Differential Equations 2 (751873002) 微分方程式 （二）
General Information
- Begins ~ ends: February 17, 2025 ~ June 20, 2025
- Instructor: Pu-Zhao Kow
- Email: pzkow [at] g.nccu.edu.tw
- Office hour: Thursday (16:10 ~ 17:00)
- Teaching Language: Chinese and English
- Lecture Note (main): Pu-Zhao Kow, An introduction to partial differential equations and functional analysis. Note: The lecture note may update during the course.
- Lecture Note (supplementary): Pu-Zhao Kow, Fourier analysis and distribution theory. Note: The lecture note may update during the course.
References
Note. See my lecture note for some more advance monographs.- H. Brezis, Functional analysis, Sobolev spaces and partial differential equations, Universitext, Springer, New York, 2011. MR2759829, Zbl:1220.46002, doi:10.1007/978-0-387-70914-7
- L. C. Evans, Partial differential equations, volume 19 of Grad. Stud. Math. AMS, Providence, RI, second edition, 2010. MR2597943, Zbl:1194.35001, doi:10.1090/gsm/019
- D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order (reprint of the 1998 edition), volume 224 of Classics in Mathematics, Springer-Verlag Berlin Heidelberg, 2001. MR1814364, Zbl:1042.35002, doi:10.1007/978-3-642-61798-0
- P.-F. Hsieh and Y. Sibuya, Basic theory of ordinary differential equations Universitext, Springer-Verlag, New York, 1999 MR1697415, doi:10.1007/978-1-4612-1506-6
- F. John, Partial differential equations, volume 1 of Appl. Math. Sci., Springer-Verlag, New York-Berlin, third edition, 1978. MR0514404, Zbl:0426.35002
Prerequisite
- Real and complex analysis
Homeworks
- Homework 1: Return to the instructor (via email) by March 6, 2025 (Thursday) 23:59
- Homework 2: Return to the instructor (via email) by March 13, 2025 (Thursday) 23:59
- Homework 3: Return to the instructor (via email) by March 20, 2025 (Thursday) 23:59
- Homework 4: Return to the instructor (via email) by March 27, 2025 (Thursday) 23:59
- Homework 5: Return to the instructor (via email) by April 10, 2025 (Thursday) 23:59
- Homework 6: Return to the instructor (via email) by April 17, 2025 (Thursday) 23:59
Schedule
- The lectures are on Thursday (13:10-16:00) at 志希070116.
| Time | Room | Activities |
|---|---|---|
| 20.02.2025 13:10-16:00 | 志希070116 | Week 1 - Lecture (Thursday): Recall some preliminaries and introducing PDE (in classical sense) |
| 27.02.2025 13:10-16:00 | 志希070116 | Week 2 - No class |
| 06.03.2025 13:10-16:00 | 志希070116 | Week 3 - Lecture (Thursday): Weak derivatives and distribution derivatives [Return Homework 1 by 23:59] |
| 13.03.2025 13:10-16:00 | 志希070116 | Week 4 - Lecture (Thursday): Some Sobolev spaces and Hilbert spaces [Return Homework 2 by 23:59] |
| 20.03.2025 13:10-16:00 | 志希070116 | Week 5 - No class [Return Homework 3 by 23:59] |
| 27.03.2025 13:10-16:00 | 志希070116 | Week 6 - Lecture (Thursday): Some Hilbert spaces [Return Homework 4 by 23:59] |
| 03.04.2025 13:10-16:00 | 志希070116 | Week 7 - No class: children's day and tomb sweeping day |
| 10.04.2025 13:10-16:00 | 志希070116 | Week 8 - Lecture (Thursday): Solving elliptic PDE for a small wave number [Return Homework 5 by 23:59] |
| 17.04.2025 13:10-16:00 | 志希070116 | Week 9 - Lecture (Thursday): Eigenvalue problem [Return Homework 6 by 23:59] |
| 24.04.2025 13:10-16:00 | 志希070116 | Week 10 - No class |
| 01.05.2025 13:10-16:00 | 志希070116 | Week 11 - Lecture (Thursday): talks
click me to see the title and abstract of today's first talk (50 minutes)
Speaker. Cheng, Huan-Chang Title. Reading Reflection on Random Matrix Methods for Machine Learning, by Romain Couillet and Zhenyu Liao Abstract. Numerous and large dimensional data is now a default setting in modern ma- chine learning (ML). Standard ML algorithms, starting with kernel methods such as support vector machines and graph-based methods like the PageRank algorithm, were however initially designed out of small-dimensional intuitions and tend to misbehave, if not completely collapse, when dealing with real-world large datasets. Random matrix theory has recently developed a broad spectrum of tools to help understand this new "curse of dimensionality" to help repair or completely recreate the suboptimal algorithms, and most importantly to provide new intuitions to deal with modern data mining. This book primarily aims to deliver these intuitions, by providing a digest of the recent theoretical and applied breakthroughs of random matrix theory into ML. click me to see the title and abstract of today's second talk (50+50 minutes)
Speaker. Lin, Po-Yi Title. Leveraging Language Models to Detect Greenwashing Abstract. In recent years, climate change repercussions have increasingly captured public interest. Consequently, corporations are emphasizing their environmental efforts in sustainability reports to bolster their public image. Yet, the absence of stringent regulations in review of such reports allows potential greenwashing. In this study, we introduce a novel preliminary methodology to train a language model on generated labels for greenwashing risk. Our primary contributions encompass: developing a preliminary mathematical formulation to quantify greenwashing risk, a fine-tuned Climate-BERT model for this problem, and a comparative analysis of results. On a test set comprising of sustainability reports, our best model achieved an average accuracy score of 86.34% and F1 score of 0.67, demonstrating that our proof-of-concept methodology shows a promising direction of exploration for this task. |
| 08.05.2025 13:10-16:00 | 志希070116 | Week 12 - Lecture (Thursday) |
| 15.05.2025 13:10-16:00 | 志希070116 | Week 13 - Lecture (Thursday) |
| 22.05.2025 13:10-16:00 | 志希070116 | Week 14 - Lecture (Thursday) |
| 29.05.2025 13:10-16:00 | 志希070116 | Week 15 - Lecture (Thursday) |
| 05.06.2025 13:10-16:00 | 志希070116 | Week 16 - Lecture (Thursday) |
| 12.06.2025 13:10-16:00 | 志希070116 | Week 17 - No class |
| 19.06.2025 13:10-16:00 | 志希070116 | Week 18 - Lecture (Thursday) |
Completion
- The course can be taken for credit by attending the lectures, returning written solutions (60%) in LaTeX and giving (at least) 2 presentations (each 20%).