|Course Name||Code||Semester||T+U Hours||Credit||ECTS|
|Differential Equations||MAT 211||3||4 + 0||4||6|
|Recommended Optional Courses|
|Course Level||Bachelor's Degree|
|Course Coordinator||Öğr.Gör.Dr. EMİNE ÇELİK|
|Course Lecturers||Öğr.Gör.Dr. EMİNE ÇELİK,|
|Course Category||Available Basic Education in the Field|
The general purpose of this course is to provide an understanding of ordinary differential equations (ODEs), and to give methods for solving them. Because differential equations express relationships between changing quantities, this material is applicable to many fields, and is essential for students of engineering and physical sciences.
This course covers topics in ordinary differential equations: First-order differential equations; Modeling with first-order differential equations; Higher-order differential equations; Modeling with higher-order differential equations; Laplace transform; Series solutions of Linear Equations.
|#||Course Learning Outcomes||Teaching Methods||Assessment Methods|
|1||Students will obtain a thorough knowledge of solution techniques for first- order and for second- and higher-order constant coefficient linear homogenous and nonhomogeneous initial value problems using standard methods of undetermined coefficients and variation of parameters.||Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving,||Testing,|
|2||In addition, the students will acquire a general understanding of how to apply the Laplace transform in solving initial value problems and convolution integral equations.||Lecture, Question-Answer, Drilland Practice, Problem Solving,||Testing,|
|3||Students will gain an appreciation for some of the applications of ordinary differential equations in biology and engineering.||Lecture, Question-Answer, Drilland Practice, Problem Solving,||Testing, Homework,|
|Week||Course Topics||Preliminary Preparation|
|1||Definitions and Terminology. Basic Concepts and Classifying Differential Equations. Obtaining differential equations. Initial-Value Problems.|
|2||Separable differential equations. Linear Equations. Differential Equations as Mathematical Models.|
|3||Homogeneous functions, homogenous differential equations. Engineering Applications.|
|4||Solution of differential equations by changing to the linear form. Bernoulli differential equation. Ricatti differential equation. Modeling with First-Order Differential Equations.|
|5||Higher-Order Differential Equations. Preliminary Theory.|
|6||Homogeneous Equations. Nonhomogeneous Equations. Reduction of Order.|
|7||Homogeneous Linear Equations with Constant Coefficients. Undetermined Coefficients.|
|8||Variation of Parameters. Cauchy-Euler Equations. Modeling with Higher-Order Differential Equations.|
|10||Series Solutions of Linear Equations. Solutions about ordinary points. Solutions about singular points. Special Functions.|
|11||The Laplace transform. Inverse Transforms and Transforms of Derivatives. Operational Properties.|
|12||Operational Properties. The Dirac Delta Function. Engineering Applications.|
|13||Systems of Linear First-Order Differential Equations. Preliminary Theory. Homogeneous Linear Systems.|
|14||Solutions of Homogeneous Linear Systems. Undetermined Coefficients and Laplaca Transform Methods. Engineering Applications.|
|Course Notes||<p>Lecture Notes.</p>|
 Differential Equations with Boundary-Value Problems, 9th edition, by D.G. Zill and M.R. Cullen, published by Cengage.
 Çözümlü Problemlerle Diferansiyel Denklemler, E. S. Türker, ve M. Başarır, 2003, Değişim Kitabevi, Sakarya.
 Adi Diferansiyel Denklemler, 7. baski, M. Cagliyan, N. Celik, S. Dogan, Dora Yayinevi, Bursa 2018.
|Semester Studies||Contribution Rate|
|1. Ara Sınav||70|
|1. Kısa Sınav||10|
|2. Kısa Sınav||10|
|3. Kısa Sınav||10|
|1. Yıl İçinin Başarıya||50|
|ECTS - Workload Activity||Quantity||Time (Hours)||Total Workload (Hours)|
|Course Duration (Including the exam week: 16x Total course hours)||16||4||64|
|Hours for off-the-classroom study (Pre-study, practice)||16||3||48|
|Total Workload / 25 (Hours)||5.84|