MATZ211 Calculus III

5 ECTS - 4-0 Duration (T+A)- 3. Semester- 4 National Credit

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 Belirsiz
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

To teach students the concept of multivariable functions and to make them apply limit, continuity and derivative applications 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

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 Knows functions of several variables and their properties.
LO02 Understands the topology of R.
LO03 Comprehend limit and continuity in multivariable functions and calculate the limits of functions.
LO04 Students will have operation skills for the concepts of function sequences and series.
LO05 Expresses partial derivative, geometric interpretation, directional derivative in multivariable functions
LO06 Knows higher order derivatives of functions of several variables and chain rule.
LO07 Makes applications related to partial derivative of functions of several variables, geometric interpretation of directional derivative.


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

Update Time: 14.11.2024 07:59