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國立中山大學 114學年度第2學期 課程教學大綱
National Sun Yat-sen University 114Academic year Course syllabus
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中文名稱
Course name(Chinese) |
物理數學與數值方法（二） |
課號
Course Code |
PHYS222 |
英文名稱
Course name(English) |
MATHEMATICS AND CODING ON PHYSICS (II) |
課程類別
Type of the course |
講授類 | 必選修
Required/Selected | 必修 |
系所
Dept./faculty |
物理學系 |
授課教師
Instructor |
岩本祥
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學分
Credit |
3 |
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課程大綱 Course syllabus |
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An intermediate-level mathematics course designed for physics learners. We will cover linear algebra, Fourier analysis, and methods of numerical analysis. Prerequisites for this course include a foundational understanding of calculus, matrix arithmetic, and ordinary differential equations.
After reviewing the basics of matrices, you first learn linear algebra with an emphasis on practical handling of matrices and eigenvalue problems. You then learn fundamentals of function analysis, particularly Fourier analysis.
Additionally, the course introduces fundamental concepts in numerical analysis and basic numerical methods for mathematical problems such as ordinary differential equations. Students will gain theoretical knowledge in numerical analysis as well as practical coding skills in Python, using the contemporary Python ecosystem.
This course does not cover the mathematical foundations of each topic. Instead, students are expected to be familiar with the topics and develop an appreciation of their usefulness.
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課程目標 Objectives |
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- I am familiar with matrix calculation. In particular, I know why rank and determination are important and can calculate them by hand.
- I can diagonalize simple matrices.
- I can perform Fourier analysis of functions.
- I understand the basic property of IEEE-754 floating point numbers.
- Utilizing Python and online resources, I can numerically solve problems in linear algebra, basic differential equations, or other topics learned in the previous semesters.
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授課方式 Teaching methods |
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評分方式﹝評分標準及比例﹞Evaluation (Criteria and ratio)等第制單科成績對照表 letter grading reference
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1.Midterm Exam (mandatory)：31%
2.Term Exam (mandatory)：23%
3.Final Coding Assignment (mandatory)：23%
4.Classroom Performance and Extra Tasks：23%
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參考書/教科書/閱讀文獻 Reference book/ textbook/ documents
〔請遵守智慧財產權觀念，不可非法影印。教師所提供之教材供學生本人自修學習使用,不得散播及做為商業用途〕
No copies for intellectual property rights. Textbooks provided by the instructor used only for self-study, can not broadcast or commercial use
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E. Kreyszig, Advanced Engineering Mathematics, 10th ed. Taiwan custom version, Wiley (2018).
- You need the textbook, preferably a physical book rather than an e-book.
- You are assumed to have learned Chapters 1–2 and 9–10. We discuss Chapters 7–8, 11, and 19–21.
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課程時數規劃 Course Hour Planning
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本校自114學年度起實施學期16週，仍以1學分18小時為原則。教師課程時數安排得選擇「16週+自主學習規劃」或「16週+實體上課規劃」。
Starting from the 114th academic year, the university will implement a 16-week course schedule, while maintaining the standard of 18 hours of instruction per credit. Instructors can choose between “16-weeks + Alternative learning periods”or“16-weeks + In-person classes.”
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A.每週課程內容及預計進度 Weekly scheduled progress |
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全英課程之授課內容及主題應以英文或雙語呈現
| For courses taught entirely in English, the content and topics should be presented in English or bilingually.
| | 週次 | 日期 | 授課內容及主題 | | Week | Date | Content and topic | | 1 | 2025/02/16~2025/02/22 | Matrices and vectors. | | 2 | 2025/02/23~2025/03/01 | Linear systems of Equations. | | 3 | 2025/03/02~2025/03/08 | Rank. | | 4 | 2025/03/09~2025/03/15 | Determinant. Inverse. | | 5 | 2025/03/16~2025/03/22 | Eigenvalue problem. | | 6 | 2025/03/23~2025/03/29 | Matrices with special names. | | 7 | 2025/03/30~2025/04/05 | Diagonalization and bases. | | 8 | 2025/04/06~2025/04/12 | *Midterm Exam | | 9 | 2025/04/13~2025/04/19 | Numeric linear algebra. | | 10 | 2025/04/20~2025/04/26 | IEEE-754 floating point numbers. | | 11 | 2025/04/27~2025/05/03 | Basic numerical analysis. | | 12 | 2025/05/04~2025/05/10 | Review of ODEs. | | 13 | 2025/05/11~2025/05/17 | Numerics for ODEs. | | 14 | 2025/05/18~2025/05/24 | Fourier series expansion. | | 15 | 2025/05/25~2025/05/31 | Fourier transformation. | | 16 | 2025/06/01~2025/06/07 | *Term Exam | | 17 | 2025/06/08~2025/06/14 | Review on complex numbers. Basic group theory. | | 18 | 2025/06/15~2025/06/21 | (No class: alternative learning period) |
| | B.自主學習規劃 Alternative learning periods | |
課程規劃學生自主學習內容（每1學分2小時）
| Alternative learning periods planned for the course (with each credit corresponding to two hours of activity)
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| | C.實體上課規劃 In-Person Class Plan | |
若無規劃學生自主學習，則請教師規劃2次實體上課(每1學分2小時)，上課時間由師生自行討論，得利用週三下午4-7點或其他時段進行。
| | If there are no alternative learning periods planned for the course, the instructor should plan 2 in-person classes (2 hours of activity per credit). Class schedules can be arranged through discussions between instructors and students, utilizing Wednesday 4:00PM-7:00PM or other suitable time slots. | ＊第一次實體上課內容及主題(Content and topic for the first In-Person class)：
| ＊第二次實體上課內容及主題(Content and topic for the second In-Person class)：
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課業討論時間 Office hours |
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時段1 Time period 1:
時間 Time：星期一15:30–17:30
地點 Office/Laboratory：理SC2006‒1
時段2 Time period 2：
時間 Time：星期三12:30–14:30
地點 Office/Laboratory：理SC2006‒1
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系所學生專業能力/全校學生基本素養與核心能力 basic disciplines and core capabilitics of the dcpartment and the university |
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本課程與SDGs相關項目：The course relates to SDGs items: |
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本課程校外實習資訊: This course is relevant to internship: |
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