教學大綱 Syllabus

每周課程進度與作業要求 Course Schedule & Requirements

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.

期中報告（預計第10週）及期末報告日期（預計第17週）視教學進度而定。
The date of midterm (expect the 10th week) and final presentations (expect the 17th week) will depend on the actual situation.

1. 介紹常微分方程 Introduction to ODE 「第1週 1st week」
   • 一些數學模型 Some mathematical models
   • 常微分方程的分類 Classification of ODE
2. 一階非線性常微分方程 First order nonlinear
   • 解存在唯一性 Existence and uniqueness of solution 「第3週 3rd week」
   • 一些計算技巧 Some techniques 「第4週 4th week」
   • 與偏微分方程之間的關係 Relation with partial differential equations (PDE) 「第5-6週 5th-6th week」
3. 線性常微分方程 Linear ODE
   • 常係數齊次常微分方程 Homogeneous ODE with constant coefficients 「第7-9週 7th-9th week」
   • 變係數齊次常微分方程 Homogeneous ODE with variable coefficients 「第11週 11th week」
   • 非齊次常微分方程 Nonhomogeneous ODE 「第12週 12th week」
   • 高階線性常微分方程 Higher order linear ODE 「第13週 13th week」
   • Strum-Liouville 特徵值問題 Strum-Liouville eigenvalue problem 「第14週 14th week」
4. 傅里葉級數 Fourier series 「第15-16週 15-16th week」

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.