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| MAT2011 | Differential Equations | 4+0+0 | ECTS:6 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of MATHEMATICS | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Haskız COŞKUN | | Co-Lecturer | DOCTOR LECTURER Pelin ŞENEL, | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to show that many problems in science and engineering can be formulated as mathematical models in the form of differential equations and teach basic methods for determining solutions to such equations. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | learn that many problems in science and engineering can be formulated as differential equations | 1,2,3 | 1, | | LO - 2 : | learn to formulate well-defined models | 1,2,3 | 1, | | LO - 3 : | learn to solve a well-defined problem | 1,2,3 | 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 | | |
| First order differential equations and applications. Existance and uniqueness of the solutions. First order linear differential equations. Bernoulli differential equation. Seperable differential equations. Exact differential equations . integrating factor for non exact differential equations.introduction to higher order linear differential equations.Second order linear differential equations. Linear independence and wronskian. Reduction of order. Homogeneous constant coefficient second order linear equations. Cauchy-Euler equation, Nonhomogeneous equations Undetermined coefficients and variation of parameters. Laplace transformation and solution of initial value problems by Laplace transformation.Systems of differential equations. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | First order differential equations, existance and uniqueness of solutions | | | Week 2 | First order linear equations; Bernoulli equations, seperable equations and applications | | | Week 3 | Exact equations,homogeneous equations and applications | | | Week 4 | Solution of some nonlinear equations ,clairaut equation | | | Week 5 | introduction to higher order differential equations,second order linear differential equations | | | Week 6 | operator notation,reduction of order | | | Week 7 | | | | Week 8 | Review | | | Week 9 | | | | Week 10 | Cauchy Euler equation. | | | Week 11 | Laplace transformation, properties of the transformation | | | Week 12 | Solution of initial value problems by Laplace transformation | | | Week 13 | Systems of linear differential equatios | | | Week 14 | Solution of systems by Laplace transformation | | | Week 15 | Variable coefficient equations and solution by series method | | | Week 16 | | | | |
| 1 | C.Henry Edwards and David E. Penny, Bilgisayar destekli ve Matematiksel Modellemeli Diferansiyel denklemler ve Sınır Değer Problemleri, Çeviri Editörü: Prof. Dr. Ömer Akın, Palmiye Yayıncılık | | | |
| 1 | Campbell ,Stephen L. , 1990; An Introduction to Differential Equations and their Applications,Wadsworth Publishing Company Belmont, California ,596 pp | | | 2 | Coşkun, H., 2002 ;Diferansiyel Denklemler (Kalitatif, Analitik ve Sayısal Yaklaşım),KTÜ Yayınları,Trabzon | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 20/11/2020 | 1 | 50 | | End-of-term exam | 17 | 15/01/2021 | 1 | 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 | 3 | 14 | 42 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 1 | 2 | | Ödev | 9 | 2 | 18 | | Dönem sonu sınavı için hazırlık | 18 | 1 | 18 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 148 |
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