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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 STATISTICS and COMPUTER SCIENCES | | Prerequisites and co-requisites | None | | Mode of Delivery | Face to face | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Prof. Dr. Ömer PEKŞEN | | Co-Lecturer | None | | 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, | 4,5 | 1 | | LO - 3 : | interprate the solution whithin the concept of the phenomenon being modelled. | 4,5,6 | 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 | | |
| 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 (undetermined 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. |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | First order differential equations,existance and uniquieness of solutions,slope fields and solution curves | | | Week 2 | Linear First order equations,Bernoulli equations,seperable equations and applications | | | Week 3 | Substitution methods and exact equations,homogeneous equations and their applications | | | Week 4 | Solution of some nonlinear differential equations,clairaut equations | | | Week 5 | Mathematical models,population models,equlibrium solutions and stability | | | Week 6 | Reduction of order,linear equations of higher order,introduction to second order linear equations | | | Week 7 | General solutions of linear equations,homogeneous equations with constant coefficients,some applications,nonhomogeneous equations | | | Week 8 | Undetermined coefficient and variation of parameters methods,Cauchy Euler equations | | | Week 9 | Mid-term exam | | | Week 10 | Application of higher order equations,end point problems and eigenvalues | | | Week 11 | Laplace transform methods;laplace transforms and inverse transforms,translation and partial fractions,solution of initial value problems by Laplace transform method
| | | Week 12 | İntroduction to systems of differential equations,first order systems and applications | | | Week 13 | Linear systems of differential equations,the eigenvalue method for homogeneous systems | | | Week 14 | Multiple eigenvalue solutions,matrix exponentials,nonhomogeneous linear systems
| | | Week 15 | Power series methods;introduction,series solutions near ordinary points,regular singular points,method of Frobenius | | | Week 16 | End-of-term exam | | | |
| 1 | C.Henry Edwards and David E. Penny, 2007; Differential Equations and Boundary Value problems: Computing and Modeling, Pearson Publishing Company | | | |
| 1 | Campbell ,Stephen L. , 1990 ; An İntroduction to Differential Equations and their Applications,Wadsworth Publishing Company Belmont,California ,596 pp | | | 2 | Coşkun, H., 2002 ;Diferensiyel 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 | 18/11/2013 | 2 | 50 | | End-of-term exam | 16 | 06/01/2014 | 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 | 3 | 14 | 42 | | Arasınav için hazırlık | 10 | 1 | 10 | | Arasınav | 2 | 2 | 4 | | Ödev | 9 | 2 | 18 | | Kısa sınav | 1 | 1 | 1 | | Dönem sonu sınavı için hazırlık | 18 | 1 | 18 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 151 |
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