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Course Description Course Name : Differential Equations Course Code : MT 235 Course Type : Compulsory Level of Course : First Cycle Year of Study : 2 Course Semester : Fall (16 Weeks) ECTS : 6 Name of Lecturer(s) : Prof.Dr. HAYRULLAH AYIK Learning Outcomes of the Course : Recognizes and classifies differential equations. Recognizes first order differantial equations Recognizes exact differantial equations. Recognizes and solves linear differantial equations. Recognizes and solves Cauchy – Euler equations. Recognizes and solves systems of linear differantial equations. Recognizes Laplace transformation. Mode of Delivery : Face-to-Face Prerequisites and Co-Prerequisites : None Recommended Optional Programme Components : None Aim(s) of Course : Students recognize differential equations and its clasifications, first order differantial equations, exact differantial equations; they recognize and solve linear differantial equations, Bernoulli differantial equations, Cauchy – Euler equations, systems of linear differantial equations, and Laplace transformations. Course Contents : Differential equations and their solutions, clasification of differential equations, initial value problems, boundary value problems and existence of solutions, exact differential equations and integrating factor, seperable equations and equations reducible to this form, Linear equations ve Bernoulli equations, explicit methods of solving higher order linear differantial equations, homogeneous linear equations with constant coefficients, the method of undetermined coefficients, variations of parameters, Cauchy – Euler equations, system of linear differantial equations, Laplace transformations, Basic properties of Laplace transformations Language of Instruction : Turkish Work Place : Faculty of Arts and Sciences Annex Classrooms   Course Outline /Schedule (Weekly) Planned Learning Activities Week Subject Student's Preliminary Work Learning Activities and Teaching Methods 1 Differential equations and their solutions Required readings Lecture and discussion 2 Classification of differential equations Required readings Lecture and discussion 3 Initial value problems, Boundary value problems and existence of solutions Required readings Lecture and discussion 4 Exact differential equations and integrating factor Required readings Lecture and discussion 5 Seperable equations and equations reducible to this form Required readings Lecture and discussion 6 Linear equations ve Bernoulli equations Required readings Lecture and discussion 7 Explicit methods of solving higher order linear differantial equations Required readings Lecture and discussion 8 Midterm Exam and Problem Solving Required readings Written Exam 9 The homogeneous linear equations with constant coefficients Required readings Lecture and discussion 10 The method of undetermined coefficients Required readings Lecture and discussion 11 Variations of parameters Required readings Lecture and discussion 12 Cauchy – Euler equations Required readings Lecture and discussion 13 System of linear differantial equations Required readings Lecture and discussion 14 Laplace transformations Required readings Lecture and discussion 15 Basic properties of Laplace transformations Required readings Lecture and discussion 16/17 Final Exam Review Written Exam   Required Course Resources Resource Type Resource Name Recommended Course Material(s)  2. Differentiel Equuations, Yazar: L.Shipley Ross Required Course Material(s)    3. Differentiel Equuations, Yazar:Frank Ayres  4. Differential Equations, Yazar: Lester R. Ford   Assessment Methods and Assessment Criteria Semester/Year Assessments Number Contribution Percentage     Mid-term Exams (Written, Oral, etc.) 1 100     Homeworks/Projects/Others 0 0 Total 100 Rate of Semester/Year Assessments to Success 40   Final Assessments 100 Rate of Final Assessments to Success 60 Total 100   Contribution of the Course to Key Learning Outcomes # Key Learning Outcome Contribution* 1 Is able to prove Mathematical facts encountered in secondary school. 2 2 Recognizes the importance of basic notions in Algebra, Analysis and Topology 4 3 Develops maturity of mathematical reasoning and writes and develops mathematical proofs. 5 4 Is able to express basic theories of mathematics properly and correctly both written and verbally 2 5 Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. 3 6 Expresses clearly the relationship between objects while constructing a model 0 7 Draws mathematical models such as formulas, graphs and tables and explains them 4 8 Is able to mathematically reorganize, analyze and model problems encountered. 5 9 Knows at least one computer programming language 5 10 Uses effective scientific methods and appropriate technologies to solve problems 4 11 Knows programming techniques and is able to write a computer program 0 12 Is able to do mathematics both individually and in a group. 0 13 Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians 0 14 In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields 0 * Contribution levels are between 0 (not) and 5 (maximum).   Student Workload - ECTS Works Number Time (Hour) Total Workload (Hour) Course Related Works     Class Time (Exam weeks are excluded) 14 4 56     Out of Class Study (Preliminary Work, Practice) 14 4 56 Assesment Related Works     Homeworks, Projects, Others 0 0 0     Mid-term Exams (Written, Oral, etc.) 1 15 15     Final Exam 1 20 20 Total Workload: 147 Total Workload / 25 (h): 5.88 ECTS Credit: 6