1. SECOND CYCLE - MASTER'S DEGREE
  2. THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
  3. MATHEMATICS DEPARTMENT
  4. 1441 Mathematics
Course Information Course Learning Outcomes Course's Contribution To Program ECTS Workload Course Details
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COURSE INFORMATION
Course CodeCourse TitleL+P HourSemesterECTS
MAT 580THEORY OF FUNCTIONS OF A REAL VARIABLE3 + 02nd Semester7,5

COURSE DESCRIPTION
Course Level Master's Degree
Course Type Elective
Course Objective To teach the basic concepts and techniques used in real analysis.
Course Content The Real Number System. Lebesque Measure. Measurable functions. Lebesque Integral . Limit Theorems for Lebesque Integral. Differentiation and Integration. Absolute Continuity of Indefinite Lebesque Integral. Spaces of Integrable Functions. Stieltjes Integral.
Prerequisites No the prerequisite of lesson.
Corequisite No the corequisite of lesson.

COURSE LEARNING OUTCOMES
1Learns the structure of the real number system.
2Defines the Lebesque Measure and finds the Measurable functions.
3Learns the Lebesque integrali. and proves the theorems about Lebesque integral.
4Learns the rules of differentiation and integration.
5Knows the concept of Absolute Continuity of Indefinite Lebesque Integral.
6Studies the Spaces of Integrable Functions and Stieltjes Integral.

COURSE'S CONTRIBUTION TO PROGRAM
PO 01PO 02PO 03PO 04PO 05PO 06PO 07PO 08
LO 00154 54   
LO 00255 44   
LO 00344 55   
LO 00445 45   
LO 00554 44   
LO 00645 55   
Sub Total2727 2727   
Contribution55055000

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
ActivitiesQuantityDuration (Hour)Total Work Load (Hour)
Course Duration (14 weeks/theoric+practical)14342
Hours for off-the-classroom study (Pre-study, practice)14798
Assignments155
Mid-terms11515
Final examination13535
Total Work Load

ECTS Credit of the Course





195

7,5
COURSE DETAILS
 Select Year   


 Course TermNoInstructors
Details 2025-2026 Fall1ALP ARSLAN KIRAÇ


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Course Details
Course Code Course Title L+P Hour Course Code Language Of Instruction Course Semester Mode of Delivery
MAT 580 THEORY OF FUNCTIONS OF A REAL VARIABLE 3 + 0 1 Turkish 2025-2026 Fall Face to Face
Course Coordinator  E-Mail  Phone Number  Course Location Attendance
Prof. Dr. ALP ARSLAN KIRAÇ aakirac@pau.edu.tr FEN A0203 %80
Goals To teach the basic concepts and techniques used in real analysis.
Content The Real Number System. Lebesque Measure. Measurable functions. Lebesque Integral . Limit Theorems for Lebesque Integral. Differentiation and Integration. Absolute Continuity of Indefinite Lebesque Integral. Spaces of Integrable Functions. Stieltjes Integral.
Topics
WeeksTopics
1 The Real Number System
2 Lebesque Measure
3 Measurable functions
4 Lebesque Integral
5 Lebesque Integral
6 Limit Theorems for Lebesque Integral
7 Limit Theorems for Lebesque Integral
8 Differentiation and Integration
9 Absolute Continuity of Indefinite Lebesque Integral
10 Absolute Continuity of Indefinite Lebesque Integral
11 Spaces of Integrable Functions
12 Spaces of Integrable Functions
13 Stieltjes Integral
14 Stieltjes Integral
Materials
Materials are not specified.
Resources
Course Assessment
Assesment MethodsPercentage (%)Assesment Methods Title
Final Exam50Final Exam
Midterm Exam50Midterm Exam
L+P: Lecture and Practice
PQ: Program Learning Outcomes
LO: Course Learning Outcomes