강의계획서
| 교과목코드 | JDA01497 | 교과목명 | 응용해석학 |
|---|---|---|---|
| 강의학과 | 수학과 | 교수 | 윤갑진 |
| 교수소속 | 자연교양 | 이수학년 | 4학년 |
| 과목구분 | 이론 | 과정구분 | |
| 이메일 | gabjin@mju.ac.kr | 전화번호 | 031-330-6163 |
| 주차 | 주제 |
|---|---|
| 1주차 | ntroduction to the Lebesgue integral, comparison with the Riemann integration |
| 2주차 | Measurable sets and measurable functions |
| 3주차 | Measures, measure spaces, almost everywhere, |
| 4주차 | The integral of nonnegative measurable functions and the Monotone Convergence Theorem |
| 5주차 | Integrable real-valued functions, the Lebesgue Dominated Convergence theorem |
| 6주차 | Normed linear spaces, the Lp spaces |
| 7주차 | Hölders Inequality, Minkowskis Inequality, the Completeness Theorem |
| 8주차 | 중간고사 |
| 9주차 | Modes of Convergence - convergence in mean, uniform con- vergence |
| 10주차 | almost uniform convergence, Egoroffs Theorem, the Vitali Convergence Theorem |
| 11주차 | Decomposition of Measures 1 |
| 12주차 | Decomposition of Measures 2 |
| 13주차 | Generation of Measures, Measures on algebras of sets |
| 14주차 | Product Measures |
| 15주차 | 기말고사 |
| 16주차 |