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Information
| Code | FZK309 |
| Name | Numerical Methods in Physics |
| Term | 2024-2025 Academic Year |
| Semester | 5. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 4 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. METİN ÖZDEMİR |
| Course Instructor |
Prof. Dr. METİN ÖZDEMİR
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
To introduce the students to basic purpose of numerical analysis, its application and sources of errors through teaching of subject together with the usage example programs. The student is expected to have a knowledge of freshman calculus and to have taken a programming language.
Course Content
Error, sources of errors, precision, stability; solution of non linear equations with one independent variable (root finding), bisection, regula falsi, secant and Newton-Raphson metods; Numerical derivative, Euler's method, Runge-Kutta methods, solution of initial value ordinary differential equations; solution of system of lineer equations, direct methods, iterative methods; eigen value and eigen vector problems and their numerical solutions; introduction to random numbers, their numerical generation, term project.
Course Precondition
none
Resources
Fizikte Sayısal Yöntemler (Ders notu). Metin Özdemir- Öğrencilere dijital olarak verilecek.
Notes
Homeworks and their solutions.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | knows how to plot numerically a given function or data stored in a file. |
| LO02 | using the programming language the student has studied before, knows how to read data from the computer screen or from a file and knows how to print the results to screen to a file. |
| LO03 | knows the basic purpose of numerical analysis. |
| LO04 | knows the sources of error in numerical calculations. |
| LO05 | knows how to find the real roots of a function by numerical methods. |
| LO06 | knows how to take derivatives numerically. |
| LO07 | knows how to solve initial value ordinary differential equation by Runge-Kutta methods. |
| LO08 | knows how to solve systems of linear equations by direct and iterative methods. |
| LO09 | knows how to compute eigenvalues and eigenvectors. |
| LO10 | have knowledge on random numbers. |
| LO11 | knows how to modify programs written in a programming language to solve a specific problem to solve her/his own problems. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Explain the basic concepts and principles in the field of physics. | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Follows the developments in the field of Physics and uses scientific methods and techniques. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Combine the knowledge gained in the field of Physics with the knowledge in other scientific fields and explains the method of producing scientific knowledge. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Identify problems in the field of physics and for the solutions apply the analytical and simulative methods. | 2 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Use the advanced theoretical and practical knowledge he has acquired in the field of Physics and designs experiments related to his field. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Take responsibility as a team or alone to overcome the problems encountered in the field of physics . | |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Classify, use and critically evaluate the knowledg taken by his/her efforts. | 3 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Improves himself by knowing that the learning process is lifelong. | 3 |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Knowing the importance of individual development, she/he implements what is necessary. | |
| PLO10 | Yetkinlikler - Öğrenme Yetkinliği | Evaluates the developments in the field of physics in terms of social ethics by watching and learning them. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | NUmerical function plotting, the purpose of numerical analysis, error, precision, stability | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Gösterip Yaptırma |
| 2 | In the programming language of students' choice execution of simple input/output programs, modification of those programs. | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 3 | Root finding, bisection and regula falsi methods, execution of programs | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 4 | root finding (cont'd), secant and Newton-Raphson methods, execution of programs | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Numerical differentiation, Euler's method, execution of programs | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Euler-Richardson and Runge-Kutta methods, program execution | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Solution of systems of linear equations | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 9 | Solution of systems of lineer equations (cont'd), Gauss-Jordan method, iterative methods, program execution | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | solution of example problems | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 11 | eigenvalue and eigenvector problems | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | numerical solution of eigenvalue and eigenvector problems | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | random numbers, some test mechanisms | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 14 | Some applications of random numbers | Study the relevant section in the textbook | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | completion of term project | Prepare for the presentation of term project | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 16 | Term Exams | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | 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 | 3 | 42 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 7 | 7 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 109 | ||
| Total Workload / 25 (h) | 4,36 | ||
| ECTS | 4 ECTS | ||