Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits | MAT510 | MEASURE THEORY II | Elective | 1 | 1 | 6 |
|
Level of Course Unit |
Second Cycle |
Objectives of the Course |
To introduce to student concept of measure. |
Name of Lecturer(s) |
Doç. Dr. Abdullah SÖNMEZOĞLU |
Learning Outcomes |
1 | To define concepts of measurable sets and functions | 2 | To identify and apply the concept of Lebesgue integral | 3 | To learn relationship between Riemann integral and Lebesgue integral |
|
Mode of Delivery |
Formal Education |
Prerequisites and co-requisities |
None |
Recommended Optional Programme Components |
None |
Course Contents |
Clusters can not be measured
Measurable Functions
Riemann Integral
Measure the limited functions on a set of finite Lebesgue integral
Integral non-negative functions, general Lebesgue integral
Convergence in measure
Differential and Integral
Functions of bounded variation
Absolute Contiunity
Convex functions
Monotonous functions, Derivatives of monotonous functions, Derivative of integral with respect to upper bound, Functions of bounded variation, Derivative of Lebesgue indefinite integral, Absolute continuous functions and properties, Lp spaces |
Weekly Detailed Course Contents |
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1 | Clusters can not be measured | | | 2 | Measurable Functions | | | 3 | Measurable Functions | | | 4 | Riemann Integral | | | 5 | Measure the limited functions on a set of finite Lebesgue integral | | | 6 | Integral non-negative functions, general Lebesgue integral | | | 7 | Convergence in measure | | | 8 | Mid-Term Exam | | | 9 | Convergence in measure | | | 10 | Differential and Integral | | | 11 | Differential and Integral | | | 12 | Functions of bounded variation | | | 13 | Functions of bounded variation | | | 14 | Absolute Contiunity | | | 15 | Convex functions | | | 16 | Final Exam | | |
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Recommended or Required Reading |
A. Dönmez, Reel Analiz, Seçkin Yayıncılık, 2001.
J. Yeh, Lectures on Real Analaysis, World Scientific Publishing Company, 2001. |
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 | 2 | 2 |
Final Examination | 1 | 2 | 2 |
Self Study | 14 | 5 | 70 |
Individual Study for Mid term Examination | 7 | 8 | 56 |
Individual Study for Final Examination | 7 | 8 | 56 |
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Contribution of Learning Outcomes to Programme Outcomes |
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* Contribution Level : 1 Very low 2 Low 3 Medium 4 High 5 Very High |
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Yozgat Bozok University, Yozgat / TURKEY • Tel (pbx): +90 354 217 86 01 • e-mail: uo@bozok.edu.tr |