國立中山大學114學年度第2學期物理數學與數值方法（二）課程大綱

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

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

課程大綱 Course syllabus

An intermediate-level mathematics course designed for physics learners.
The course introduces linear algebra, Fourier analysis, basic special functions, and methods of numerical analysis.
Rigorous mathematical foundations and detailed proofs are not the focus of this course.
Instead, students are expected to be familiar with each topic and understand how to apply it to typical problems.

Prerequisites for this course include a basic understanding of calculus, matrix arithmetic, and ordinary differential equations.
The course begins with linear algebra; you focus on the practical handling of matrices, including eigenvalue problems and matrix diagonalization.
After the midterm exam, you learn fundamental ideas of function analysis, in particular Fourier analysis and basic special functions, as a natural continuation of the fall semester lecture.

The course also introduces fundamental concepts of numerical analysis.
Students will gain necessary knowledge of numerical methods as well as practical skills using Python. 

Course webpage: https:/www2.nsysu.edu.tw/iwamoto/physmath2.html

課程目標 Objectives

- I can perform basic matrix operations by hand and understand the roles of rank and determinants in linear algebra.
- I can solve simple eigenvalue problems and diagonalization problems by hand.
- I can carry out basic Fourier analysis of functions.
- I am familiar with basic special functions and understand where and why they appear.
- I understand the basic features and limitations of the IEEE-754 floating-point standard.
- I can apply numerical methods to typical problems in linear algebra and related topics.

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：45%
2.Term Exam：35%
3.Coding Assignment：20%

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

序號	作者	書名	出版社	出版年	出版地	ISBN#
No.	Auther	Title	Publisher	Year of publish	Publisher place	ISBN#
1	E. Kreyszig	Advanced Engineering Mathematics, 10th ed., Taiwan custom version	Wiley	2018		9781119934165

課程時數規劃 Course Hour Planning

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.”

本門課程為「16週+自主學習規劃」：教師需於「A.每週課程內容及預計進度」欄位填寫16週課程進度，並於「B.自主學習規劃」欄位填寫每1學分2小時學生自主學習內容。
16 weeks + alternative learning periods: The instructor will include a 16-week course plan in the weekly scheduled progress section(16 hours of instruction per credit) and provide details of the learning plan (two hours of activity per credit) in the alternative learning period section.

本門課程為「16週+實體上課規劃」：教師需於「A.每週課程內容及預計進度」欄位填寫16週課程進度，並於「C.實體上課規劃」填寫2次授課內容及主題。
16 weeks + in-person classes: The instructor will include a 16-week course plan in the weekly scheduled progress section (16 hours of instruction per credit) and specify the content and topics of the 2 in-person classes in the in-person class plan section.

A.每週課程內容及預計進度 Weekly scheduled progress

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	2026/02/22~2026/02/28	Introduction: Logic.
2	2026/03/01~2026/03/07	Matrices and Linear systems of Equations.
3	2026/03/08~2026/03/14	Rank and Linear independence.
4	2026/03/15~2026/03/21	Determinant and Inverse Inverse.
5	2026/03/22~2026/03/28	Eigenvalue problem.
6	2026/03/29~2026/04/04	Matrix with special names.
7	2026/04/05~2026/04/11	Matrix diagonalization.
8	2026/04/12~2026/04/18	Midterm Exam (Apr. 13)
9	2026/04/19~2026/04/25	Modern programming. IEEE-754 Floating point numbers.
10	2026/04/26~2026/05/02	Basic numerical analysis.
11	2026/05/03~2026/05/09	Fourier series expansion.
12	2026/05/10~2026/05/16	Fourier transformation.
13	2026/05/17~2026/05/23	Gamma function. Review of ODE.
14	2026/05/24~2026/05/30	Orthogonal polynomials.
15	2026/05/31~2026/06/06	Bessel function.
16	2026/06/07~2026/06/13	Term Exam (Jun. 8)

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)

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)

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)：

課業討論時間 Office hours

時段1 Time period 1:
時間 Time：星期二14:00-16:00
地點 Office/Laboratory：理SC2006‒1
時段2 Time period 2：
時間 Time：星期五16:00–18:00
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.

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.

課外閱讀 Outside reading.

※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.

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.

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 skills

2.探究與批判思考能力。 2. Inquisitive and critical thinking abilities

3.終身學習能力。 3. Lifelong learning

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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