TÜRKÇE
ENGLISH
Information
| Code | MT333 |
| Name | Numerical Analysis |
| Term | 2022-2023 Academic Year |
| Semester | 5. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. ZEYNEP ÖZKURT |
| Course Instructor |
Doç. Dr. ZEYNEP ÖZKURT
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
This course aims to introduce a variety of methods of numerical analysis and to solve the mathematical problems in different areas with the methods of numerical analysis.
Course Content
Meaning and Importance of Numerical Analysis, Number systems and general information about error, Solution methods of nonlinear equations, Solution methods of linear equations, interpolation, numerical integration
Course Precondition
none
Resources
Behiç Çağal (1989), Sayısal Analiz, Seç Yayın Dağıtım, İstanbul. Lee W. Johnson, R. Dean Riess (1982) Numerical Analysis, Addison-Wesley Publishing Company.
Notes
Lee W. Johnson, R. Dean Riess (1982) Numerical Analysis, Addison-Wesley Publishing Company.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Comments on the source of the error of numerical solutions. |
| LO02 | solves nonlinear systems |
| LO03 | Calculates the roots of a function. |
| LO04 | Solves Linear sistems. |
| LO05 | Knows and uses the methods of finding the inverse of matrices. |
| LO06 | calculates determinants |
| LO07 | Calculates the approximate values of polynomial functions of one variable |
| LO08 | calculates numerical integration |
| LO09 | Examines errors in calculations |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | |
| PLO02 | Bilgi - Kuramsal, Olgusal | Understands importance of basic consepts of Algebra, Analaysis and Topology. | 3 |
| PLO03 | Yetkinlikler - Öğrenme Yetkinliği | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to express the basic theories of mathematics both correctly. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | 3 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | 3 |
| PLO09 | Bilgi - Kuramsal, Olgusal | Comprehends at least one of the computer programming languages. | |
| PLO10 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | 3 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | In addition to their professional development, they demonstrate their ability to continuously improve themselves by identifying their educational needs in scientific, cultural, artistic and social areas in line with their interests and abilities. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Demonstrates the ability to study mathematics both independently and as a group. | 3 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | Bilgi - Kuramsal, Olgusal | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | Bilgi - Kuramsal, Olgusal | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | 3 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Importance and meaning of numerical analysis, Number systems and errors in numerical procedures | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 2 | Number systems and errors in numerical procedures | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 3 | Bisection and Newtons method | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 4 | Bairstow method | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 5 | Gauss and Gauss-Jordan Methods | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 6 | Gauss and Gauss-Jordan Methods for finding Inverse of a matrix and Determinant | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 7 | Gauss-Seidel method for solving Linear equations | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 8 | Mid-Term Exam | Required readings and solving problems | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Interpolation, Linear interpolasyon | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 10 | Lagrange interpolation | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 11 | Divided differences interpolation | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 12 | Differences İnterpolation | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 13 | Calculation Methods for Numerical integration | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 14 | Calculation Methods for Numerical integration on an ınterval | Required readings and solving problems | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama |
| 15 | Exercises | Required readings and solving problems | Öğretim Yöntemleri: Alıştırma ve Uygulama |
| 16 | repeat | Required readings and solving problems | Öğretim Yöntemleri: Anlatım |
| 17 | Term Exams | Required readings and solving problems | 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 | 12 | 12 |
| Final Exam | 1 | 18 | 18 |
| Total Workload (Hour) | 114 | ||
| Total Workload / 25 (h) | 4,56 | ||
| ECTS | 5 ECTS | ||