CANKIRI KARATEKIN UNIVERSITY

Bologna Information System

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

PARTIAL DIFFERENTIAL EQUATIONS | MAT206 | SPRING | 4+0 | C | 6 |

Learning Outcomes | 1-To solve initial value problems of quasilinear equations. 2-To classify second order equations with two variables and reduce to canonical form. 3-To reduce second order equations with two variables to canonical form. 4-To compute fourier series of piecewise continuous functions. 5-To solve initial value and initial-boundary value problems for one-dimensional wave equation. 6-To apply separation of variables method to boundary value problems. 7-To solve initial-boundary value problems for one-dimensional heat equation. 8-To solve different boundary value problems of laplace equation. |

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 | 16 | 16 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 180 | |||

Total Workload (hours) / 30 (s) | 6 ---- (6) | |||

ECTS Credit | 6 |

Week | Topics | Study Metarials |

1 | Basic equations and concepts, classification of partial differential equations, integral curves of vector fields | |

2 | Constructing integral curves of a vector field | |

3 | Constructing integral surfaces of a vector field containing a given curve | |

4 | First order quasilinear equations | |

5 | Classification of second order equations with two variables, canonical forms, equations of mathematical physics, well-posed problems | |

6 | Cauchy-Kowalewskaya theorem, initial value problem for one dimensional wave equation, d`Alembert formula, domain of dependence | |

7 | Initial-boundary value problems for one dimensional wave equation | |

8 | Fourier series and their convergence, Fourier sine and cosine series | |

9 | Separation of variables, initial-boundary value problem for one-dimensional wave equation, existence and uniqueness of the solution | |

10 | Initial-boundary value problem for one-dimensional heat equation, existence and uniqueness of the solution | |

11 | Nonhomogeneous problems | |

12 | Boundary value problems, Laplace equation, harmonic functions, maximum and minimum principles, uniqueness and continuity of Dirichlet problem | |

13 | Dirichlet problem for a circle, mean value theorem, Dirichlet problem for a circular annulus | |

14 | Neumann problem for a circle, Dirichlet and Neumann problems for a rectangle |

Prerequisites | ANALYSIS I, ANALYSIS II, ADVANCED ANALYSIS I, ORDINARY DIFFERENTIAL EQUATIONS |

Language of Instruction | Turkish |

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

Instructors | - |

Assistants | - |

Resources | Kısmi Diferansiyel Denklemler, İbrahim Ethem Anar, Palme Yayınevi, 2005. |

Supplementary Book | [1] Linear Partial Differential Equations for Scientists and Engineers, 4th Ed., Tyn Myint-U, Lokenath Debnath, 2007. [2] Kısmi Türevli Denklemler, Alemdar Hasanoğlu (Hasanov), Literatür Yayıncılık, 2010. [3] Kısmi Diferensiyel Denklemler, Mehmet Çağlıyan, Okay Çelebi, Dora Basım Yayın, 2010. [4] Kısmi Türevli Denklemler ve Çözümlü Problemler, A. Neşe Dernek, Nobel Yayın Dağıtım, 2009. [5] Kısmi Diferensiyel Denklemler, David W. Zachmann, Paul DuChateau, Çeviri: H. Hilmi Hacısalihoğlu, Nobel Yayın Dağıtım [6] Kısmi Türevli Denklemler, Kerim Koca, Gündüz Eğitim ve Yayıncılık, 2001. |

Document | Lecture notes. |

Goals | To teach basic theory and solution techniques of partial 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 | 4 |

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 | 4 |

9 | To adopt the necessity of learning constantly by observing the improvement of scientific accumulation over time | 2 |

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 | - |

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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