國立中山大學 113學年度第2學期 課程教學大綱

National Sun Yat-sen University 113Academic year Course syllabus

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

學分
Credit

 3

因應嚴重特殊傳染性肺炎等傳染病，倘若後續需實施遠距授課，授課方式調整如下：
　　　　　　　　 同步遠距【透過網路直播技術，同時進行線上教學，得採Microsoft Teams、Adobe connect等軟體進行】
同步遠距含錄影【透過網路直播技術，同時進行線上教學並同時錄影，課程內容可擇日再重播，得採Microsoft Teams、Adobe connect等軟體進行】
非同步遠距【課堂錄影或錄製數位教材放置網路供學生可非同時進行線上學習，得採EverCam、PPT簡報錄影、錄音方式進行】
實作類課程，經評估無法採遠距課程教學，後續復課後密集補課

★遠距教學軟體操作說明連結

因應嚴重特殊傳染性肺炎等傳染病，倘若後續需實施遠距授課，評分方式調整如下：

　　　　　　　　 尚未建立傳染性肺炎等傳染病之課程評分方式﹝評分標準及比例﹞

課程大綱 Course syllabus
　　　　　　　　 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.

課程目標 Objectives
　　　　　　　　 - 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.

授課方式 Teaching methods
　　　　　　　　 In-person lectures.





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

　　　　　　　　
1.Midterm Exam (mandatory)：31%
2.Term Exam (mandatory)：23%
3.Final Coding Assignment (mandatory)：23%
4.Classroom Performance and Extra Tasks：23%

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

　　　　　　　　 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.



彈性暨自主學習規劃 Alternative learning periods
本門課程是否有規劃實施學生彈性或自主學習內容（每1學分2小時）
Is any alternative learning periods planned for this course (with each credit corresponding to two hours of activity)?
否：教師需於「每週課程內容及預計進度」填寫18週課程進度（每1學分18小時之正課內容）。
No:The instructor will include an 18-week course plan in the weekly scheduled progress (each credit corresponds to 18 hours of instruction)
是：教師需於「每週課程內容及預計進度」填寫16週課程內容（每1學分16小時之正課內容），並於下列欄位填寫每1學分2小時學生彈性或自主學習內容。
Yes:The instructor will include a 16-week course plan in the weekly scheduled progress (each credit corresponds to 16 hours of instruction);
the details of the planned alternative learning periods are provided below (each credit corresponds to two hours of activity).

本門課程規劃學生彈性或自主學習內容（每1學分2小時）：
Alternative learning periods planned for the course (each credit corresponds to two hours of activity):
學生彈性或自主學習活動
Alternative learning periods		勾選或填寫規劃內容
Place a check in the appropriate box or provide details		時數
Number of hours
學生分組實作及討論
Group work and discussion
參與課程相關作業、作品、實驗
Participation in course-related assignments, work, or experiments
參與校內外活動（研習營、工作坊、參訪）或競賽
Participation in on- or off-campus activities (e.g., seminars, workshops, and visits) or competitions
課外閱讀
Extracurricular reading
線上數位教材學習
Learning with online digital learning materials
其他（請填寫規劃內容）
Other (please provide details)

每週課程內容及預計進度 Weekly scheduled progress
　　　　　　　　
週次日期授課內容及主題
WeekDateContent and topic
12025/02/16~2025/02/22Matrices and vectors.
22025/02/23~2025/03/01Linear systems of Equations.
32025/03/02~2025/03/08Rank.
42025/03/09~2025/03/15Determinant. Inverse.
52025/03/16~2025/03/22Eigenvalue problem.
62025/03/23~2025/03/29Matrices with special names.
72025/03/30~2025/04/05Diagonalization and bases.
82025/04/06~2025/04/12*Midterm Exam
92025/04/13~2025/04/19Numeric linear algebra.
102025/04/20~2025/04/26IEEE-754 floating point numbers.
112025/04/27~2025/05/03Basic numerical analysis.
122025/05/04~2025/05/10Review of ODEs.
132025/05/11~2025/05/17Numerics for ODEs.
142025/05/18~2025/05/24Fourier series expansion.
152025/05/25~2025/05/31Fourier transformation.
162025/06/01~2025/06/07*Term Exam
172025/06/08~2025/06/14Review on complex numbers. Basic group theory.
182025/06/15~2025/06/21(No class: alternative learning period)

