課程名稱 |
偏微分方程式一 Partial Differential Equations (Ⅰ) |
開課學期 |
104-1 |
授課對象 |
理學院 數學研究所 |
授課教師 |
王振男 |
課號 |
MATH5218 |
課程識別碼 |
221 U0330 |
班次 |
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學分 |
3 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期二3,4(10:20~12:10)星期四6(13:20~14:10) |
上課地點 |
天數102天數102 |
備註 |
研究所基礎課。 總人數上限:50人 外系人數限制:10人 |
課程網頁 |
http://www.math.ntu.edu.tw/~jnwang/courses/pde2015/ |
課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
課程大綱
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課程概述 |
This is a graduate course for students who are interested in the theory of partial differential equations. The main goal of the course is to familiarize students with basic analytic techniques in studying partial differential equations. Unlike the PDE course for undergraduates, we will focus more on the fundamental questions such as existence, uniqueness, regularity, etc. We shall begin with harmonic functions and the Laplace equation. The study of second order elliptic equations is the main theme of the course. In addition, we will also study hyperbolic and parabolic equations. |
課程目標 |
We will follow closely the book by Jurgen Jost (see below). In the first semester, we plan to cover the first part of the book on some basic properties of elliptic, hyperbolic, parabolic equations. The prerequisites for this course are undergraduate PDE, Advanced Calculus, Real Analysis. |
課程要求 |
Two exams and weekly homework assignments.
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預期每週課後學習時數 |
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Office Hours |
每週二 14:00~16:00 |
指定閱讀 |
Jurgen Jost, Partial Differential Equations, 3rd Edition, Graduate Texts in Mathematics 214, Springer 2013. |
參考書目 |
★ L.C. Evans, Partial Differential Equations. Graduate Studies in Mathematics 19, AMS, 2010.
★ F. John, Partial Differential Equations. Springer, New York, 1982.
★ D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer,
Berlin, 1983.
★ Q. Han and F.H. Lin, Elliptic Partial Differential Equations. Courant Lecture Notes in
Mathematics, 1997.
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評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
Midterm |
30% |
Week 9 |
2. |
Final |
30% |
Week 18 |
3. |
Homework |
40% |
Weekly |
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