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Information
| Code | MATZ210 |
| Name | Calculus IV |
| Term | 2024-2025 Academic Year |
| Semester | 4. Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 4 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. AYTEN PINAR BAL |
| Course Instructor |
1 |
Course Goal / Objective
In this course, the student who learns analytical techniques in general learns the structure of real numbers completely with all the evidence. Thus, it is equipped with the basic infrastructure of real analysis and reaches a level where it can easily grasp advanced abstract analytical concepts.
Course Content
In this course, the concepts of limit, continuity and derivative of functions are discussed in detail. The calculation of limit values of functions, continuity conditions and derivative operations will be examined and the basic properties of these concepts will be emphasized. In addition, sequences and series of functions will be introduced and the properties, convergence conditions and applications of these sequences and series will be covered.
Course Precondition
There are no prerequisites.
Resources
Introduction to Real Analysis, Robert G. Bartle, Donald R. Sherbert http://matematik.cu.edu.tr/Dersler/MT241/MT241.htm Balcı M. (2016) Analiz Palme Yayıncılık Prof. Dr. Ahmet A. KARADENİZ Yüksek Matematik. Cilt 1, 2. 4. Baskı, 1985. Prof Dr. Mustafa BAYRAKTAR Analize giriş I, II. 2. Baskı, 2008. Prof. Dr. Mustafa BALCI, Analiz 1,2. 7. Baskı, 2008. Doç. Dr. Ahmet TEKCAN, İleri Analiz. DORA 2010.
Notes
Principles of Mathematical Analysis, Walter Rudin
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Explains the properties of the concepts of continuous function and uniform continuity. |
| LO02 | Solves problems related to monotonic and inverse functions |
| LO03 | Understands information about derivative and differential calculus. |
| LO04 | Makes applications related to the mean value theorem. |
| LO05 | Explains the properties of the expansion of functions into Taylor series. |
| LO06 | Understands how to define new functions using function arrays and series.Defines new functions using function arrays and series |
| LO07 | Understands the Weirstrass M-test and the possibilities provided by uniform convergence. |
| LO08 | Explains limits of functions and limit theorems |
| LO09 | Explains the Mean Value theorem |
| LO10 | Numerical calculations regarding Taylor series of functions does |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has enough knowledge about mathematics. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Has pedagogical knowledge about teaching profession and field. | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Implements classroom management approaches to be used in educational environments effectively. | |
| PLO04 | Bilgi - Kuramsal, Olgusal | Prepares the learning environments in which appropriate teaching methods are used for effective mathematics education in accordance with development and age levels. | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Knows the relationship between Mathematics-Society-Environment-History and uses it in professional and daily life. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Uses Turkish properly and effectively according to the rules. | |
| PLO07 | Bilgi - Kuramsal, Olgusal | Selects and designs appropriate materials, in mathematics teaching. | |
| PLO08 | Bilgi - Kuramsal, Olgusal | Monitors students' progress using different assessment and evaluation methods and techniques. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Takes responsibility as an individual and as a team member to solve problems related to the field. | 2 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Has life-long learning awareness. | 2 |
| PLO11 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Shares his/her knowledge and skills, problems and solutions that he/she identified by means of oral and written communication with the expert and non-expert people. | 3 |
| PLO12 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Uses information and communication technologies and other related materials for an effective mathematics teaching. | |
| PLO13 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Has enough foreign language knowledge to follow foreign resources related to the field. | |
| PLO14 | Yetkinlikler - Öğrenme Yetkinliği | Has the knowledge of the purpose, structure and functioning of the Turkish education system. | |
| PLO15 | Yetkinlikler - Öğrenme Yetkinliği | Becomes a teacher who adheres to Atatürk's principles and revolutions. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Limits and properties of functions. | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 2 | Limit theorems | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 3 | Continuous functions and their properties | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 4 | Continuous functions on intervals. | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 5 | smooth continuity | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 6 | Continuity of monotonic and inverse functions | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 7 | Derivative, differential 1 | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 8 | Mid-Term Exam | Examining relevant sources | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Türev Diferensiyel 2 | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 10 | Mean value theorem and its applications | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 11 | Taylor's Theorem and its applications | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 12 | Function sequences and series 1 | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 13 | Function sequences and series 2 | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 14 | Point and uniform convergence, Weirstarass M-test and its applications | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 15 | Change of limit order in function sequences | Examining relevant sources | Öğretim Yöntemleri: Anlatım |
| 16 | Term Exams | source review | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | source review | 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 | 6 | 6 |
| Final Exam | 1 | 12 | 12 |
| Total Workload (Hour) | 102 | ||
| Total Workload / 25 (h) | 4,08 | ||
| ECTS | 4 ECTS | ||