MATZ210 Calculus IV

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

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

Notes

Principles of Mathematical Analysis, Walter Rudin


Course Learning Outcomes

Order Course Learning Outcomes
LO01 Understands the limits of functions and limit theorems, continuous functions and uniform continuity.
LO02 Uses the most basic theorems about monotonic and inverse functions to solve the problems that encounter.
LO03 Understands information about derivative and differential calculus.
LO04 Understands the Mean Value Theorem and its applications.
LO05 Understands the expansion of functions into Taylor series and how it can be used in numerical calculations.
LO06 Understands how to define new functions using function arrays and series.
LO07 Understands the Weirstrass M-test and the possibilities provided by uniform convergence.


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.
PLO10 Beceriler - Bilişsel, Uygulamalı Has life-long learning awareness.
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.
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

Update Time: 14.11.2024 08:12