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Course Information

Course's Contribution to Prog.

ECTS- Workload Calculation Tool

Program Information

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

Topology II | MATH206 | SPRING | 4+0 | C | 6 |

Learning Outcomes | 1-Solves initial value and initial-boundary value problems for onedimensional wave equation. 2-Solves initial-boundary value problems for one-dimensional heat equation. 3-Solves 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 | 6 | 84 | |

Assignments | 0 | 0 | 0 | 0 |

Short-Term Exams (exam + preparation) | 0 | 0 | 0 | 0 |

Midterm exams (exam + preparation) | 40 | 1 | 14 | 14 |

Project | 0 | 0 | 0 | 0 |

Laboratory | 0 | 0 | 0 | 0 |

Final exam (exam + preparation) | 60 | 1 | 14 | 14 |

Other | 0 | 0 | 0 | 0 |

Total Workload (hours) | 168 | |||

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

ECTS Credit | 6 |

Week | Topics | Study Metarials |

1 | Basic equations and concepts, classification of partial differential equations, integral curves of vector fields | R1) Lecture notes |

2 | Constructing integral curves of a vector field | R1) Lecture notes |

3 | Constructing integral surfaces of a vector field containing a given curve | R1) Lecture notes |

4 | First order quasilinear equations | R1) Lecture notes |

5 | Classification of second order equations with two variables, canonical forms, equations of mathematical physics, wellposed problems | R1) Lecture notes |

6 | Cauchy-Kowalewskaya theorem, initial value problem for one dimensional wave equation, d`Alembert formula, domain of dependence | R1) Lecture notes |

7 | Initial-boundary value problems for one dimensional wave equation | R1) Lecture notes |

8 | Midterm exams | |

9 | Fourier series and their convergence, Fourier sine and cosine series | R1) Lecture notes |

10 | Separation of variables, initialboundary value problem for one-dimensional wave equation, existence and uniqueness of the solution | R1) Lecture notes |

11 | Initial-boundary value problem for one-dimensional heat equation, existence and uniqueness of the solution | R1) Lecture notes |

12 | Nonhomogeneous problems | R1) Lecture notes |

13 | Boundary value problems, Laplace equation, harmonic functions, maximum and minimum principles, uniqueness and continuity of Dirichlet problem | R1) Lecture notes |

14 | Dirichlet problem for a circle, mean value theorem, Dirichlet problem for a circular annulus | R1) Lecture notes |

15 | Neumann problem for a circle, Dirichlet and Neumann problems for a rectangle | R1) Lecture notes |

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

Language of Instruction | English |

Coordinator | Prof. Dr. Ahmet Yaşar Özban |

Instructors | - |

Assistants | Dr. Harun Baldemir |

Resources | K1) Bleecker, D., & Csordas, G. Basic Partial Differential Equations. 1996. Chapman Hall, New York. K2) Folland, G. B. (1995). Introduction to partial differential equations. Princeton university press. Chicago K3) Linear Partial Differerential Equations for Scientists and Engineering, 4th Ed., Tyn Myint-U, Lokenath Debnath, 2007. |

Supplementary Book | [1] Kısmi Türevli Denklemler, Alemdar Hasanoğlu (Hasanov), Literatür Yayıncılık, 2010. [2] Kısmi Differensiyel Denklemler, Mehmet Çağlıyan, Okay Çelebi, Dora Basım Yayın, 2010. [3] Kısmi Türevli Denklemler ve Çözümlü Problemler, A. Neşe Dernek, Nobel Yayın Dağıtım, 2009. [4] Kısmi Diferensiyel Denklemler, David W. Zachmann, Paul Du Chateau, Çeviri: H.Hilmi Hacısalihoğlu, Nobel Yayın Dağıtım, 2000. [5] Kısmi Türevli Denklemler, Kerim Koca, Gündüz Eğitim ve Yayıncılık, 2001. |

Goals | Teaches basic theory and solution techniques of partial differential equations. |

Content | Partial differential equations, their types, their solution ways and some applications. |

Program Learning Outcomes | Level of Contribution | |

1 | To have a grasp of theoretical and applied knowledge in main fields of mathematics | 3 |

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

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

4 | To be able to relate the gained mathematical acquisitions with different disciplines and apply in real life | 3 |

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

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 | - |

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

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 | - |

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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