Type of Credit: Elective
Credit(s)
Number of Students
本課程爲本系大碩合開選修課程。本學期將着重討論一階以及二階線性偏微分方程。
This is a selective course for both undergraduate and graduete students. In this semester, we will focus on first order and second order linear partial differential equations (PDE).
能力項目說明
1. 加強高維度微積分基本運算。
Enhance basic computations in higher dimensional calculus
2. 以偏微分方程爲動機，我們會介紹一些泛函分析的工具，包含廣義函數（也稱作“分佈”）、Sobolev空間、Fourier級數、Fourier變換、等等。
Motivated by partial differential equations, we will introduce some Functional analysis tools, including generalized function (also known as "distributions"), Sobolev spaces, Fourier series, Fourier analysis, etc.
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
期中考試（預計第10週）及期末考試日期（預計第16週）視教學進度而定。建議每週花至少3小時寫自習。實際考試範圍以上課爲準，課本以及下列課綱只供參考，會隨着實際教學狀況而調整，也請見“課程相關連結”。
The date of midterm (expect the 10th week) and final exams (expect the 16th week) will depend on the actual situation. It is recommend to spend at least 3 hours for self-study. The scope of each quiz and exam depends on the actual teaching, textbook and the following syllabus are just a reference, which wil be adjusted depending on actual situation, see also "課程相關連結" below.
預計教學進度 Expected teaching schedule:
Week 1: What is partial differential equations (PDE), first order PDE
Week 2: Linear PDE of second order, wave equation
Week 3: Wave equation
Week 4: Wave equation
Week 5: Wave equation
Week 6: Weak derivatives and distribution derivatives
Week 7: Definition and elementary properties of Sobolev spaces, Hilbert spaces
Week 8: Solving elliptic PDE for small wave number, the maximum principle
Week 9: Solving elliptic PDE: Eigenvalue problem and Fedholm alternative
Week 10: Midterm
Week 11: Fourier series
Week 12: Distirbution with compact support and convolution, Fundamental solution of Laplacian
Week 13: Formulation of weak solutions of wave equations, existence of solutions
Week 14: Existence of solutions
Week 15: Self study (I will participate an international conference)
Week 16: Uniqueness of solutions
Week 17: Final
Week 18: Return exam paper
期中考試 Midterm exam 20%
期末考試 Final exam 20%
作業 homeworks 60%
考試範圍爲所有上課教過的地方，大綱只供參考 The exam scope is all materials taught in class, the syllabus is just for reference only
如果不克出席考試（例如病假），請事前通知，否則成績以0分計算。注意：補考考卷的題目會比較困難。
If you unable to attend the exam (e.g. sick leave), please let me know before that, otherwise 0 mark will be counted. Note. The questions in make-up exam will be more difficult.
考試規則：
1. 考試中不允許使用課本或其他參考資料 Textbook or other materials are not allowed to be used during exams and quizes.
2. 考試中禁止使用任何電子設備（包含計算機、智慧型手機、平板、電腦...） All electronic devices (including calculator, smartphone, pad, computer, ...) are prohibited during exams and quizes.
3. 考試中上述物品不允許放在桌上，請在考試開始前10分鐘放置在書包內或椅子下。
4. 考生不允許攜帶任何其他紙張入場。助教會提供作答所需的紙張 One also not allowed to bring your own extra paper. TA will provide answer sheets
5. 考試期間上廁所前請先告知 Before go to washroom, one must inform us before do so.
6. 如果考生違反上述任何規則，我們會立即中止該考生的作答且該次測驗成績爲0 If you violate one of the above rule, we will immednate terminate your writing and the marks of the exam/quiz will be 0.
7. 考生必須出示學生證或國民身份證或全民健康保險卡或護照或居留證（不接受駕照）以供查驗。考試開始前助教應提醒考生。如果在考試期間無法出示上述證件，將視爲作弊且該次測驗成績爲0 One must show student card or national identity card or national health insurance card or passport or resident certificate (driving license not accepted) for verification. Before the exam begins, TA should reminds all of you to bring it. If one fails to show it during exam, we consider this as a cheating and the marks of the quiz will be 0.
本課程會使用我自己寫的筆記爲課本（隨着教學更新） I prepare the following lecture note for this course (will updated during the teaching)
Pu-Zhao Kow, An introduction to partial differential equations and functional analysis, lecture note, National Chengchi University. https://puzhaokow1993.github.io/homepage/teaching/Lecture_Note/ver1_Lecture_Note_PDE.pdf
我在筆記的“Bibliography”也有提供其他參考書目，包含下列：
I also provide some other references in the "Bibliography" section of the above lecture note, including the followings:
個人網頁 https://puzhaokow1993.github.io/homepage/teaching/courses_pages/PDE_701925-751944_2024_Spring/PDE_701925-751944_2024_Spring.html