NCHU Course Outline

Course Name	(中) 偏微分方程之數值方法(3220)
	(Eng.) Numerical Methods for Partial Differential Equations
Offering Dept	Department of Applied Mathematics (Data Science and Computing Program)
Course Type	Required	Credits	3	Teacher	TENG CHUN HAO
Department	Department of Applied Mathematics (Data Science and Computing Program)/Undergraduate	Language	English	Semester	2025-FALL
Course Description	Many scientific problems are described by partial differential equations. However, the analytical solution of partial differential equations has its limitations, often only applicable to linear problems with constant coefficients, and cannot be applied to real scientific and engineering problems. Numerical methods for partial differential equations are an applied mathematical tools that utilize the theoretical results and numerical methods to construct discrete systems of equations that mimic the properties of the original equations. Through computer computations, approximate solutions to partial differential equations are obtained to compensate for the shortcomings of analytical methods. 許多的科學問題是以偏微分方程的形式來描述。但偏微分方程的解析解法卻有其侷限性，往往只能用於常係數線性問題，對於真實的科學和工程問題解析方法往往無法應用。偏微分方程數值方法是一門應用數學方法，其精神是運用偏微分方程的理論結果和數值方法，建構一離散但仿原方程式的性質的系統方程式，透過計算機執行，求偏微分方程的近似解，以彌補解析方法的不足。
Prerequisites				self-directed learning in the course	Y

Relevance of Course Objectives and Core Learning Outcomes(%)			Teaching and Assessment Methods for Course Objectives
Course Objectives	Competency Indicators	Ratio(%)	Teaching Methods	Assessment Methods
1. Understand the basic concepts of numerical partial differential equations and how to use numerical methods to design calculation formats and obtain approximate solutions to partial differential equations. 2. Have a foundation in studying advanced numerical partial differential equations. 3. Have the basic research ability to conduct relevant topics. 1.了解數值偏微分方程的基本概念和如何使用數值方法設計計算格式，求得偏微分方程的近似解。 2.具備修習高等數值偏微分方程的基礎。 3.具備進行相關專題的基本研究能力。	2.Professional Knowledge in Mathematical Analysis 4.Professional Knowledge in Scientific Computation 5.Professional Knowledge in Computer Science	30 35 35	topic Discussion/Production Networking/Distance Education Visit Exercises Discussion Practicum Lecturing	Written Presentation Oral Presentation Quiz Attendance Assignment
Course Content and Homework/Schedule/Tests Schedule
Week Course Content Week 1 Course Introduction Basic concepts of numerical partial differential equations Week 2 Advection equaltions: Wellposed-ness Week 3 Summation-by-parts methods for numerical partial differential equations Week 4 Numerical schemes for advection equations: stability analysis Week 5 Wave equations on a spherical surface Grid construction: Cubed-sphere Week 6 Numerical scheme for advcection equations on spherical surfaces (1) Week 7 Numerical scheme for advcection equations on spherical surfaces (2) Week 8 Numerical scheme for advcection equations on spherical surfaces (2) Week 9 Mid-term: Presentation Week 10 Shallow water equations on a sphere Skew-symmetric form Week 11 Numerical scheme for shallow water equations on spherical surfaces (1) Scheme construction Week 12 Numerical scheme for shallow water equations on spherical surfaces (2) Validation Week 13 Numerical scheme for shallow water equations on spherical surfaces (3) Simulation of flow over an isolated mountain Week 14 Numerical scheme for shallow water equations on spherical surfaces (4) Simulation of other wave problems Week 15 Final: presentation Week 16 self-directed learning    02.Viewing multimedia materials related to industry and academia.
Evaluation
Attendence: 10% Homework: 20% Mid-term (30%): Presentation(10%) and written report(20%) Final(40%): Presnetation (20%) and written report (20%)
Textbook & other References
NA
Teaching Aids & Teacher's Website
Lecture notes will be provided in the I-learning system
Office Hours
Mon. 15:00-16:00
Sustainable Development Goals, SDGs(Link URL)
02.Viewing multimedia materials related to industry and academia. include experience courses：N

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Update Date, year/month/day：2025/06/12 15:59:07	Printed Date, year/month/day：2025 / 6 / 18
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