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| HRT2035 | Differential Equations | 4+0+0 | ECTS:5 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of GEOMATICS ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. İdris ÖREN | | Co-Lecturer | Other instructors assigned for the course.
| | Language of instruction | Turkish | | 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.
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| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | formulate mathematical models for a variety of problems. | 1 | 1 | | LO - 2 : | solve the model using analytical, qualitative and partically some numerical methods. | 1 | 1 | | LO - 3 : | interprate the solution within the concept of the phenomenon being modelled. | 1 | 1 | | LO - 4 : | obtain solution for models studied within the scope of the course. | 1 | 1 | | 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 | | |
| 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.
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Background(Basic integration techniques), differential equations and mathematical models, basic concepts, applications.
| | | Week 2 | Slope fields and solution curves, existence and uniqueness, separable equations with applications.
| | | Week 3 | First order lineer equations, applications, change of variables, homogeneous equations
| | | Week 4 | Bernoulli equation, exact differential equations, second order reduciable equations.
| | | Week 5 | Applications: population model, acceleration-velocity model, temperature problems, steady solutions, stability, Euler method
| | | Week 6 | Second-order constant coefficient linear equations, existence and uniqueness, general solution of homogeneous equations
| | | Week 7 | Method of undetermined coefficients and variation of parameters for nonhomogeneous equations
| | | Week 8 | Applications(forced vibrations or electrical network problems), boundary value problems and applications
| | | Week 9 | Midterm exam
| | | Week 10 | Matrices and first order system of differential equations, superposition, applications
| | | Week 11 | Eigenvalues and eigenvectors, method of eigenvalues for homogeneous systems(distinct real of complex eigenvalues), applications
| | | Week 12 | Second order linear systems and applications
| | | Week 13 | Laplace and inverse Laplace transforms | | | Week 14 | Convolution and applications, solution of equations with periodic and piecewise input functions using Laplace transform method.
| | | Week 15 | Power series and solution around a regular point.
| | | Week 16 | Final exam | | | |
| 1 | Edwards, C.H., Penney, D.E. (Çeviri Ed. AKIN, Ö). 2006; Diferensiyel Denklemler ve Sınır Değer Problemleri (Bölüm 1-7), Palme Yayıncılık, Ankara. | | | |
| 1 | COŞKUN, H. 2002; Diferansiyel Denklemler, KTÜ Yayınları, Trabzon. | | | 2 | BAŞARIR, M., TUNCER, E.S. 2003; Çözümlü Problemlerle Diferansiyel Denklemler, Değişim Yayınları, İstanbul. | | | 3 | KREYSZIG, E. 1997; Advenced Engineering Mathematics, New York. | | | 4 | BRONSON, R. (Çev. Ed: HACISALİHOĞLU, H.H.) 1993; Diferansiyel Denklemler, Nobel Yayınları, Ankara. | | | 5 | SPIEGEL, M.R. 1965; Theory and Problems of Laplace Transforms, McGraw-Hill Book company, New York. | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 27.11.2023 | 2 | 50 | | End-of-term exam | 16 | 22.01.2024 | 2 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 6 | 14 | 84 | | Arasınav için hazırlık | 3 | 1 | 3 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 4 | 1 | 4 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 152 |
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