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課程名稱 |
偏微分方程式二
Partial Differential Equations (Ⅱ) |
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開課學期 |
111-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
阮文先 |
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課號 |
MATH5219 |
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課程識別碼 |
221EU0340 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期二3,4(10:20~12:10)星期四6(13:20~14:10) |
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上課地點 |
天數201天數201 |
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備註 |
本課程以英語授課。研究所基礎課。
總人數上限：30人
外系人數限制：5人 |
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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 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
The aim of this course is to introduce modern methods for studying linear and
nonlinear partial differential equations (PDEs) including elliptic and parabolic equations.
It is addressed to graduate students and anyone with an interest in the topic.
The content of the course is built around some of the following themes:
- calculus of variations,
- nonvariational techniques,
- spectral analysis,
- theory of viscosity solutions.
The course also includes simulation and symbolic calculation from Matlab Toolbox
for solving nonlinear PDEs.
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課程目標 |
Students will learn/ be introduced:
- Functional space and operator theory for nonlinear analysis.
- Various modern methods for solving nonlinear PDEs including second-order
elliptic and parabolic equations.
- Essential ideas for the basic issues of existence, uniqueness, and regularity
for nonlinear PDEs.
- Simulation and symbolic Math Toolbox for solving PDEs. |
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課程要求 |
Some basic knowledge of real analysis, and functional analysis along with
undergraduate Linear Algebra, ODEs, and PDEs are strongly recommended.
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預期每週課後學習時數 |
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Office Hours |
備註： Thursday 15:00 - 16:30 |
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指定閱讀 |
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參考書目 |
1. Partial Differential Equations by Lawrence C. Evans,
2. Superlinear Parabolic Problems by P. Quitnner and P. Souplet
3. Functional Analysis, Sobolev spaces and Partial Differential Equations by H. Brezis |
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評量方式
(僅供參考) |
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針對學生困難提供學生調整方式 |
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上課形式 |
提供學生彈性出席課程方式 |
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作業繳交方式 |
書面報告取代口頭報告 |
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考試形式 |
書面(口頭)報告取代考試, 考試取代書面(口頭)報告 |
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其他 |
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