FK603 Numerical Solution of Ordinary and Partial Differential Equations

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code FK603
Name Numerical Solution of Ordinary and Partial Differential Equations
Term 2024-2025 Academic Year
Semester . Semester
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 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

Update Time: 09.05.2024 12:17