Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | MAT-23-226 | REAL ANALİZ-II | Elective | 1 | 2 | 6 |
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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 |
1 | How 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. | 2 | Understands 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; | 3 | Understands the Lebesgue spaces and their properties, the connection between them, and also the metric and norm defined on them |
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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 |
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1 | The definition of Lebesgue integral and the connection between this definition and the definition of the Riemann integral | | | 2 | Properties of integrable functions in Lebesgue meaning | | | 3 | The properties of Lebesgue integral | | | 4 | Operations on a set of integrable functions | | | 5 | Convergence of sequences of integrable functions | | | 6 | Lebesgue limit theorems and results | | | 7 | | | | 8 | | | | 9 | | | | 10 | | | | 11 | | | | 12 | | | | 13 | | | | 14 | | | | 15 | | | |
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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
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Planned Learning Activities and Teaching Methods |
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Assessment Methods and Criteria | |
Midterm Examination | 1 | 100 | SUM | 100 | |
Final Examination | 1 | 100 | SUM | 100 | Term (or Year) Learning Activities | 40 | End Of Term (or Year) Learning Activities | 60 | SUM | 100 |
| Language of Instruction | | Work Placement(s) | None |
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Workload Calculation |
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Midterm Examination | 1 | 1 | 1 |
Final Examination | 1 | 2 | 2 |
Practice | 14 | 3 | 42 |
Criticising Paper | 14 | 3 | 42 |
Individual Study for Mid term Examination | 1 | 50 | 50 |
Individual Study for Final Examination | 1 | 50 | 50 |
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Contribution of Learning Outcomes to Programme Outcomes |
LO1 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | LO2 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | LO3 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Iğdır University, Iğdır / TURKEY • Tel (pbx): +90 476
226 13 14 • e-mail: info@igdir.edu.tr
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