuration (hours pw)

No of weeks / Number of activity

Hours in total per term
Yüz yüze eğitim 4 14 56
Sınıf dışı çalışma 5 14 70
Arasınav için hazırlık 8 1 8
Arasınav 2 1 2
Dönem sonu sınavı için hazırlık 10 1 10
Dönem sonu sınavı 2 1 2
Total work load148