TÜRKÇE
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Information
| Code | MATZ207 |
| Name | Analysis III |
| Semester | 3. Semester |
| Duration (T+A) | 2-0 (T-A) (17 Week) |
| ECTS | 3 ECTS |
| National Credit | 2 National Credit |
| Teaching Language | Türkçe |
| Level | Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Doç. Dr. Gülfem SARPKAYA AKTAŞ |
Course Goal
Teaching the concept of multivariable functions and having limit, continuity and derivative applications in multivariable functions.
Course Content
Multivariable functions, topology of R, limit, continuity, function sequences and series, derivative, directional derivative, partial derivative, geometric interpretation of partial derivative, higher order derivatives and chain rule
Course Precondition
Not avaible
Resources
Balcı, M. ( 2021). Analysis II. Palme publishing
Notes
Bagci, M. N. (2021). Multivariable functions and approximation problems (Master's thesis, Balikesir University Institute of Science and Technology). YİTMEZ, B. G., YILMAZ, S., & DİNÇER, B. Investigation of Primary School Mathematics Education Undergraduate Students' Misconceptions About Limit and Continuity of Multivariate Functions. Dokuz Eylul University Buca Education Faculty Journal, (53), 611-637. Balcı M. (1997), Solved Mathematical Analysis Problems 2, Vol 2.Ankara: Balcı Publications Berkey, D. (1998), Calculus, second edition, Boston University. Lecture note Hacısalihoğlu, H.H., Balcı, M. (2000). Basic and General Mathematics, volume 3. Mirsollav, L., Vector Calculus, (2007). Eigenvalue, A., Eigenvalue, N.(1996), Higher Mathematical Problems with Solutions, vol II
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Knows multivariable functions and properties. |
| LO02 | Understands the topology of R. |
| LO03 | Comprehends the limit and continuity in functions of several variables and calculates the limits of functions. |
| LO04 | Know the concepts of function sequences and series and have processing skills for these concepts. |
| LO05 | Expresses partial derivative, geometric interpretation, directional derivative in multivariable functions and makes applications. |
| LO06 | Knows the higher order derivatives and chain rule of multivariable functions. |
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. | 5 |
| 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. | 5 |
| 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. | |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Has life-long learning awareness. | 4 |
| 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. | 5 |
| 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. | 4 |
| 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. | 5 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | The concept of the multivariable function, and domain and range of functions | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 2 | Drawing of graphs of multivariable functions | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 3 | Topology of R | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 4 | Limit concept in multivariable functions | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 5 | Continuity concept in multivariable functions | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 6 | The differentiation, the partial differentiation in multivariable functions | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 7 | The geometric interpretation of the partial derivative in multivariable functions | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 8 | Mid-Term Exam | Ölçme Yöntemleri: Yazılı Sınav |
|
| 9 | The directional derivative | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 10 | The higher order partial derivatives | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 11 | Zincir kuralı | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 12 | The function sequences | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 13 | The function series | Examining the related sources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 14 | General review and question solution-1 | Examining the related sources | Öğretim Yöntemleri: Soru-Cevap, Alıştırma ve Uygulama |
| 15 | General review and question solution-2 | Examining the related sources | Öğretim Yöntemleri: Soru-Cevap, Alıştırma ve Uygulama |
| 16 | Term Exams-1 | Ölçme Yöntemleri: Yazılı Sınav |
|
| 17 | Term Exams-2 | Ölçme Yöntemleri: Yazılı Sınav |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 2 | 28 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 2 | 28 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 6 | 6 |
| Final Exam | 1 | 16 | 16 |
| Total Workload (Hour) | 78 | ||
| Total Workload / 25 (h) | 3,12 | ||
| ECTS | 3 ECTS | ||