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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 |
99-1 |
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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302 |
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備註 |
上機時間：星期一17:30~20:15。
總人數上限：80人
外系人數限制：15人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/991compmath |
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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 |
- Introduction to Matlab
- Root finding (Solutions of equations of one variable, Solutions of nonlinear systems of equations)
- Approximation (Interpolation and polynomial approximation, Approximation theory),
- Numerical differentiation and integration
- Numerical linear algebra (Direct and iterative methods for linear system, Approximating eigenvalues)
- Numerical differential equations (Initial-value and boundary-value problems for ordinary differential equations, partial differential equations) |
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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, advanced 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] 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) |
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參考書目 |
[1] Introduction to Scientific Computing (2nd Edition) by Charles F. van Loan
[2] Scientific Computing: An Introductory Survey (2nd Edition) by Michael T. Heath
[3] Numerical Analysis: Mathematics of Scientific Computing (3rd edition) by David Kincaid and Ward Cheney
[4] MATLAB Guide (2nd edition) by Desmond J. Higham and Nicholas J. Higham
[5] 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. |
一分鐘報告 |
5% |
上課（不含 lab）後繳交，每次 0.5%，上限為 5%。若繳交18次以上，額外加學期總成績3分。 |
2. |
小考 |
30% |
共7次，每次5分。取6次較高成績計算，小考不能補考。 |
3. |
期末考 或 計畫 |
30% |
期中考獲得80分且前4次小考合計16分以上同學，可以選擇以執行計畫（個人或小組計畫）代替期末考。另外，執行計畫同學也可經提案審查後，將百分比改為計畫 40% 與與小考 20%。 |
4. |
期中考 |
35% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/13,9/15 |
9/13: Course introduction,<br>        Chap 1 Math Preliminaries and Error Analysis ([BF] pp. 1-19)<br>
9/13: Introduction to Matlab (lab)<br>
9/15: Chap 1 ([BF] pp. 20-43) |
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第2週 |
9/20,9/22 |
9/20: Chap 1 ([BF]pp. 44-48).<br>        Chap 2 Solutions of Equations in One Variable ([BF] pp. 1-14)<br>
9/20: [M] Section 1.7 (lab), <font color=red>Quiz 1</font><br>        <font color=green>HW: [BF] read Chap 01; [M] read Sec. 1.7 and Ex. 1.33, 1.34, 1.35, 1.39 </font><br>
9/22: <font color=red>中秋節放假</font><br> |
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第3週 |
9/27,9/29 |
9/27: Chap 2 ([BF] pp. 15-44, except 37-39)<br>
9/27: Chap 2 (lab): [M] 4.1-4.4. See attached file for details. <br>
9/29: Chap 2 ([BF] pp. 37-39 and 47-60)<br>        <font color=green>HW: [BF] Sec. 2.2 (3, 7), Sec. 2.4 (6, 8, 13) </font> |
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第4週 |
10/04,10/06 |
10/04: Chap 2 (lab): [M] Sec. 4.5, 4.6, 4.7 and 4.8, <font color=red>Quiz 2</font><br>        <font color=green>HW: [M] Ex. 4.1 (a,c,e,g), 4.3, 4.15</font><br>
10/06: Chap 3 Interpolation and Polynomial Approximation ([BF] pp. 1-28) |
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第5週 |
10/11,10/13 |
10/11: Chap 3 (lab) Largrange and piecewise linear interpolating polynomial<br>        <font color=green>HW: [M] Ex. 3.3, 3.4, 3.8, 3.9</font><br>
10/13: Chap 3 ([BF] pp. 41-66, except 48-50) |
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第6週 |
10/18,10/20 |
10/18: Chap 3 (lab) Matlab debugger, cubic spline, <font color=red>Quiz 3</font><br>
10/20: Chap 4 Numerical differentiation and Integration ([BF] pp. 1-21) |
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第7週 |
10/25,10/27 |
10/25: Chap 4 (lab) Composite Simpson's rule<br>
10/27: Chap 4 |
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第8週 |
11/01,11/03 |
11/01: Chap 4 (lab) Adaptive quadrature (extrapolated Simpson's rule)<br>
11/03: Chap 4 |
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第9週 |
11/08,11/10 |
11/08: Review of Chap 1-4, <font color=red>Quiz 4</font><br>
11/10: <font color=red>期中考</font><br> |
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第10週 |
11/15,11/17 |
11/15: <font color=red>校慶放假</font><br>
11/17: Chap 5 Initial-Value Problems for Ordinary Differential Equations |
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第11週 |
11/22,11/24 |
11/22: Chap 5 (lab)<br>
11/24: Return midterm exam; Chap 5 ode23 |
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第12週 |
11/29,12/01 |
11/22: Chap 5 (lab)<br>
11/24: Chap 5 Error analysis of Euler's method, higher order methods |
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第13週 |
12/06,12/08 |
12/06: Chap 8 (lab), <font color=red>Quiz 5</font><br>
12/08: Chap 5 Multiple methods (explicit AB, implicit AM), stiffness |
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第14週 |
12/13,12/15 |
12/13: Chap 6 (lab) [M] Section 2.11, Exercise 2.23 and 2.25<br>
12/15: Chap 5 Consistent, Convergent, and Stable; <br>          Chap 6 Direct Methods for Solving Linear System |
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第15週 |
12/20,12/22 |
12/20: Chap 6 (lab) [M] Section 2.10, Ex. 2.5, 2.8, 2.19<br>
12/22: Chap 6 Direct Methods for Solving Linear Systems |
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第16週 |
12/27,12/29 |
12/27: Eigenvalue and Singular Values (lab) (a) [M] Sections 10.1-10.3, 10.11 (b) [M] Exercise 10.14, <font color=red>Quiz 6</font><br>
12/29: Chap 7 Jacobi and Gauss-Seidel Methods |
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第17週 |
1/03,1/05 |
01/03: Chap 7 Lab: Jacobi and Gauss-Seidel Methods<br>
01/05: Chap 7 <font color=red>Quiz 7 (take home)</font> |
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第18週 |
1/12 |
01/10: <font color=red>期末考</font> |
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