National Taiwan Normal University Course Outline
 Fall , 2026

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I.Course information
Serial No. 2661 Course Level Master / PhD
Course Code MAC0001 Chinese Course Name 微分方程（一）
Course Name Differential Equations (I)
Department Department of Mathematics
Two/one semester 1 Req. / Sel. Sel.
Credits 3.0 Lecturing hours Lecture hours: 3
Teach in English Y Teach in National Languages
Prerequisite Course ◎1. This is a cross-level course and is available for junior and senior undergraduate students, master's students and PhD students. 2. If the listed course is a doctroal level course, it is only available for master's students and PhD students.
Comment
Course Description
Day & Class Period/Location Fri. 2-4 Gongguan M311
Curriculum Goals Corresponding to the Departmental Core Goal
1.　讓學生瞭解微分方程的一些基本理論 Master:
　1-1 Equipped with professional mathematics competences
　1-2 Being able to reason and induct with mathematical logic
　1-4 Possessing the abilities to propose and solve questions in advanced mathematics
　3-1 Being able to seek out answers with the attitudes of patience, diligence, concentration, and curiosity
　3-4 Having insights, intuitions, and senses of mathematics
Doctor:
　1-1 Equipped with professional mathematics competences
　1-2 Being able to reason and induct with mathematical logic
　1-4 Possessing the abilities to propose and solve questions in advanced mathematics
　3-1 Being able to seek out answers with the attitudes of patience, diligence, concentration, and curiosity
　3-4 Having insights, intuitions, and senses of mathematics
2.　認識其他領域所推導出的方程並瞭解在數學分析的背後原始問題的意義 Master:
　1-5 Being able to use mathematics as tools to learn other subjects
　4-4 Possessing global views from both scientific and humanistic perspectives, and being able to appreciate the values of other knowledge fields
Doctor:
　1-5 Being able to use mathematics as tools to learn other subjects
　4-4 Possessing global views from both scientific and humanistic perspectives, and being able to appreciate the values of other knowledge fields

II. General Syllabus
Instructor(s) CHERN, Jann-Long/ 陳建隆
Schedule

本課程的主題與目標如下：

(1) 研究來自生物學、數據科學和物理學等領域的基本數學模型。

(2) 學習常微分方程(ODE)的基本定理

(3) 探討來自生物學、數據科學和物理學等領域的基本數學模型的相關穩定性數學理論與應用.

(4) 相關動力系統和模型的進一步主題

在本課程中，我們同時學習以下內容：

(1) 來自生物學、數據科學、圖像處理和物理學等領域的基本數學模型。

(2) 一階微分方程，常微分方程的線性系統：

(3) 具有常數和周期係數的線性系統，Floquettheory；

(4) 二維自主系統的像平面分析 (Phase plane analysis)；

(5) 非線性常微分方程、Dulac Q.、Omega 極限集和不變量集的基本定性性質，

(6) Poincare-Bendixson 定理和相關動力系統的應用。

(7) ODEs 的相關應用。

The themes and objectives of this course are as follows:
(1) Study fundamental mathematical models from fields such as biology, data science, and physics.
(2) Learn the fundamental theorems of ordinary differential equations (ODEs).
(3) Explore the relevant stability mathematical theories and applications of fundamental mathematical models from fields such as biology, data science, and physics.
(4) Further topics related to dynamical systems and models.

In this course, we will also learn the following:
(1) Fundamental mathematical models from fields such as biology, data science, image processing, and physics.
(2) First-order differential equations, linear systems of ordinary differential equations:
(3) Linear systems with constants and periodic coefficients, Floquet theory;
(4) Phase plane analysis of two-dimensional autonomous systems;
(5) Fundamental qualitative properties of nonlinear ordinary differential equations, Dulac Q., Omega limit sets, and invariant sets;
(6) Poincare-Bendixson theorem and applications of relevant dynamical systems.
(7) Relevant applications of ODEs.
Instructional Approach
Methods Notes
Formal lecture 來自生物學、數據科學和物理學等領域的基本數學模型來舉例學習與研究
Group discussion 讓同學分組討論課堂數學建模與相關習題實作.
Problem-based learning 讓同學分組討論課堂數學建模與相關習題實作.
Lab/Studio 同學分組討論課堂數學建模與相關習題實作.
Grading assessment
Methods Percentage Notes
Assignments 30 % 每位學生必須在規定的截止日期前完成並提交各學習章節的指定練習。 Each student is required to complete and submit the assigned exercises for each learning chapter within the specified deadline.
Final exam 30 % 期末考試將在學習期的最後一周舉行。 The final examination will be held during the last week of the study period.
Class discussion involvement 10 % 每位學生都必須參加課堂討論。Each student is required to attend the assigned discussions in the learning classes.
Attendances 10 % 每位學生都必須積極出席課堂學習。Each student is required to participate in the learning classes.
Presentation 20 % 每位學生必須在規定的截止日期前完成並提交各指定學習章節的指定報告。 Each student is required to complete and report the assigned topics exercises for each learning chapter within the specified deadline.
Adjustment methods for students
Required and Recommended Texts/Readings with References

References (參考書目) :
(1) Sze-Bi Hsu, Ordinary Differential Equations withApplications: Second Editions

(2) J. D. Murray, Mathematical BiologyVol I-II

(3) Related Notes

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