課業討論時間 Office hours
　　　　　　　　 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

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
　　　　　　　　
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 capabilities of the department and the university		課堂活動與評量方式
Class activities and evaluation
本課程欲培養之能力與素養 This course enables students to achieve.
本課程欲培養之能力與素養 This course enables students to 		紙筆考試或測驗 Test.課堂討論︵含個案討論︶ Group discussion (case analysis).個人書面報告、作業、作品、實驗 Indivisual paper report/ assignment/ work or experiment.群組書面報告、作業、作品、實驗 Group paper report/ assignment/ work or experiment.個人口頭報告 Indivisual oral presentation.群組口頭報告 Group oral presentation.課程規劃之校外參訪及實習 Off-campus visit and intership.證照/檢定 License.參與課程規劃之校內外活動及競賽 Participate in off-campus/ on-campus activities and competitions.
※系所學生專業能力 Basic disciplines and core capabilities of the department
1.具備通盤認知基礎物理學識之能力 1. A broad knowledge of fundamental physics.VV V V    
2.具備深入了解物理各領域學識之能力 2. Competence of developing in-depth knowledge in all sub-fields of physics.          
3.具備物理相關數學之能力 3. Solid mathematical foundation essential to physics.VV V V    
4.具備實作物理及應用物理學識之能力 4. Experiences in hands-on practice and competences in applications of physics.          
5.具備探索未知之精神及實踐之能力 5. The curiosity and practice of exploring the unknown.          
※全校學生基本素養與核心能力 Basic disciplines and core capabilities of the university
1.表達與溝通能力。 1. Articulation and communication skillsVV V V    
2.探究與批判思考能力。 2. Inquisitive and critical thinking abilitiesVV V V    
3.終身學習能力。 3. Lifelong learningV  V      
4.倫理與社會責任。 4. Ethnics and social responsibility          
5.美感品味。 5. Aesthetic appreciation          
6.創造力。 6. Creativity          
7.全球視野。 7. Global perspective          
8.合作與領導能力。 8. Team work and leadership          
9.山海胸襟與自然情懷。 9. Broad-mindedness and the embrace of nature　          

本課程與SDGs相關項目：The course relates to SDGs items:

　　　　　　　　
SDG1-消除貧窮(No Poverty)
SDG2-消除飢餓 (Zero Hunger)
SDG3-良好健康與福祉(Good Health and Well-being)
SDG4-教育品質(Quality Education)
SDG5-性別平等(Gender Equality)
SDG6-乾淨水源與公共衛生(Clean Water and Sanitation)
SDG7-可負擔乾淨能源(Affordable and Clean Energy)
SDG8-優質工作與經濟成長(Decent Work and Economic Growth)
SDG9-工業、創新和基礎建設(Industry,Innovation and Infrastructure)
SDG10-減少不平等(Reduced Inequalities)
SDG11-永續城市(Sustainable Cities and Communities)
SDG12-責任消費與生產(Responsible Consumption and Production)
SDG13-氣候行動(Climate Action)
SDG14-海洋生態(Life Below Water)
SDG15-陸域生態(Life on Land)
SDG16-和平、正義和穩健的制度(Peace,Justice And Strong Institutions)
SDG17-促進目標實現的全球夥伴關係(Partnership for the Goals)
本課程和SDGS無關

本課程校外實習資訊: This course is relevant to internship:

　　　　　　　　 本課程包含校外實習（本選項僅供統計使用，無校外實習者，得免勾記）
The course includes internship.(For statistical use only. If the course without internship, please ignore this item.)

實習定義：規劃具有學分或時數之必修或選修課程，且安排學生進行實務與理論課程實習，於實習終了取得考核證明繳回學校後，始得獲得學分；或滿足畢業條件者。(一般校內實習請勿勾選此欄位)

Internship: The required or elective courses should include credits and learning hours. Students should participate in the corporative company or institution to practice and learn the real skills. An internship certification must be handed in at the end of internship to get the credits or to fulfil the graduation requirements.

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