課程名稱 |
數值偏微分方程式一 Numerical Partial Differential Equations (Ⅰ) |
開課學期 |
105-2 |
授課對象 |
理學院 數學研究所 |
授課教師 |
薛克民 |
課號 |
MATH7409 |
課程識別碼 |
221 U1310 |
班次 |
|
學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期二5(12:20~13:10)星期四8,9(15:30~17:20) |
上課地點 |
天數430天數430 |
備註 |
總人數上限:12人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052MATH7409_npde201 |
課程簡介影片 |
|
核心能力關聯 |
本課程尚未建立核心能力關連 |
課程大綱
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
課程概述 |
Partial differential equations are of fundamental importance
in modeling many applications in science and technology.
Since in general it is difficult to find analytical solutions
for real-world problems, finding approximate solutions is necessary.
The goal of this course is to discuss various numerical approaches for the
construction of approximate solutions for ordinary and partial differential equations.
The topics to be covered in the course can be found in Ceiba's 大綱內容.
|
課程目標 |
Both the analytical and computational tools will be emphasized in this course
in the hope to have a better understanding of the computed solutions as
well as the solutions of original problems.
|
課程要求 |
Prerequisite:
(1) Introduction to differential equations (both ODEs and PDEs)
(2) Introduction to computational mathematics |
預期每週課後學習時數 |
|
Office Hours |
另約時間 |
指定閱讀 |
Lecture notes given by A. Bergara on ``Finite difference numerical methods of partial differential equations in finance with Matlab'' (see bulletin board) |
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) |
評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
Homework |
60% |
|
2. |
Midterm exam |
20% |
Time: 15:30-17:20, 04/13, 2017, open book and note. |
3. |
Final exam |
20% |
Time: 15:30-17:20, 06/20, 2017, open book and note. |
|
週次 |
日期 |
單元主題 |
第18週 |
06/22 |
Final exam |
第1-1週 |
02/21 |
Course overview, and examples |
第1-2週 |
02/23 |
Basic numerical differentiation approximation,
two-point boundary value problems |
第2-1週 |
02/28 |
No class: National holiday |
第7-1週 |
04/04 |
No class: National holiday |
第8-2週 |
04/13 |
Midterm exam |
第12-1週 |
05/09 |
No class: Self-learning week begin |
第12-2週 |
05/11 |
No class: Self-learning week end |
第15-1週 |
05/30 |
No class: National hoilday |
|