|
Description of Individual Course Units| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | | DUİM2012016252 | DIFFERENTIAL EQUATIONS | Compulsory | 2 | 3 | 4 |
| | Level of Course Unit | | First Cycle | | Objectives 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. | | Name of Lecturer(s) | | | Learning Outcomes | | 1 | formulate mathematical models for a variety of problems. | | 2 | solve the model using analytical, qualitative and partically some numerical methods. | | 3 | interprate the solution within the concept of the phenomenon being modelled. | | 4 | obtain solution for models studied within the scope of the course. |
| | Mode of Delivery | | Formal Education | | Prerequisites and co-requisities | | None | | Recommended Optional Programme Components | | None | | Course Contents | | 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, accelerationvelocity model, temperature problems). Change of variables. Reducible differential equations (single variable and nonlinear 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 nonhomogenous 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). | | Weekly Detailed Course Contents | |
| 1 | Differential equations and basic concepts. Differential equations as mathematical model (Ordinary differential equations, order and degree of differential equations. Derivation of differential equations)
| | | | 2 | General, particular and singular solutions of the differential equations. Existence and uniqueness theorems. Direction fields and solution curves. | | | | 3 | Separable, homogenous, exact differential equations and transforming to exact differential equation by using integrating factor. | | | | 4 | Linear differential equations, Bernoulli differential equation and applications of the first order differential equations (Population model, acceleration-velocity model, temperature problems)
| | | | 5 | Change of variables. Reducible differential equations (single variable and non-linear differential equations) | | | | 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 | | | | 7 | Solutions of the constant coefficient non-homogenous equations. (Undetermined coefficients, change of parameters)
| | | | 8 | Mid-term exam | | | | 9 | Initial Value Problems (IVP) and Boundary Value Problems (BVP) (Eigenvalues and eigenfunctions for boundary value problems. Physical applications, mechanical vibrations, electrical circuits) | | | | 10 | Variable coefficient homogenous and non-homogenous differential equations (Cauchy-Euler, Legendre differential equations). Reduction of order.
| | | | 11 | Power series solutions of differential equations around ordinary points. | | | | 12 | Laplace and inverse Laplace transformations. | | | | 13 | Solutions of constant and variable coefficient boundary value problems and differential equations containing Dirac-Delta function and transformation functions by using Laplace transformations. | | | | 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. | | | | 15 | Application of the Laplace transformation to system of differential equations. Numerical solutions of differential equations (Euler and Runge-Kutta methods) | | | | 16 | End-of-term exam | | |
| | Recommended or Required Reading | | Edwards, C.H., Penney, D.E. (Çeviri Ed. AKIN, Ö). 2006; Diferensiyel Denklemler ve Sınır Değer Problemleri (Bölüm 17), Palme Yayıncılık, Ankara.
Coşkun, H. 2002; Diferansiyel Denklemler, KTÜ Yayınları, Trabzon.
Başarır, M., Tuncer, E.S. 2003; Çözümlü Problemlerle Diferansiyel Denklemler, Değişim Yayınları, İstanbul
Kreyszig, E. 1997; Advenced Engineering Mathematics, New York.
Bronson, R. (Çev. Ed: Hacısalihoğlu, H.H.) 1993; Diferansiyel Denklemler, Nobel Yayınları, Ankara.
Spiegel, M.R. 1965; Theory and Problems of Laplace Transforms, Mcgrawhill Book Company, New York.
| | Planned Learning Activities and Teaching Methods | | | Assessment Methods and Criteria | |
| SUM | 0 | |
| SUM | 0 | | Yarıyıl (Yıl) İçi Etkinlikleri | 40 | | Yarıyıl (Yıl) Sonu Etkinlikleri | 60 | | SUM | 100 |
| | Language of Instruction | | Turkish | | Work Placement(s) | | None |
| | Workload Calculation | |
| Midterm Examination | 1 | 2 | 2 | | Final Examination | 1 | 2 | 2 | | Attending Lectures | 14 | 3 | 42 | | Self Study | 6 | 5 | 30 | | Individual Study for Mid term Examination | 4 | 4 | 16 | | Individual Study for Final Examination | 5 | 4 | 20 | |
| Contribution of Learning Outcomes to Programme Outcomes | | LO1 | 5 | 1 | 2 | 1 | 5 | 2 | 1 | 2 | 1 | 2 | 1 | 2 | | LO2 | 5 | 2 | 1 | 2 | 5 | 2 | 1 | 1 | 2 | 1 | 2 | 2 | | LO3 | 5 | 2 | 2 | 1 | 5 | 1 | 2 | 2 | 1 | 2 | 1 | 1 | | LO4 | 5 | 1 | 1 | 1 | 5 | 1 | 1 | 2 | 2 | 1 | 2 | 2 |
| | * Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
|
|
|
|
Ordu University Rectorate Building ,Cumhuriyet Campus , Center / ORDU / TURKEY • Tel: +90 452 226 52 00
|
|
|