BAHÇEŞEHİR UNIVERSITY BİLGİ PAKETİ / DERS KATALOĞU
| MATHEMATICS (TURKISH, PHD) | |||||
| PhD | TR-NQF-HE: Level 8 | QF-EHEA: Third Cycle | EQF-LLL: Level 8 | ||
Course Introduction and Application Information
| Course Code | Course Name | Semester | Theoretical | Practical | Credit | ECTS |
| MAT6009 | Advanced Calculus I | Spring | 3 | 0 | 3 | 8 |
| This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester. |
Basic information
| Language of instruction: | Turkish |
| Type of course: | Departmental Elective |
| Course Level: | |
| Mode of Delivery: | Face to face |
| Course Coordinator : | Assoc. Prof. ERSİN ÖZUĞURLU |
| Recommended Optional Program Components: | None |
| Course Objectives: | To teach fundamental concepts of real analysis, teaching fundamental proof methods, to gain ability of solving theoretical questions. |
Learning Outcomes
|
The students who have succeeded in this course; He/She knows Riemann and Lebesgue integrals. He/She knows taking integrals by using definition of Lebesgue integral and its properties. |
Course Content
| Basic concepts, some important theorems and definitions on point sets, countability, measure theory, sets of measure zero, Lusin, Egoroff and Lebesgue theorems, unmeasurable sets, measurable functions, Riemann integral, applications of Lebesgue theory, general measure and integral theories. |
Weekly Detailed Course Contents
| Week | Subject | Related Preparation |
| 1) | Basic concepts, some important theorems on point sets. | |
| 2) | Countability | |
| 3) | Measure theory. | |
| 4) | Measure theory (continue) | |
| 5) | Sets of measure zero. | |
| 6) | Lusin, Egoroff and Lebesgue theorems. | |
| 7) | Unmeasurable sets. | |
| 8) | Measurable functions, | |
| 9) | Measurable functions(continue) | |
| 10) | Riemann's integral, some applications of Lebesgue's theory. | |
| 11) | Riemann's integral, some applications of Lebesgue's theory. | |
| 12) | Theories of general measure and integral. | |
| 13) | Theories of general measure and integral. | |
| 14) | Theories of general measure and integral (continued) |
Sources
| Course Notes / Textbooks: | Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, 1999, Wiley Publications. |
| References: | H. L. Royden, Real Analysis, 1988, Prentice-Hall, Inc. So Bon Chae, Lebesgue integration, 1998, Springer Verlag. A. N. Kolmogorov, S. V. Fomin, Introductory Real Analysis 2000, Dover Publications. Paul R. Halmos, Measure Theory, 1978, Springer Verlag. |
Evaluation System
| Semester Requirements | Number of Activities | Level of Contribution |
| Project | 1 | % 20 |
| Midterms | 1 | % 30 |
| Final | 1 | % 50 |
| Total | % 100 | |
| PERCENTAGE OF SEMESTER WORK | % 30 | |
| PERCENTAGE OF FINAL WORK | % 70 | |
| Total | % 100 | |
ECTS / Workload Table
| Activities | Number of Activities | Duration (Hours) | Workload |
| Course Hours | 14 | 3 | 42 |
| Study Hours Out of Class | 14 | 3 | 42 |
| Project | 1 | 60 | 60 |
| Midterms | 1 | 26 | 26 |
| Final | 1 | 30 | 30 |
| Total Workload | 200 | ||
Contribution of Learning Outcomes to Programme Outcomes
| No Effect | 1 Lowest | 2 Low | 3 Average | 4 High | 5 Highest |
| Program Outcomes | Level of Contribution |