Differential Equations 1 (751873001) 微分方程式 （一）
General Information
- Begins ~ ends: September 1, 2025 ~ December 19, 2025
- Instructor: Pu-Zhao Kow
- Email: pzkow [at] g.nccu.edu.tw
- Office hour: Friday (12:10 ~ 13:00)
- Teaching Language: Chinese and English
- Lecture Note: Pu-Zhao Kow, An introduction to ordinary differential equations. Note: The lecture note may update during the course.
References
- J. W. E. Boyce and R. C. DiPrima, Elementary differential equations and boundary value problems, John Wiley and Sons, Inc., Hoboken, NJ, 12th edition, 2022. MR0179403, Zbl:1492.34001
- P.-F. Hsieh and Y. Sibuya, Basic theory of ordinary differential equations, Universitext, Springer-Verlag, New York, 1999. MR1697415, Zbl:0924.34001, doi:10.1007/978-1-4612-1506-6
Prerequisite
- Real and complex analysis
Homeworks
- Homework 1: Return by September 19, 2025 (Friday) 23:59
- Homework 2: Return by September 26, 2025 (Friday) 23:59
- Homework 3: Return by October 10, 2025 (Friday) 23:59
- Homework 4: Return by October 17, 2025 (Friday) 23:59
Schedule
- The lectures are on Friday (09:10-12:00) at 志希070116.
| Time | Room | Activities |
|---|---|---|
| 5.9.2025 09:10-12:00 | 志希070116 | Week 1: Fundamental theorem of ODE |
| 12.9.2025 09:10-12:00 | 志希070116 | Week 2: Some techniques for solving ODE, from ODE to PDE, Linear equations |
| 19.9.2025 09:10-12:00 | 志希070116 | Week 3: Homogeneous ODE with constant coefficients, fundamental matrix solution (Return Homework 1 by 23:59) |
| 26.9.2025 09:10-12:00 | 志希070116 | Week 4: Computations of the matrix exponential \(\exp : \mathbb{C}^{n\times n} \rightarrow {\rm GL}(n,\mathbb{C})\) (Return Homework 2 by 23:59) |
| 3.10.2025 09:10-12:00 | 志希070116 | Week 5: matrix logarithm, one parameter subgroup, 1-1 correspondence between matrix Lie group \(\mathscr{G}={\rm GL}(n,\mathbb{C}),{\rm U}(n,\mathbb{C}),{\rm SL}(n,\mathbb{C}),{\rm SU}(n,\mathbb{C})\) and Lie algebra \(\mathfrak{g}=\mathfrak{gl}(n,\mathbb{C}),\mathfrak{u}(n,\mathbb{C}),\mathfrak{sl}(n,\mathbb{C}),\mathfrak{su}(n,\mathbb{C})\) |
| 10.10.2025 09:10-12:00 | 志希070116 | Week 6 - No class: national day (Return Homework 3 by 23:59) |
| 17.10.2025 09:10-12:00 | 志希070116 | Week 7: ODE with variable coefficients (Return Homework 4 by 23:59)
click me to see the title and abstract of today's first talk (30 minutes)
Speaker. Wu, Pei-Wei Title. Curvature 曲率 Abstract. 介紹何謂高斯曲率以及如何推導。 |
| 24.10.2025 09:10-12:00 | 志希070116 | Week 8 - No class: Retrocession Day |
| 31.10.2025 09:10-12:00 | 志希070116 | Week 9
click me to see the title and abstract of today's first talk (30 minutes)
Speaker. Kao, An-Hsien Title. Krylov Subspace and Arnoldi Abstract. This presentation introduces the Krylov subspace method, focusing on how the Arnoldi iteration is applied to solve eigenvalue problems for large, sparse matrices efficiently. |
| 7.11.2025 09:10-12:00 | 志希070116 | Week 10 |
| 14.11.2025 09:10-12:00 | 志希070116 | Week 11 |
| 21.11.2025 09:10-12:00 | 志希070116 | Week 12 |
| 28.11.2025 09:10-12:00 | 志希070116 | Week 13 |
| 5.12.2025 09:10-12:00 | 志希070116 | Week 14 |
| 12.12.2025 09:10-12:00 | 志希070116 | Week 15 |
| 19.12.2025 09:10-12:00 | 志希070116 | Week 16 |
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%).