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Information
| Code | MN0026 |
| Name | Numerical Techniques and Applications |
| Term | 2024-2025 Academic Year |
| Semester | . Semester |
| Duration (T+A) | 2-2 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | İngilizce |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator |
Course Goal / Objective
To teach the fundamentals of numerical analysis.
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
Numerical Recipes, the art of scientific computing, William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery, Cambridge University Press (1986)
Notes
Lecture notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the error sources in numerical methods and how to reduce them to a minimum. |
| LO02 | Know how to make the plot of a function using computer resources. |
| LO03 | Knows how to finde the roots of one or more non-lineraf functions numerically. |
| LO04 | Knows how to compute derivatives numerically. |
| LO05 | Knows how to compute integrals numerically. |
| LO06 | Knows how to solve systems of linear equations numerically. |
| LO07 | Knows how to calculate eigenvalues and eşgenfunctios numerically. |
| LO08 | Knows the generation of random numbers, their test procedures and their use in various applications. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Based on the qualifications gained during PhD studies, develops and deepens the current and advanced knowledge in the area by unique means of thinking and / or research at mastery level and comes up with original definitions which bring about novelty to the area. | 3 |
| PLO02 | Beceriler - Bilişsel, Uygulamalı | Can effectively use the equipment used in the field. | |
| PLO03 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Selects experimental measurement methods of various physical quantities and uses instruments in accordance with their sensitivity limits. | |
| PLO04 | Yetkinlikler - Alana Özgü Yetkinlik | Interprets experimental and observational results. | 2 |
| PLO05 | Yetkinlikler - Öğrenme Yetkinliği | Can draw conclusions from the information obtained during the preparation for the PhD qualifying exam. | 3 |
| PLO06 | Bilgi - Kuramsal, Olgusal | Can interpret the information acquired about the field orally and in writing. | 3 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Uses mathematical methods related to the field of study. | 4 |
| PLO08 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Have knowledge about the logic, design, conclusion and dissemination of results of scientific research. | 2 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Uses the theoretical and applied knowledge gained in the field of materials and nanotechnology at the level of expertise. | 4 |
| PLO10 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Gains high-level skills in using research methods in studies related to materials science and nanotechnology. | 3 |
| PLO11 | Bilgi - Kuramsal, Olgusal | Develops a scientific method that brings innovation to science. | |
| PLO12 | Yetkinlikler - Alana Özgü Yetkinlik | Makes critical analysis, synthesis and evaluation of new ideas related to the field. | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Can carry out independent research on a specific topic related to materials and nanotechnology. | 3 |
| PLO14 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Be able to lead in the execution of interdisciplinary studies. | 3 |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Follows the developments in the her/his field of study and constantly renews herself/himself. | 3 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Calculate the predictions of the theories and compare them with the experimental results. | 3 |
| PLO17 | Yetkinlikler - Öğrenme Yetkinliği | Comprehends the interdisciplinary interaction that the field of study is related to. | 4 |
| PLO18 | Yetkinlikler - Alana Özgü Yetkinlik | He/she shares his/her own ideas and suggestions regarding the problems in the field of study with groups in and outside the field by supporting them with quantitative and qualitative data. | 2 |
| PLO19 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Can develop original solutions for problems in the field. | 3 |
| PLO20 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Can prepare a scientific article and publish scientific articles in international refereed journals. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Error, precision, stability, machine accuracy | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 2 | Variables, functions, some simple input/output algorithms and programs, plotting | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 3 | Root finding (nonlinear equations), bisection, regula falsi methods | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 4 | Secant and Newton-Raphson methods, generalization of NR methods to a system of equations | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 5 | Numerical derivatives, numerical solution of ordinary differential equations, Eulers method | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 6 | Euler-Richardson and Runge-Kutta methods, program execution | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Solution of system of lineer equations | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-term exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 9 | Direct and iterative methods | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 10 | Eigenvalue and eigenvector problems and their solution | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 11 | Applications: one dimensional quantum mechanical problem | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 12 | Random numbers, numerical generation of RN, tests | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 13 | Application of random numbers | Study the relevant section in the textbook. | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 14 | Term project | Choose a project and get prepared for the project. | Öğretim Yöntemleri: Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 15 | Term project (cont'd) | Complete the project and get ready for the presentation of it. | Öğretim Yöntemleri: Soru-Cevap, Tartışma, Alıştırma ve Uygulama |
| 16 | Final exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | Final exam | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 4 | 56 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 1 | 2 | 2 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 12 | 12 |
| Final Exam | 1 | 28 | 28 |
| Total Workload (Hour) | 154 | ||
| Total Workload / 25 (h) | 6,16 | ||
| ECTS | 6 ECTS | ||