TÜRKÇE
ENGLISH
Information
| Unit | FACULTY OF SCIENCE AND LETTERS |
| MATHEMATICS PR. | |
| Code | MT406 |
| Name | Functional Analysis |
| Term | 2019-2020 Academic Year |
| Semester | 8. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Belirsiz |
| Type | Normal |
| Label | E Elective |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. DOĞAN DÖNMEZ |
| Course Instructor |
Prof. Dr. DOĞAN DÖNMEZ
(Bahar)
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
To grasp the ralationship between vector spaces and normed spaces. To understand Banch spaces.
Course Content
Metric spaces, completeness, vector spaces and norms, continuous linear tranformations.
Course Precondition
Resources
Notes
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Grasps convergence in metric spaces and understands the Cauchy sequence and completeness concepts. |
| LO02 | Understands the relationship between vector spaces and normed spaces. |
| LO03 | Understands that every normed space is a vector space. |
| LO04 | Can explain the convergence and continity concepts with examples |
| LO05 | Can relate the basic theorems of analysis with the concepts of normed spaces. |
| LO06 | Grasps the importance of the norm of a linear transformation |
| LO07 | Can define Banach space and give examples. |
| LO08 | Has a thorough and systematic knowledge of the basic topics of analysis |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | - | Comprehend the ability to prove the mathematical knowledge gained in secondary education on the basis of theoretical basis. | |
| PLO02 | - | Understands importance of basic consepts of Algebra, Analaysis and Topology. | |
| PLO03 | - | Mathematical reasoning demonstrates the ability to develop and write mathematical proofs by gaining maturity. | |
| PLO04 | - | Demonstrate the ability to express the basic theories of mathematics both correctly. | |
| PLO05 | - | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | |
| PLO06 | - | Comprehends the ability to understand the relationships between the objects in the most understandable way while creating a model for any problem. | |
| PLO07 | - | Comprehend and explain mathematical models such as formulas, graphs, tables and schema. | |
| PLO08 | - | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | |
| PLO09 | - | Comprehends at least one of the computer programming languages. | |
| PLO10 | - | Demonstrate the ability to use scientific methods and appropriate technologies effectively in problem solving. | |
| PLO11 | - | Understands sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians | |
| PLO12 | - | 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 | - | Understands the programming techniques and shows the ability to do programming. | |
| PLO14 | - | Demonstrates the ability to study mathematics both independently and as a group. | |
| PLO15 | - | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | |
| PLO16 | - | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | |
| PLO17 | - | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | |
| PLO18 | - | Gains the ability to use information technologies effectively for contemporary mathematical applications. | |
| PLO19 | - | Gains the ability to design, conduct experiments, field work, data collection, analysis, archiving, text solving and / or interpretation according to mathematics fields. | |
| PLO20 | - | Gains the consciousness of prefesional ethics and responsibility. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Review of matric spaces. Definitions and examples. | Studying the relevant parts of the textbooks | |
| 2 | Relationship between convergence and continuity in metric spaces | Studying the relevant parts of the textbooks | |
| 3 | Problem solving | Studying the relevant parts of the textbooks | |
| 4 | Cauchy sequences and completeness in metrik spaces. | Studying the relevant parts of the textbooks | |
| 5 | Some examples of complete metric spaces. | Studying the relevant parts of the textbooks | |
| 6 | Problem solving. | Studying the relevant parts of the textbooks | |
| 7 | Review of basic properties of vector spaces | Studying the relevant parts of the textbooks | |
| 8 | Mid-Term Exam | Review and problem solving | |
| 9 | Examples of some special vector spaces. | Studying the relevant parts of the textbooks | |
| 10 | Review of basic properties of linear transformations | Studying the relevant parts of the textbooks | |
| 11 | Normed spaces. Examples | Studying the relevant parts of the textbooks | |
| 12 | Relationship between normed and metric spaces. | Studying the relevant parts of the textbooks | |
| 13 | Convergence in normed spaces and norm of a linear transformation. | Studying the relevant parts of the textbooks | |
| 14 | Banach spaces. Examples. | Studying the relevant parts of the textbooks | |
| 15 | Finite dimensional normed spaces. | Studying the relevant parts of the textbooks | |
| 16 | Term Exams | Review and problem solving | |
| 17 | Term Exams | Review and problem solving |
Assessment (Exam) Methods and Criteria
| Assessment Type | Midterm / Year Impact | End of Term / End of Year Impact |
|---|---|---|
| 1. Midterm Exam | 100 | 20 |
| General Assessment | ||
| Midterm / Year Total | 100 | 20 |
| 1. Final Exam | - | 80 |
| Grand Total | - | 100 |