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| MAT2011 | Differential Equations | 4+0+0 | ECTS:5 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of CIVIL ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Dr. Öğr. Üyesi Hüsnü Anıl ÇOBAN | | Co-Lecturer | Lecturers from the mathematics department | | 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, qualitative and numerical methods, as well as interpreting solutions within the concept of physical problem at hand. |
| 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 | 1,2 | 1 | | LO - 2 : | solve the model using analytical, qualitative and partically some numerical methods, | 1,2 | 1 | | LO - 3 : | interprate the solution within the concept of the phenomenon being modelled. | 1,2 | 1 | | LO - 4 : | obtain solution for models studied within the scope of the course | 1,2 | 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 | | |
| 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). |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Differential equations and basic concepts. Differential equations as mathematical model (Ordinary differential equations, order and degree of differential equations. Derivation of differential equations.)
| | | Week 2 | General, particular and singular solutions of the differential equations. Existence and uniqueness theorems. Direction fields and solution curves. | | | Week 3 | Separable, homogenous, exact differential equations and transforming to exact differential equation by using integrating factor. | | | Week 4 | Linear differential equations, Bernoulli differential equation and applications of the first order differential equations(Population model, acceleration-velocity model, temperature problems) | | | Week 5 | Change of variables. Reducible differential equations (single variable and non-linear differential equations) | | | Week 6 | 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.
| | | Week 7 | Solutions of the constant coefficient non-homogenous equations. (Undetermined coefficients, change of parameters) | | | Week 8 | Mid-term exam | | | Week 9 | Initial Value Problems (IVP) and Boundary Value Problems (BVP) (Eigenvalues and eigenfunctions for boundary value problems. Physical applications, mechanical vibrations, electrical circuits)
| | | Week 10 | Variable coefficient homogenous and non-homogenous differential equations (Cauchy-Euler, Legendre differential equations). Reduction of order. | | | Week 11 | Power series solutions of differential equations around ordinary points.
| | | Week 12 | Laplace and inverse Laplace transformations. Short Exam.
| | | Week 13 | Solutions of constant and variable coefficient boundary value problems and differential equations containing Dirac-Delta function and transformation functions by using Laplace transformations.
| | | Week 14 | 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.
| | | Week 15 | Application of the Laplace transformation to system of differential equations. Numerical solutions of differential equations (Euler and Runge-Kutta methods) | | | Week 16 | End-of-term 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 | 08 | 30/03/2010 | 2 | 30 | | In-term studies (second mid-term exam) | 12 | 30/04/2010 | 2 | 20 | | End-of-term exam | 17 | 02/06/2010 | 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 | 5.5 | 14 | 77 | | Arasınav için hazırlık | 6 | 1 | 6 | | Arasınav | 2 | 1 | 2 | | Kısa sınav | 2 | 1 | 2 | | Dönem sonu sınavı için hazırlık | 7 | 1 | 7 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 152 |
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