TÜRKÇE
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Information
| Code | MATZ211 |
| Name | Calculus III |
| Term | 2024-2025 Academic Year |
| Semester | 3. Semester |
| Duration (T+A) | 4-0 (T-A) (17 Week) |
| ECTS | 5 ECTS |
| National Credit | 4 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 Instructor |
Doç. Dr. Gülfem SARPKAYA AKTAŞ
(A Group)
(Ins. in Charge)
|
Course Goal / Objective
The aim of this course is to enable students to define the concept of multivariable function and to apply the topics of limit, continuity and derivative in multivariable functions.
Course Content
In this course, functions of several variables and the topology of the space R will be discussed. The concepts of limit and continuity will be analyzed in the context of functions of several variables, sequences and series of functions will be introduced. In addition to the concept of derivative, directional derivative and partial derivative will be covered and geometric interpretation of partial derivative will be emphasized. In addition, advanced topics related to derivatives such as higher order derivatives and chain rule will be covered in the course to improve students' analysis skills.
Course Precondition
No prerequisites
Resources
Balcı, M. ( 2021). Analysis II. Palme publishing Prof. Dr. Ahmet A. KARADENİZ Higher Mathematics. Volume 1, 2. 4th Edition, 1985. Prof Dr. Mustafa BAYRAKTAR Introduction to Analysis I, II. 2nd Edition, 2008. Assoc. Dr. Ahmet TEKCAN, Advanced Analysis. DORA 2010.
Notes
Bağcı, M. N. (2021). Multivariable functions and approximation problems (Master's thesis, Balıkesir University Graduate School of Natural and Applied Sciences). YİTMEZ, B. G., YILMAZ, S., & DİNÇER, B. Investigation of the Misconceptions of Elementary Mathematics Teaching Undergraduate Students on the Limits and Continuity of Functions of Several Variables. Dokuz Eylül University Buca Education Faculty Journal, (53), 611-637. Balcı M. (1997),Solved Mathematics Analysis Problems 2, Volume 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. Mirsolav, L., Vector Calculus, (2007). Özdeğer, A., Özdeğer, N. (1996), Solved Higher Mathematics Problems, volume II
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Define multivariable functions and properties. |
| LO02 | Explains the topology of R and the concepts it contains. |
| LO03 | Defines the concepts of limit and continuity in multivariable functions. |
| LO04 | Applies processing skills to problems regarding the concepts of function sequences and series. |
| LO05 | Explains partial derivatives and geometric interpretations of directional derivatives in multivariable functions. |
| LO06 | Explain higher order derivatives of functions of several variables and chain rule. |
| LO07 | Makes applications related to partial derivative in multivariable functions. |
| LO08 | Question the geometric interpretation of functions of several variables. |
| LO09 | Distinguish the properties of directional derivative in functions of several variables. |
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. | |
| 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. | |
| 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 | The concept of multivariable function, definition and value sets | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 2 | Drawing graphs of multivariable functions | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 3 | Topology of R | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 4 | Limit concept in functions of several variables | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 5 | The concept of continuity in multivariable functions | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 6 | Derivative, partial derivative of functions of several variables | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 7 | Geometric interpretation of the partial derivative in functions of several variables | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 8 | Mid-Term Exam | exam preparation | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | The concept of directional derivative | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 10 | Higher order derivatives | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 11 | Chain rule | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 12 | Function arrays | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 13 | Function series | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 14 | General review and question solution-1 | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 15 | General review and question solution-2 | Examination of related resources | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma |
| 16 | Term Exams | exam preparation | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | exam preparation | 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 | ||