Description of Individual Course Units
Course Unit CodeCourse Unit TitleType of Course UnitYear of StudySemesterNumber of ECTS Credits
MAT-23-226REAL ANALİZ-IIElective126
Level of Course Unit
Second Cycle
Objectives of the Course
The aim of this course is to generalize the concept of measure and in this sense to explain the measurable sets and functions, equivalence classes of functions. Properties of measurable sets and functions, explaining the properties of the space of measurable functions, explaining the properties of integralable functions in the Lebesgue sense; To describe Lebesgue spaces and their properties and their connections;
Name of Lecturer(s)
Prof. Dr. Kamal Soltanov
Learning Outcomes
1How they generalize the concept of integral seen before; In the new sense, it understands the properties of the space of integrable functions and integral of functions and in this sense can compare the new integral with the Riemann integral, which they already know; knows the Lebesgue spaces and their properties, the connection between them and the metric defined on them.
2Understands the properties of the space of integrable functions and integral of functions in the new sense and in this sense can compare the new integral with the Riemann integral, which they already know;
3Understands the Lebesgue spaces and their properties, the connection between them, and also the metric and norm defined on them
Mode of Delivery
Daytime Class
Prerequisites and co-requisities
To know the basic concepts of Mathematics Analysis, Linear Algebra, Real Analysis, Abstract Algebra and Topology courses at undergraduate level
Recommended Optional Programme Components
None
Course Contents
-Teaching the concept of measure in general terms to the students and to explain they that for what is need the generalization -To explain the properties of measurable sets and functions -To explain the measurable functions spaces, their properties and their connections to measurable sets in the general sense. -To explain the students the Lebesgue spaces and their properties and their connections
Weekly Detailed Course Contents
WeekTheoreticalPracticeLaboratory
1The definition of Lebesgue integral and the connection between this definition and the definition of the Riemann integral
2Properties of integrable functions in Lebesgue meaning
3The properties of Lebesgue integral
4Operations on a set of integrable functions
5Convergence of sequences of integrable functions
6Lebesgue limit theorems and results
7
8
9
10
11
12
13
14
15
Recommended or Required Reading
Natanson I. P - Theory of Function of Real Variable. New York , 1959-1961 Royden, H. L. - Real Analysis. Mac Millan New York 1968. Kolmogorov A. N, Fomin S. V. - Introductory Real Analysis. New York ,1975 Rao M. M. - Measure Theory and İntegration. New York Wiley, 1984 Shilov G. E., Gurevich B. L. - Integral, Mesure and Derivative: A unified approach. Prentice-Hall, 1966 Howes N. R. – Modern Analysis and Topology. Springer-Verlag, 1995
Planned Learning Activities and Teaching Methods
Assessment Methods and Criteria
Term (or Year) Learning ActivitiesQuantityWeight
Midterm Examination1100
SUM100
End Of Term (or Year) Learning ActivitiesQuantityWeight
Final Examination1100
SUM100
Term (or Year) Learning Activities40
End Of Term (or Year) Learning Activities60
SUM100
Language of Instruction
Work Placement(s)
None
Workload Calculation
ActivitiesNumberTime (hours)Total Work Load (hours)
Midterm Examination111
Final Examination122
Practice14342
Criticising Paper14342
Individual Study for Mid term Examination15050
Individual Study for Final Examination15050
TOTAL WORKLOAD (hours)187
Contribution of Learning Outcomes to Programme Outcomes
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PO
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PO
11
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High
 
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