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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 |
101-1 |
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授課對象 |
理學院 數學系 |
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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 |
必修 |
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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 |
上機教室:天數301。
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/1011icm |
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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 introduction course to scientific computing. This introduction level course covers basic scientific computing topics. We will discuss both mathematical principles, numerical algorithms, and software development for solving problems arising in sciences and engineering by using sequential and parallel computers. |
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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 (like MATLAB, C, or Fortran), 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, Third Edition, 2010
(http://www.springerlink.com/content/h83u61/#section=707430&page=1) |
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參考書目 |
[1] Numerical Analysis (8th edition) by Richard L. Burden and J. Douglas Faires
[2] Numerical Computing with MATLAB by Cleve Moler (http://www.mathworks.com/moler/chapters.html)
[3] Introduction to Scientific Computing (2nd Edition) by Charles F. van Loan
[4] Scientific Computing: An Introductory Survey (2nd Edition) by Michael T. Heath
[5] Numerical Analysis: Mathematics of Scientific Computing (3rd edition) by David Kincaid and Ward Cheney
[6] MATLAB Guide (2nd edition) by Desmond J. Higham and Nicholas J. Higham
[7] MATLAB 程式設計 [入門篇]，張智星 |
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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 or Quizzes |
35% |
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2. |
Midterm Exam |
30% |
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3. |
Final Exam or Term Project |
35% |
Option 1: Final Exam<br>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 |
9/10,9/12 |
M: Chap. 1 What can’t be ignored<br>
W: Chap. 1 What can’t be ignored |
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第2週 |
9/17,9/19 |
M: Course introduction and Chap. 3 Approximation (Slides pp. 1-19)<br>
W: Chap. 1 What can’t be ignored (Lab) |
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第3週 |
9/24,9/26 |
M: Chap. 3 Approximation (pp. 20-32)<br>
W: Chap. 3 Approximation (Lab) |
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第4週 |
10/01,10/03 |
M: Chap. 3 Approximation (pp. 32-49)<br>
<font color="#008000">Chap. 3 HW (pp. 105-106): 1, 2, 3, 5, 8, 10, 14.</font><br>
W: Chap. 3 Approximation (pp. 50-54)<br>
W: Chap. 4 Numerical Integration (Overall introduction) |
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第5週 |
10/08,10/10 |
M: Chap. 4 Numerical Integration (pp. 1-17)<br>
M: <font color=#FF0000>Quiz 1 (Chap 3)</font><br>
W: No Class (National Day) |
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第6週 |
10/15,10/17 |
M: Chap. 4 Numerical Integration (pp. 18-29)<br>
W: Chap. 4 Numerical Integration (Lab for Gaussian quadrature) |
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第7週 |
10/22,10/24 |
M: Chap. 5 Linear Systems (Part 1: pp. 1-18)<br>
W: Chap. 5 Linear Systems (Lab: LU and Cholesky factorization) |
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第8週 |
10/29,10/31 |
M: Chap. 5 Linear Systems (Part 1: pp. 19-29)<br>
W: Chap. 5 Linear Systems (Part 1: pp. 30-40) |
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第9週 |
11/05,11/07 |
M: Chap. 5 Linear Systems (Part 1: pp 41-45, Part 2: pp 1-14)<br>
W: Chap. 5 Linear Systems |
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第10週 |
11/12,11/14 |
M: Midterm<br>
W: Chap. 5 Linear Systems (Lab The team project) |
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第11週 |
11/19,11/21 |
M: Chap. 5 Linear Systems (Part 2: pp 15-34)<br>
W: Chap. 5 Linear Systems (Part 2: pp 35-42), Midterm discussion<br><font color=#FF0000>HW Chap 5: 11, 13, 15, 16,17, 18 (p. 178)</font> |
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第12週 |
11/26,11/28 |
M: Chap. 6 Eigenvalue (pp. 1-13)<br>
W: Chap. 6 Eigenvalue (Lab for power method based eigensolver) |
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第13週 |
12/03,12/05 |
M: Chap. 6 Eigenvalue (pp. 14-26);<br>M: Chap. 2 Nonlinear Equations (pp. 1-5)<br>
W: Chap. 6 Eigenvalue (Lab for QR based eigensolver)<br><font color=#FF0000>HW Chap 6: 5, 6, 7, 8, 10 (p. 198)</font> |
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第14週 |
12/10,12/12 |
M: Chap. 2 Nonlinear Equations (pp. 6-17)<br>
W: Chap. 2 Nonlinear Equations (Lab)<br><font color=#FF0000>HW Chap 2: 2, 5, 6, 8, 11, 14-18 (p. 72)</font> |
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第15週 |
12/17,12/19 |
M: Chap. 2 Nonlinear Equations (pp. 18-32)<br>
W: Chap. 2 Nonlinear Equations (Lab) |
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第16週 |
12/24,12/26 |
M: Chap. 2 Nonlinear Equations (pp. 33-38)<br>
M: Chap. 7 ODE (pp. 1-13)<br>
W: Chap. 7 ODE (pp. 14-30)<br>
<font color=#FF0000>HW Chap 7: 1, 4, 7, 12, 15, 17, 18 (p. 72)</font> |
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第17週 |
12/31,1/02 |
M: No Class (New Year)<br>
W: Chap. 7 ODE (pp. 35-42), Introduction to Scientific Computing I for the next semester |
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第18週 |
1/7 |
M: Final Exam |
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