COURSE UNIT TITLE

: ELECTIVE LV. REAL ANALYSIS

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
OMT 3026 ELECTIVE LV. REAL ANALYSIS ELECTIVE 3 0 0 4

Offered By

Mathematics Teacher Education

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSOCIATE PROFESSOR ADEM ÇELIK

Offered to

Mathematics Teacher Education

Course Objective

To introduce with Cesaro type uniform convergence and convergence of sequences and series, to create the theory of metric spaces, to give fixed point and its applications

Learning Outcomes of the Course Unit

1   Knowing the relationship between the concept of uniform convergence with the concept of a point of convergence
2   Knowing to Summability theory
3   To have knowledge of Metric space and special states is the same as in previous years to be aware of familiar spaces
4   To make generalizations about Analysis
5   To make specificilizations about Analysis

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Reminder of the concept of a real number sequence and convergence in series
2 Cesaro convergence-divergence in sequences
3 Cesaro convergence-divergence in series
4 Pointwise and uniform convergence of sequences of functions
5 Related theorems and applications
6 Pointwise and uniform convergence in function series,
7 Related theorems and applications
8 Midterm exam
9 The concept of the metric and the metric space, exemplifications
10 The concept of sphere in metric spaces, exemplifications
11 Convergent series of the metric space, Cauchy sequences in metric space
12 Continuity of functions of the metric space, equivalent to the concept of metric
13 The concept of a complete metric space, exemplifications
14 Contraction transformations and applications, Fixed point theorem and an application of differential equations
15 Final exam

Recomended or Required Reading

An Introduction to Real Analysis, Tosun Terzioğlu, Matematik Analiz, Cilt II, Mustafa Balcı

Planned Learning Activities and Teaching Methods

lecture based instruction, question-answer, group working

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 STT TERM WORK (SEMESTER)
3 FINS FINAL EXAM
4 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.30 + STT * 0.10 + FINS * 0.60
5 RST RESIT
6 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + RST * 0.60

Further Notes About Assessment Methods

None

Assessment Criteria

Midterm exam and final exam

Language of Instruction

Turkish

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

adem.celik@deu.edu.tr

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Preparations before/after weekly lectures 13 2 26
Preparation for midterm exam 1 10 10
Preparation for final exam 1 15 15
Preparing assignments 2 7 14
Preparing presentations 1 2 2
Final 1 2 2
Midterm 1 2 2
TOTAL WORKLOAD (hours) 110

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15PO.16PO.17PO.18
LO.1552
LO.2552
LO.3552
LO.4552
LO.5552