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FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES

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FACULTY of SCIENCE / DEPARTMENT of STATISTICS and COMPUTER SCIENCES /
Katalog Ana Sayfa
  Katalog Ana Sayfa  KTÜ Ana Sayfa   Katalog Ana Sayfa
 
 

MAT2011Differential Equations4+0+0ECTS:6
Year / SemesterFall Semester
Level of CourseFirst Cycle
Status Compulsory
DepartmentDEPARTMENT of STATISTICS and COMPUTER SCIENCES
Prerequisites and co-requisitesNone
Mode of DeliveryFace to face, Group study
Contact Hours14 weeks - 4 hours of lectures per week
LecturerProf. Dr. Ömer PEKŞEN
Co-LecturerDOCTOR LECTURER Ayşe KABATAŞ,ASSOC. PROF. DR. Yasemin SAĞIROĞLU,
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 partically some numerical methods,1,21
LO - 3 : interprate the solution within the concept of the phenomenon being modelled.1,21
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. 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, superposition 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) Physical applications, mechanical vibrations, electrical circuits. Variable coefficient homogenous and non-homogenous differential equations (Cauchy-Euler differential equation). 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.
 
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.
 Week 2 Derivation of differential equations. General, particular and singular solutions of the differential equations.
 Week 3Separable, homogenous differential equations,
 Week 4Exact differential equations and transforming to exact differential equation by using integrating factor.
 Week 5Linear differential equations, Bernoulli differential equation, change of variables method
 Week 6Applications: Population model, acceleration-velocity model, temperature problems
 Week 7General 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.
 Week 8Solutions of the constant coefficient non-homogenous equations. (Undetermined coefficients, change of parameters)
 Week 9Midterm exam
 Week 10Physical applications, mechanical vibrations, electrical circuits
 Week 11Variable coefficient homogenous and non-homogenous differential equations (Cauchy-Euler, differential equation). Reduction of order method.
 Week 12Power series solutions of differential equations around ordinary points.
 Week 13Laplace and inverse Laplace transformations.
 Week 14Solutions of constant and variable coefficient boundary value problems and differential equations containing Dirac-Delta function and transformation functions by using Laplace transformations.
 Week 15Review
 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.
2Edwards, 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.
2Coşkun, H. 2002; Diferansiyel Denklemler, KTÜ Yayınları, Trabzon.
3Başarır, M., Tuncer, E.S. 2003; Çözümlü Problemlerle Diferansiyel Denklemler, Değişim Yayınları, İstanbul.
4Başarır, M., Tuncer, E.S. 2003; Çözümlü Problemlerle Diferansiyel Denklemler, Değişim Yayınları, İstanbul.
5Kreyszig, E. 1997; Advenced Engineering Mathematics, New York.
6Kreyszig, E. 1997; Advenced Engineering Mathematics, New York.
7Bronson, R. (Çev. Ed: Hacısalihoğlu, H.H.) 1993; Diferansiyel Denklemler, Nobel Yayınları, Ankara.
8Bronson, R. (Çev. Ed: Hacısalihoğlu, H.H.) 1993; Diferansiyel Denklemler, Nobel Yayınları, Ankara.
9Spiegel, M.R. 1965; Theory and Problems of Laplace Transforms, McGraw-Hill Book company, New York.
10Spiegel, 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 30/11/2020 2 50
End-of-term exam 17 25/01/2021 2 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 12 1 12
Arasınav 2 1 2
Kısa sınav 1 1 1
Dönem sonu sınavı için hazırlık 15 1 15
Dönem sonu sınavı 2 1 2
Total work load158