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FACULTY of ENGINEERING / DEPARTMENT of INDUSTRIAL ENGINEERING

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FACULTY of ENGINEERING / DEPARTMENT of INDUSTRIAL ENGINEERING /
Katalog Ana Sayfa
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MAT2011Differential Equations4+0+0ECTS:5
Year / SemesterFall Semester
Level of CourseFirst Cycle
Status Compulsory
DepartmentDEPARTMENT of INDUSTRIAL ENGINEERING
Prerequisites and co-requisitesNone
Mode of Delivery
Contact Hours14 weeks - 4 hours of lectures per week
LecturerProf. Dr. Yasemin SAĞIROĞLU
Co-LecturerOther instructors assigned for the course.
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 and qualitative 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 some numerical methods,1,21
LO - 3 : interprate the phenomenon via the solution of model1,21
LO - 4 : obtain solution for properly posed problems within the scope of the course.1,21
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
Initial value problems, slope fields and solution curves, existence and uniqueness, separable equations, first order lineer equations, homogeneous equations, Bernoulli equation, exact differential equations. Second order reducible equations, logistic equation, steady solution and stability, Euler method, second-order equations, applications, matrices and linear system of differential equations, method of eigenvalues, second-order systems and applications, Laplace transform and solution by Laplace transform, power series solution around an ordinary point.
 
Course Syllabus
 WeekSubjectRelated Notes / Files
 Week 1Background(Basic integration techniques), differential equations and mathematical models, basic concepts, applications.
 Week 2Slope fields and solution curves, existence and uniqueness, separable equations with applications.
 Week 3First order lineer equations, applications, change of variables, homogeneous equations
 Week 4Bernoulli equation, exact differential equations, second order reduciable equations.
 Week 5Applications: population model, acceleration-velocity model, temperature problems, steady solutions, stability, Euler method
 Week 6Second-order constant coefficient linear equations, existence and uniqueness, general solution of homogeneous equations
 Week 7Method of undetermined coefficients and variation of parameters for nonhomogeneous equations
 Week 8Applications(forced vibrations or electrical network problems), boundary value problems and applications
 Week 9Midterm exam
 Week 10Matrices and first order system of differential equations, superposition, applications
 Week 11Eigenvalues and eigenvectors, method of eigenvalues for homogeneous systems(distinct real of complex eigenvalues), applications
 Week 12Second order linear systems and applications
 Week 13Laplace and inverse Laplace transforms
 Week 14Convolution and applications, solution of equations with periodic and piecewise input functions using Laplace transform method.
 Week 15Power series and solution around a regular point.
 Week 16Final exam
 
Textbook / Material
1Edwards, C.H., Penney, D.E. (Çeviri Ed. Akın, Ö). 2006; Diferensiyel Denklemler ve Sınır Değer Problemleri (Bölüm 1-7), Palme Yayıncılık, Ankara.
 
Recommended Reading
1Coşkun, H. 2002; Diferansiyel Denklemler, KTÜ Yayınları, Trabzon.
2Başarır, M., Tuncer, E.S. 2003; Çözümlü Problemlerle Diferansiyel Denklemler, Değişim Yayınları, İstanbul.
3Kreyszig, E. 1997; Advenced Engineering Mathematics, New York.
4Bronson, R. (Çev. Ed: Hacısalihoğlu, H.H.) 1993; Diferansiyel Denklemler, Nobel Yayınları, Ankara.
5Spiegel, M.R. 1965; Theory and Problems of Laplace Transforms, McGraw-Hill Book company, New York.
 
Method of Assessment
Type of assessmentWeek NoDate

Duration (hours)Weight (%)
Mid-term exam 9 27.11.2023 1,5 50
End-of-term exam 16 17.01.2024 1,5 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
Laboratuar çalışması 0 0 0
Arasınav için hazırlık 10 1 10
Arasınav 2 1 2
Uygulama 0 0 0
Klinik Uygulama 0 0 0
Ödev 0 0 0
Proje 0 0 0
Kısa sınav 0 0 0
Dönem sonu sınavı için hazırlık 10 1 10
Dönem sonu sınavı 2 1 2
Diğer 1 0 0 0
Diğer 2 0 0 0
Total work load150