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課程名稱 |
計算數學導論
Introduction to Computational Mathematics |
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開課學期 |
103-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
王偉仲 |
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課號 |
MATH5407 |
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課程識別碼 |
221 U4280 |
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班次 |
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學分 |
3 |
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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 |
星期一7,8(14:20~16:20)星期三7,8(14:20~16:20) |
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上課地點 |
新505新103 |
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備註 |
總人數上限：60人
外系人數限制：10人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1031icm |
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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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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 |
This is an introductory course to scientific computing. This introduction level course covers basic scientific computing topics, including nonlinear equations, approximation, numerical differentiation and integration, linear systems, eigenvalues and eigenvectors, numerical optimization, and numerical differential equations. We will discuss both mathematical principles, numerical algorithms, and software development for solving realistic scientific and engineering problems. One distinguishing feature of the course is "learning-by-doing". |
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課程目標 |
Students are expected
- to obtain an intuitive and working understanding of basic numerical methods,
- to gain appreciation of the concept of computational error and of the need to analyze and predict it,
- to implement numerical methods by using a computer language (mainly MATLAB), and
- to develop teamwork experience plus oral communication and writing skills. |
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課程要求 |
Basic programming skills, Calculus, Multivariable Calculus, Linear Algebra |
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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 |
[1] "Scientific Computing with MATLAB and Octave" by Alfio Quarteroni, Fausto Saleri and Paola Gervasio, Fourth Edition, 2014
(You can download the book via the NTU network from the URL "http://link.springer.com/book/10.1007%2F978-3-642-45367-0") |
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參考書目 |
[1] "Numerical Analysis" by Richard L. Burden and J. Douglas Faires (9nd edition)
[2] "Numerical Computing with MATLAB" by Cleve Moler
(http://www.mathworks.com/moler/chapters.html)
[3] "Introduction to Scientific Computing" by Charles F. van Loan (2nd Edition)
[4] "Scientific Computing: An Introductory Survey" by Michael T. Heath (2nd Edition)
[5] "Numerical Analysis: Mathematics of Scientific Computing" by David Kincaid and Ward Cheney
(3rd edition)
[6] "Numerical Mathematics" by Alfio Quarteroni, Riccardo Sacco, Fausto Saleri.
[7] "MATLAB Guide" by Desmond J. Higham and Nicholas J. Higham (2nd edition)
[8] 「MATLAB程式設計入門篇」，張智星 (第三版)
[9] 「MATLAB程式設計進階篇」，張智星 (第二版) |
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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. |
Homeworks, Quizzes, or Lab |
35% |
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2. |
Midterm Exam |
30% |
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3. |
Final Exam or Term Project |
35% |
Option 1: Final Exam
Option 2: Term Project (You may choose this option only if your Midterm Exam and homework/quiz average are higher than 80%.) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/15,9/17 |
<font color = "FF0000"><b>Course Introduction and MATLAB</b></font><br>
M: Course Introduction and Chap. 1 What can't be ignored<br>
W: Computer Arithmetics and Rate of Convergence<br>
