MT572 Analysis I

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

Information

Code MT572
Name Analysis I
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. ALİ ARSLAN ÖZKURT


Course Goal / Objective

to give basic knowledges of measure theory, to give basic knowledges of Lebesque measure and Lebesgue integration of real and complex functions, to give Riezs representation theorem and some applications.

Course Content

Measure ,Step functions and simple functions , integral of positive and complex valued functions,Topologicl preliminaries , Riezs representation theorem, Borel measures, Lebesque measure, continuity properties of measurable functions, convex fonctions and some inequalities, Lp spaces, Banach spaces,

Course Precondition

None

Resources

Real Analysis: Modern Techniques and Their Applications, Gerald B. Folland, 2. ed., John Wiley & Sons, 2013.

Notes

Real and Complex Analysis, Walter Rudin, 3rd ed., McGraw-Hill, Inc. 1987.


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Understands the measure theory
LO02 Knows lebesgue integration of real and complex functions
LO03 Knows Riezs representation theorem
LO04 Learns Lebesgue measure in Euclidean spaces
LO05 Learns Banach and Lp spaces


Relation with Program Learning Outcome

Order Type Program Learning Outcomes Level
PLO01 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in her area of expertise and other areas of mathematics. 5
PLO02 Bilgi - Kuramsal, Olgusal Knows in detail the relationship between the results in his area of ​​expertise and other areas of mathematics. 4
PLO03 Bilgi - Kuramsal, Olgusal Establishes new mathematical models with the help of the knowledge gained in the field of specialization. 5
PLO04 Bilgi - Kuramsal, Olgusal Has basic knowledge in all areas of mathematics. 4
PLO05 Bilgi - Kuramsal, Olgusal It presents the knowledge gained in different fields of mathematics and their relations with each other in the simplest and most understandable way.
PLO06 Bilgi - Kuramsal, Olgusal Effectively uses the technical equipment needed to express mathematics. 5
PLO07 Bilgi - Kuramsal, Olgusal poses original problems related to field and presents different solution techniques.
PLO08 Bilgi - Kuramsal, Olgusal carries out original and qualified scientific studies on the subject related to its field. 4
PLO09 Bilgi - Kuramsal, Olgusal Analyzes existing mathematical theories and develops new theories. 3
PLO10 Beceriler - Bilişsel, Uygulamalı Knows the teaching-learning techniques in areas of mathematics that require expertise and uses these techniques effectively at every stage of education. 2
PLO11 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği To have knowledge of a foreign language at a level to be able to follow foreign sources related to the field and to communicate verbally and in writing with foreign stakeholders. 4
PLO12 Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği presents and publishes its original works within the framework of scientific ethical rules for the benefit of its stakeholders.
PLO13 Yetkinlikler - Öğrenme Yetkinliği Adheres to the ethical rules required by its scientific title 4


Week Plan

Week Topic Preparation Methods
1 definition of measures and elementary properties of measures Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
2 definition of measures and elementary properties of measures 2 Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
3 Step and simple functions Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
4 Integration of positive functions and integration and complex functions Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
5 Integration of positive functions and integration and complex functions 2 Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
6 Topological preliminaries (Urysohn lemma and partition of unity) Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
7 Riezs representation theorem Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
8 Mid-Term Exam Reviewed of the topics discussed in the lecture notes and source again Ölçme Yöntemleri:
Yazılı Sınav
9 Riezs representation theorem 2 Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
10 Regularity properties of Borel measures Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
11 Lebesgue measures in Euclidean spaces Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
12 Continuity properties of measurable functions Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
13 Lp spaces Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
14 Lp spaces 2 Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
15 Banach spaces Study the relevant sections in the textbook and solve problems Öğretim Yöntemleri:
Anlatım, Tartışma
16 Term Exams Reviewed of the topics discussed in the lecture notes and source again Ölçme Yöntemleri:
Yazılı Sınav
17 Term Exams Reviewed of the topics discussed in the lecture notes and source again 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 11:44