Type of Credit: Elective
Credit(s)
Number of Students
本課程的主題爲介紹微分方程。本學期主要專著在常微分方程，包含起始值問題解的存在唯一性定理、線性系統的基本性質。
The main theme of this course is to introduce differential equations. This semester will mainly focus on ordinary differential equations (ODE), including the existence and uniqueness of the initial value problem and some basic properties of lienar system.
能力項目說明
複習微積分以及介紹一些應用，以及學習使用 LaTeX 。
Review calculus and introduce some applications and learn how to use LaTeX.
本大綱只供參考，課程進行中會隨時更新。
This syllabus is just for a reference, which will be updated at any time during the course.
期中考試（預計第7週）及期末考試日期（預計第16週）視教學進度而定。
The date of midterm (expect the 7th week) and final exams (expect the 16th week) will depend on the actual situation.
我們預計根據下列計劃進行教學：
We will plan to deliver the ideas based on the followings:
| 課程主題 | 課程内容與指定閲讀 | 教學活動與作業 | |
|
第一週 1st week |
Introduction to ODE |
Some mathematical model Classification of ODE |
教師授課 佈置作業 |
|
第二週 2nd week |
First order nonlinear ODE | Existence and uniqueness of solution |
教師授課 佈置作業 |
|
第三週 3rd week |
First order nonlinear ODE | Some techniques |
教師授課 佈置作業 |
|
第四週 4th week |
First order nonlinear ODE | Relation with PDE |
教師授課 佈置作業 |
|
第五週 5th week |
First order nonlinear ODE | Relation with PDE |
教師授課 |
|
第六週 6th week |
First order nonlinear ODE | 復習 | 教師授課 |
|
第七週 7th week |
期中考試 Midterm exam | ||
|
第八週 8th week |
Linear ODE | Homogeneous ODE with constant coefficients |
教師授課 佈置作業 |
|
第九週 9th week |
Linear ODE | Homogeneous ODE with constant coefficients |
教師授課 佈置作業 |
|
第十週 10th week |
Linear ODE | Homogeneous ODE with variable coefficients |
教師授課 佈置作業 |
|
第十一週 11th week |
Linear ODE | Nonhomogeneous ODE |
教師授課 佈置作業 |
|
第十二週 12th week |
Linear ODE | Higher order linear ODE |
教師授課 佈置作業 |
|
第十三週 13th week |
Linear ODE | Strum-Liouville eigenvalue problem |
教師授課 佈置作業 |
|
第十四週 14th week |
Linear ODE | Fourier series | 教師授課 |
|
第十五週 15th week |
Linear ODE |
復習 |
教師授課 |
|
第十六週 16th week |
期末考試 Final exam |
每週會有3節正課。建議每週花至少3小時自習。
There will be 3 regular classes per week. It is recommend to spend at least 3 hours for self-study.
對於不熟悉（或不會使用） LaTeX 的學生，比起直接安裝 MiKTeX 或 TeX Live ，這里我建議可以從 Overleaf （線上編輯器，有許多模板以及使用說明）或 LyX （具有圖形界面輔助）開始，兩者皆免費。
For those students who are not familiar to (or do not know how to use) LaTeX, rather than directly install MiLTeX or Tex Live, here I suggests you can start from Overleaf (online editor, including many templates and instructions) or LyX (which is a program with graphical user interface), both of them are free.
作業（必須使用 LaTeX 編輯） Homework assignments (must be prepared using LaTeX): 60%
期中考試 Midterm Exam: 20%
期末考試 Final Exam: 20%
*視選課情形再決定考試形式
自備講義 Handouts will be provided:
https://puzhaokow1993.github.io/homepage/teaching/Lecture_Note/ver1_Lecture_Note_ODE_graduate.pdf
https://puzhaokow1993.github.io/homepage/teaching/Lecture_Note/ver1_Lecture_Note_Distributions_Fourier_Analysis.pdf
https://puzhaokow1993.github.io/homepage/teaching/courses_pages/ODE_751873001_2025_Fall/ODE_751873001_2025_Fall.html