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課程名稱 |
數值偏微分方程
Numerical Partial Differential Equations |
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開課學期 |
112-2 |
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授課對象 |
理學院 應用數學科學研究所 |
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授課教師 |
薛克民 |
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課號 |
MATH7422 |
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課程識別碼 |
221 U6170 |
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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 |
選修 |
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上課時間 |
第1,2,3,4,5,6,7,8,9,10,11,12 週
星期一4,5(11:20~13:10)星期四3,4(10:20~12:10) |
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上課地點 |
天數201天數201 |
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備註 |
密集課程。
總人數上限：30人 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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課程概述 |
Partial differential equations are of fundamental importance
in modeling many applications in science and technology.
Since, in general, it is challenging to find analytical solutions
for real-world problems, finding approximate solutions is necessary.
This course aims to discuss various numerical approaches to the
construction of approximate solutions for initial-value and boundary-value problems of
linear and nonlinear ordinary and partial differential equations,
including the recent development based on deep neural networks. |
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課程目標 |
Analytical and computational tools will be emphasized in this course
in the hope of better understanding the solutions to the problems being solved,
and the convergent properties of the numerical methods being employed |
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課程要求 |
1. Introduction to differential equations (both ODEs and PDEs)
2. Introduction to computational mathematics
3. Programming skill in Matlab, python, and/or others |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
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參考書目 |
1. Bertil Gustafsson, High Order Difference Methods for Time dependent PDE,
Springer 2008. (e-book)
2. Randall J. LeVeque, Finite Difference Methods for Ordinary and Partial
Differential Equations, steady-state and time-dependent problems, SIAM 2007
(e-book)
3. Randall J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge 2002
4. Lloyd N. Trefethen, Spectral methods in Matlab, SIAM 2000
5. Journal papers (to be posted) |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
期中報告 |
50% |
時間: 03/28, 04/01
主題: assigned by instructor
評分標準: 口頭報告25%, 書面報告25% |
2. |
期末報告 |
50% |
時間: 05/13
主題: assigned by instructor fully or partially
評分標準: 口頭報告25%, 書面報告25% |
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