主題式數學建模與計算(二)
Topical Mathematical Modeling and Computing(II)
| 節 | 週四 |
|---|---|
2 09:00–09:50 | 主題式數學建模與計算(二) SA215（光復） 3 節連堂 |
3 10:10–11:00 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
In this course, we will study the fundamental mathematical theories behind several important modeling frameworks and apply them to real-world problems. By the end of the course, you will be able to construct basic mathematical models and implement them using Python. The models introduced in this class are selected based on the instructor’s research interests and expertise, with an emphasis on applications in aerospace technology. The three primary models of the course are: (1) Geometric Mechanics on SE(3), (2) Geometric Control and Guidance, and (3) Integral Geometry for Stealth and Sensing.
linear algebra, calculus, basic differential equations, and basic group theory.
無備註
The instructor will also select several related academic papers for students to read, and some class sessions will include participant presentations.
1. Class Participation (50%) – engagement in discussions, in-class activities, and contributions to group work. 2. Final Oral Presentation and Written Report (50%)– a 20-minutes presentation and an accompanying written paper summarizing the model, analysis, and results.
教師未提供此項資料
| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction to mathematical modeling: principles and elementary methods |
| 第 2 週 | Elementary methods for modeling 1 : arguments from scale, graphical methods |
| 第 3 週 | Elementary method for modeling 2: basic optimization, and probability of analytic models. |
| 第 4 週 | Advanced methods 1: approaches to differential equations, quantitative differential equations |
| 第 5 週 | Advanced methods 2: local stability theory and optimization. |
| 第 6 週 | Model 1: Geometric Mechanics on SE(3) |
| 第 7 週 | Model 1: Geometric Mechanics on SE(3) |
| 第 8 週 | Model 1: Geometric Mechanics on SE(3) |
| 第 9 週 | Model 2: Geometric Control and Guidance |
| 第 10 週 | Model 2: Geometric Control and Guidance |
| 第 11 週 | Model 2: Geometric Control and Guidance |
| 第 12 週 | Model 3: Integral Geometry for Stealth and Sensing |
| 第 13 週 | Model 3: Integral Geometry for Stealth and Sensing |
| 第 14 週 | Model 3: Integral Geometry for Stealth and Sensing |
| 第 15 週 | Oral presentation 1 |
| 第 16 週 | Oral presentation 2 |
For model 1: (1) Geometric Mechanics - Part I: Dynamics And Symmetry (2Nd Edition) 2nd Revised ed. Edition by Darryl D. Holm (2) Marsden, J. E., & Ratiu, T. S. Introduction to Mechanics and Symmetry, Springer For model 2: (1) Bullo, F., & Lewis, A. D. Geometric Control of Mechanical Systems, Springer (2) Variational Analysis and Aerospace Engineering, conference proceedings, 2009, Springer For model 3: (1) S. Helgason, The Radon Transform, 1999, Springer (2) Natterer, F. The Mathematics of Computerized Tomography, 2001, Society for Industrial and Applied Mathematics
- 地點
- SA240
- 時間
- Every Thursday 15:30-17:00, or by appointment.
- 聯絡方式
- ychuang0802@nycu.edu.tw