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Information
| Code | MT332 |
| Name | Real Analysis |
| Term | 2024-2025 Academic Year |
| Semester | 6. 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 | Prof. Dr. GONCA AYIK |
| Course Instructor |
1 2 |
Course Goal / Objective
The aim of this course is to make students comprehend Riemann integrability criteria, integrable functions, fundamental theorem of calculus, Darbox theorem, inverse and implicit function theorem.
Course Content
In this course Riemann integral, properties of Riemann integral, fundamental theorem of calculus, integral as a limit, improper integral, uniform convergence, intercahange of limits, inverse and implicit function theorem are described.
Course Precondition
NONE
Resources
Introduction To Real Analysis - Robert G Bartle & Donald R Sherbert
Notes
Principle of Mathematical Analysis,Walter Rudin,McGraw-Hill, 1976. Analiz I,II, Erdal Coşkun, Alp Yayınevi, 2002. Introduction To Real Analysis , Robert G. Bartle, Donald R. Bartle,Wiley, 1992.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Recognizes Riemann integrability criteria. |
| LO02 | Recognizes integrable functions. |
| LO03 | Recognizes fundamental theorem of calculus. |
| LO04 | Reconizes improper integral. |
| LO05 | Uses the relationship of uniform continuity and integral. |
| LO06 | Uses integrals to find the remainder term of Taylor's formula. |
| LO07 | Recognizes the Darbox theorem. |
| LO08 | Recognizes inverse and implicit function theorems. |
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. | 4 |
| 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. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Demonstrates the ability to express the basic theories of mathematics accurately both in writing and orally. | 4 |
| PLO05 | Bilgi - Kuramsal, Olgusal | Understands the relationship between the different fields of mathematics and its relation to other disciplines. | 4 |
| 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. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to mathematically rearrange, analyze, and model the problems they encounter. | |
| 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. | 4 |
| PLO15 | Bilgi - Kuramsal, Olgusal | Demonstrate an awareness of the universal and social impacts and legal consequences of mathematical applications in the field of study. | 3 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 4 |
| PLO17 | Bilgi - Kuramsal, Olgusal | It has ability of lifelong learning awareness, access to information, monitoring developments in science and technology and self-renewal ability. | 4 |
| 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. | |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Reimann Integral | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | Reimann integrability | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 3 | Integrable functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 4 | Solving problem | Review of the relevant pages from sources | Öğretim Yöntemleri: Problem Çözme |
| 5 | Properties of Riemann integral | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 6 | Integrability of continuous and monotone functions | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 7 | Fundamental theorem of calculus | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 8 | Mid-Term Exam | Review and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Taylor formula | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 10 | Darboux theorem | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 11 | Improper Integral | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 12 | Functions of several variables | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 13 | Inverse function theorem | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma, Problem Çözme |
| 14 | Implicit function theorem | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 15 | Implicit function theorem 1 | Review of the relevant pages from sources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 16 | Term Exams | Review and problem solving | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review and problem solving | 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 | ||