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Information
| Code | FK603 |
| Name | Numerical Solution of Ordinary and Partial Differential Equations |
| Term | 2024-2025 Academic Year |
| Term | Fall |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. METİN ÖZDEMİR |
| Course Instructor |
1 |
Course Goal / Objective
To make graduate students who took the basic mathematics and computer programming courses during their undergraduate studies be aware of the basic numerical techniques and solution methodologies of ordinary and partial differential equations.
Course Content
Error, precision and stability; writing simple computer programs and their compilation, data entrance (i/o), platting; Root finding methods: bisection, regula falsi, secant, Newton-Raphson methods; numerical solution of ordinary differential equations; random numbers and their production using computers; Monte Carlo methods, Metropolis algorithm; numerical solution of lineer systems of equations; curve fitting.
Course Precondition
none
Resources
Numerical recipes in FORTRAN, THE ART OF SCIENTIFIC COMPUTING, William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian P. Flannery
Notes
Fizikte Sayısal Yöntemler (M. Özdemir)-ders notu
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Understands the sources of error in numerical calculations and how to take precautions against them. |
| LO02 | Understands the concepts of error, precision and stability. |
| LO03 | Classifies differential equations. Makes the distinction between initial value and boundary value problems. |
| LO04 | Understand numerical differentiation and applies it. |
| LO05 | Understands how to solve initial value ordinary differential equations. Applies to different problems. |
| LO06 | Makes a plot of results that obtained. |
| LO07 | Understands how to solve boundary value ordinary and partial differential equations. Applies them to various problems. |
| LO08 | Uses these methods in physics and other sciences in the solution of various problems. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has sufficient infrastructure in various subjects of Physics. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Demonstrate the knowledge of appropriate mathematical techniques used in physics. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Interpret observational and experimental results. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Makes use of the conceptual and practical knowledge acquired in the physics field at mastery level. | 3 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Has a knowledge about the logic of scientific research. | 2 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Report the solution of a physics problem, experimental results or projects in a written format or orally. | 4 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Chooses and uses the necessary publications, books and methods for a scientific research. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Accesses a knowledge about a subject in physics, does literature search and uses other sources for this purpose. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Provides solutions to the problems encountered in the physics field applying research methods. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Can perform an independent research. | 3 |
| PLO11 | Bilgi - Kuramsal, Olgusal | Can perform group work effectively in a research or industrial projects. | |
| PLO12 | Bilgi - Kuramsal, Olgusal | Becomes conscious of the necessity of lifelong learning. | 3 |
| PLO13 | Bilgi - Kuramsal, Olgusal | To keep track of the developments in physics and updates himself/herself invariably. | 3 |
| PLO14 | Bilgi - Kuramsal, Olgusal | Shares his/her ideas and suggestions for solutions to the physical problems with experts and non-experts by supporting them with quantitative and qualitative data. | |
| PLO15 | Bilgi - Kuramsal, Olgusal | Can make an effective written or oral presentation of the results obtained in a study. | 4 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Makes use of the knowledge, problem solving and / or application skills acquired in the physics field in interdisciplinary studies. | 3 |
| PLO17 | Bilgi - Kuramsal, Olgusal | Has a foundation necessary to work in a research and development organizations. | 3 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Error, precision and stability concepts. Machine precision. | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Simple i/o programs. Calculation of a computers' machine precision. | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Numerical differentiaiton | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Numerical solution of initial value ordinary differential equations, Euler's Method | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 5 | Euler-Richardson, Runge Kutta methods | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 6 | Euler-Richardson, Runge Kutta methods (cont'd), numerical solution of various problems | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Numerical solution of boundary value ordinary differential equations. | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | mid-term exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Numerical solution of time independent Schrödinger equation for various potentials. | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Bireysel Çalışma |
| 10 | Introduction to partial differential equations | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama |
| 11 | Numerical solution of initial and boundary value partial differential equations | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 12 | Numerical solution of initial and boundary value partial differential equations (cont'd) | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 13 | Stability analyses | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 14 | Various applications, solution of heat equation, wave equation etc. | study the relevant subject in the lecture notes and textbook. | Öğretim Yöntemleri: Anlatım, Bireysel Çalışma |
| 15 | Term project | prepare to present your term project | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Bireysel Çalışma |
| 16 | Term Exams | final exams | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | term exams | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||