<font color=#0000cc>HW Chap. 1: 1, 4, 5, 12, 13, 14<br>Reading: 1.2, 1.4, 1.6, 1.7. <br>Option: Explain Fig. 1.1 and Fig. 1.2.</font> |
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第2週 |
9/22,9/24 |
<font color = "FF0000"><b>Chapter 3. Approximation and Data Fitting (APP: Modeling Electricity Usage)</b></font><br>
M: Basic MATLAB (Lab)<br>
W: Chap. 3 Approximation (Lab)<br>
<font color = "0000cc">HW Chap. 3: 1, 2, 3, 5, 8, 10, 14.</font> |
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第3週 |
9/29,10/01 |
M: Chap. 3 Approximation (pp. )<br>
W: Chap. 3 Approximation (Lab)<br> |
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第4週 |
10/06,10/08 |
<font color = "FF0000"><b>Chapter 2. Nonlinear Equations (APP: Modeling Electricity Usage)</b></font><br>
M: Chap. 2 Nonlinear Equations (pp. )<br>
W: Chap. 2 Nonlinear Equations (Lab)<br>
<font color=#0000cc>HW Chap. 2: 2, 5, 6, 8, 11, 14-18</font> |
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第5週 |
10/13,10/15 |
M: Chap. 5 Linear Systems (pp. )<br>
W: Chap. 5 Linear Systems (Lab)<br> |
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第6週 |
10/20,10/22 |
<font color = "FF0000"><b>Chapter 5. Linear Systems (APP: Computer Tomography)</b></font><br>
M: Chap. 5 Linear Systems (pp. )<br>
W: Chap. 5 Linear Systems (Lab)<br>
<font color = "0000cc">HW Chap. 5: 11, 13, 15, 16,17, 18</font> |
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第7週 |
10/27,10/29 |
M: Chap. 5 Linear Systems (pp. )<br>
W: Chap. 5 Linear Systems (Lab)<br> |
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第8週 |
11/03,11/05 |
M: Chap. 5 Linear Systems (pp. )<br>
W: Chap. 5 Linear Systems (Lab)<br> |
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第9週 |
11/10,11/12 |
M: Buffer<br>
<font color=#009900><b>W: ========== Midterm Exam ==========</b></font> |
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第10週 |
11/17,11/19 |
<font color = "FF0000"><b>Chapter 6. Eigenvalue (APP: Ranking of Sport Teams and Webpages)</b></font><br>
M: Chap. 6 Eigenvalue Problem (pp. )<br>
W: Chap. 6 Eigenvalue Problem (Lab)<br>
<font color = "0000cc">HW Chap. 6: 5, 6, 7, 8, 10 </font> |
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第11週 |
11/24,11/26 |
M: Chap. 6 Eigenvalue Problem (pp. )<br>
W: Chap. 6 Eigenvalue Problem (Lab)<br> |
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第12週 |
12/01,12/03 |
<font color = "FF0000"><b>Singular Value Decomposition (APP: Model Reduction and Face Recognition)</b></font><br>
M: Singular Value Decomposition (pp. )<br>
W: Singular Value Decomposition (Lab)<br> |
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第13週 |
12/08,12/10 |
<font color = "FF0000"><b>Chapter 7. Numerical Optimization</b></font><br>
M: Chap. 7 Numerical Optimization (pp. )<br>
W: Chap. 7 Numerical Optimization (Lab)<br>
<font color = "0000cc">HW Chap. 7: TBA</font> |
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第14週 |
12/15,12/17 |
M: Chap. 7 Numerical Optimization (pp. )<br>
W: Chap. 7 Numerical Optimization (Lab)<br> |
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第15週 |
12/22,12/24 |
<font color = "FF0000"><b>Chapter 4. Numerical Differentiation and Integration</b></font><br>M: Chap. 4 Numerical Differentiation and Integration (pp. )<br>
W: Chap. 4 Numerical Differentiation and Integration (Lab)<br>
<font color = "0000cc">HW Chap. 4: TBA</font> |
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第16週 |
12/29,12/31 |
<font color = "FF0000"><b>Chapter 8. Numerical ODE (APP: Spacecraft Landing and Cardiac Action)</b></font><br>
M: Chap. 8 Numerical ODE (pp. )<br>
W: Chap. 8 Numerical ODE (Lab)<br>
<font color = "0000cc">HW Chap. 8: 1, 4, 7, 12, 15, 17, 18</font> |
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第17週 |
1/05,1/07 |
M: Chap. 8 Numerical ODE (pp. )<br>
W: Chap. 8 Numerical ODE (Lab)<br> |
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第18週 |
01/14 |
<font color=#009900><b>W: ========== Final Exam ==========</b></font> |
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