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| JFZ2011 | Differential Equations | 4+0+0 | ECTS:5 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | DEPARTMENT of GEOPHYSICAL 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 Muhammet YAZICI | | Co-Lecturer | Lecturers | | 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 | 1,3 | | | LO - 2 : | solve the model using analytical, qualitative and partically some numerical methods, | 1,4,6 | | | LO - 3 : | interprate the solution whithin the concept of the phenomenon being modelled. | 2,3,5 | | | LO - 4 : | obtain solution for models studied within the scope of the course | 3,5 | | | 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 | | |
| Basic concepts, Differential equations as mathematical models, Slope fields and solution curves, Initial value problems for first-order equations (Existence, uniqueness, analytical methos for common first-order equations) , Applications (population, Accelaration-velocity models) , General theory of n-th order linear equations, solution of constant coefficient equations, Applications (spring-mass system, electrical circuits) , Boundary-value problems (eigenvalues and eigenfunctions) , Applications for beam model, Constant coefficient nonhomogeneous equations (indetermined coefficients, variation of parameters) , Laplace and inverse Laplace transformations, Solution of initial value problems using Laplace transformations, Matrices and linear algebraic systems (a preview) , System of first-order linear differential equations, Transforming higher order equations into a first-order system, Solution of homogeneous systems using eigenvalues and eigenfuctions, Exponential matrices and solution of nonhomogeneous first-order systems, Introduction to numerical methods for initial value problems (Euler and Runge-Kutta methods) |
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