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Information
| Code | MT241 |
| Name | Advanced Calculus I |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 7 ECTS |
| National Credit | 4 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Dr. Öğr. Üyesi Doğa Can SERTBAŞ |
| Course Instructor |
Prof. Dr. ALİ ARSLAN ÖZKURT
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The student who has learned the analytical techniques in general in the MT131 and MT 132 courses, will learn the structure of real numbers with all their proofs in this course. Thus, the student will be provided with the basic background of real-analytic concepts and will be able to comprehend the concepts of advanced analysis.
Course Content
Induction, Real Numbers, Sequences, Series.
Course Precondition
None.
Resources
Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert Principles of Mathematical Analysis, Walter Rudin http://math.cu.edu.tr/Dersler/MT241/MT241.htm
Notes
Temel Gerçel Analiz I ,A. Nesin, Nesin Matematik Köyü, Calculus, M. Spivak, Türk Matematik Vakfı Yayınları
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows the concept of the Dedekind cut that forms the field of real numbers. |
| LO02 | Knows the countable sets |
| LO03 | Knows the concept of sequence |
| LO04 | Knows the limit theorems in sequences. |
| LO05 | Knows subsequences and the Bolzano-Weierstrass Theorem. |
| LO06 | Knows the Cauchy convergence criterion and that it is equivalent to the completeness of real numbers. |
| LO07 | Knows the concept of the convergence of an infinite series. |
| LO08 | Knows the convergence of infinite series, and conditional and absolute convergence tests. |
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. | |
| 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. | 2 |
| 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. | 4 |
| 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. | 2 |
| 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. | 4 |
| PLO16 | Bilgi - Kuramsal, Olgusal | Demonstrate the ability to select, use and develop effectively for contemporary mathematical applications. | 3 |
| 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. | 4 |
| PLO20 | Bilgi - Kuramsal, Olgusal | Gains the consciousness of prefesional ethics and responsibility. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Induction and inequalities | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Algebraic and order properties of real numbers | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Completeness property of real numbers | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Consequences of completeness property | Required readings | Öğretim Yöntemleri: Anlatım, Tartışma, Soru-Cevap |
| 5 | Topology of real numbers | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Convergence and limits of sequences | Required readings | Öğretim Yöntemleri: Anlatım |
| 7 | Limit theorems for sequences. | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Review of topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Monotone sequences and properties. | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Subsquences and the Bolzano-Weierstrass Theorem | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Cauchy sequences and completeness in terms of Cauchy sequences of real numbers | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Divergent sequences and their properties. | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Infinite series and convergence | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Convergence tests for series with positive terms | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Conditional convergence, absolute convergence and convergence tests | Required readings | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 16 | Term Exams | Review of topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Review of topics discussed in the lecture notes and sources | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 4 | 56 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 6 | 84 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 8 | 8 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 164 | ||
| Total Workload / 25 (h) | 6,56 | ||
| ECTS | 7 ECTS | ||