CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

Course Title | Code | Semester | Laboratory+Practice (Hour) | Pool | Type | ECTS |

ORDINARY DIFFERENTIAL EQUATIONS | MAT205 | FALL | 4+0 | C | 6 |

Learning Outcomes | 1-To classify differential equations. 2-To solve differential equations of various orders and systems. 3-To explain the fundamental theory of differential equations 4-To apply the laplace transformation to initial value problems for differential equations and systems. |

Activity | Percentage (100) | Number | Time (Hours) | Total Workload (hours) |

Course Duration (Weeks x Course Hours) | 14 | 4 | 56 | |

Classroom study (Pre-study, practice) | 14 | 5 | 70 | |

Assignments | 10 | 2 | 6 | 12 |

Short-Term Exams (exam + preparation) | 10 | 2 | 6 | 12 |

Midterm exams (exam + preparation) | 30 | 1 | 14 | 14 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 50 | 1 | 15 | 15 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 179 | |||

Total Workload (hours) / 30 (s) | 5,97 ---- (6) | |||

ECTS Credit | 6 |

Week | Topics | Study Metarials |

1 | Definition of differential equation and classification of differential equations, first order differential equations, linear equations, separable equations | |

2 | Exact differential equations and integrating factors, existence and uniqueness theorem Bernoulli equation, special integrating factors and transformations | |

3 | Higher order linear homogeneous equations with constant coefficients, characteristic equation, fundamental solutions, linear independence and Wronskian | |

4 | Complex roots and repeated roots, reduction of order | |

5 | Higher order nonhomogeneous equations, method of undetermined coefficients | |

6 | The method of variation of parameters, Cauchy-Euler equation | |

7 | Physical models and applications | |

8 | Series solutions near an ordinary point | |

9 | Series solutions near a regular singular point, Frobenius method | |

10 | Laplace transform | |

11 | Convolution integral, solution of initial value problems | |

12 | Systems of first order linear homogeneous differential equations with constant | |

13 | Coefficients, fundamental matrices, complex and repeated eigenvalues | |

14 | Nonhomogeneous systems of linear differential equations |

Prerequisites | ANALYSIS I, ANALYSIS II |

Language of Instruction | Turkish |

Course Coordinator | Assist. Prof. Dr. Müfit ŞAN |

Instructors | - |

Assistants | - |

Resources | Diferensiyel Denklemler ve Sınır Değer Problemleri, Edwards & Penney (Çeviri Editörü: Prof. Dr. Ömer AKIN), Palme Yayıncılık, 1997 |

Supplementary Book | [1] Diferensiyel Denklemler, Mustafa BAYRAM, Birsen Yayınevi, 2002. [2] Diferansiyel Denklemler ve Uygulamaları, Mehmet Aydın, Gönül Gündüz, Beno Kuryel, Galip Oturanç, Fakülteler Barış Yayınları, 2007. |

Document | Lecture Notes |

Goals | To comprehend solution techniques and basic theory of ordinary differential equations. |

Content | - |

Program Learning Outcomes | Level of Contribution | |

1 | To have a grasp of theoretical and applied knowledge in main fields of mathematics | 5 |

2 | To have the ability of abstract thinking | 4 |

3 | To be able to use the gained mathematical knowledge in the process of identifying the problem, analyzing and determining the solution steps | 5 |

4 | To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life | 4 |

5 | To have the qualification of studying independently in a problem or a project requiring mathematical knowledge | 2 |

6 | To be able to work compatibly and effectively in national and international groups and take responsibility | - |

7 | To be able to consider the knowledge gained from different fields of mathematics with a critical approach and have the ability to improve the knowledge | 3 |

8 | To be able to determine what sort of knowledge the problem met requires and guide the process of learning this knowledge | 3 |

9 | To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time | - |

10 | To be able to transfer thoughts on issues related to mathematics, proposals for solutions to the problems to the expert and non-expert shareholders written and verbally | 3 |

11 | To be able to produce projects and arrange activities with awareness of social responsibility | - |

12 | To be able to follow publications in mathematics and exchange information with colleagues by mastering a foreign language at least European Language Portfolio B1 General Level | - |

13 | To be able to make use of the necessary computer softwares (at least European Computer Driving Licence Advanced Level), information and communication technologies for mathematical problem solving, transfer of thoughts and results | - |

14 | To have the awareness of acting compatible with social, scientific, cultural and ethical values | - |

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