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課程名稱 |
數值方法
Numerical Methods |
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開課學期 |
105-2 |
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授課對象 |
工學院 工程科學及海洋工程學系 |
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授課教師 |
張恆華 |
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課號 |
ESOE2024 |
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課程識別碼 |
505 29120 |
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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 |
必帶 |
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上課時間 |
星期四2,3,4(9:10~12:10) |
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上課地點 |
工科204 |
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備註 |
限本系所學生(含輔系、雙修生)
總人數上限：51人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1052ESOE2024_nm |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
本課程介紹基礎的數值方法並強調演算法設計、分析及其實用。我們將探討一些基本和常見的數值分析技術，諸如誤差分析、非線性方程的根求解、線性代數方程求解、內插法、回歸分析、數值微分與積分、常微分方程的數值解。本課程將使用MATLAB來撰寫設計的演算法和數值方法。
This course introduces the students the fundamental numerical methods with emphasis on algorithm construction, analysis, and implementation. Common techniques will be covered such as error analysis, roots of nonlinear equations, solutions of linear algebraic equations, interpolation, regression analysis, numerical differentiation, numerical integration, and numerical solution of ordinary differential equations. We will implement the designed algorithms and methods with MATLAB. |
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課程目標 |
本課程的主旨乃是介紹數值分析方法在工程及科學問題上的運用。課程目標在提昇學生使用分析工具與數值方法進而解決真實問題的能力，並學會演算法開發與程式撰寫在工程及科學上的應用。
The essential goal of this course is to introduce numerical methods used for the solution of engineering and scientific problems. This course aims at enhancing the students’ ability to address realistic problems using analytical tools and numerical methods with emphasis in algorithm development, programming as well as applications in engineering and science. |
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課程要求 |
修課學生需修畢微積分和具備程式語言(e.g., C, Java, Matlab, etc.)撰寫能力。
The students are expected to complete Calculus and familiar with Programming Language either in C, Java, or Matlab. |
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預期每週課後學習時數 |
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Office Hours |
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參考書目 |
Numerical Methods for Engineers and Scientists: An Introduction with Applications Using MATLAB, Amos Gilat and Vish Subramaniam, John Wiley & Sons, 2008.
Numerical Analysis, 8th edition, Richard L. Burden and J. Douglas Faires, Brooks/Cole, 2005. |
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指定閱讀 |
待補 |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
2/23 |
Course Overview and MATLAB Fundamentals
Reading ‐> S.C.: pp. 1~19, 24~29 |
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第2週 |
3/02 |
Error Analysis and MATLAB Operations
Reading ‐> S.C.: pp. 88~99, 30~35 |
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第3週 |
3/09 |
Truncation Errors and MATLAB Graphics
Reading ‐> S.C.: pp. 100~120, 35~44 
Distribute: HW1 |
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第4週 |
3/16 |
Programming with MATLAB
Reading ‐> S.C.: pp. 48~82 
Distribute: HW2 |
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第5週 |
3/23 |
Roots: Bracketing Methods
Reading ‐> S.C.: pp. 126~147
Distribute: HW3
Due: HW1 |
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第6週 |
3/30 |
Roots: Open Methods
Reading ‐> S.C.: pp. 151~177
Due: HW2 |
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第7週 |
4/06 |
Optimization and Matrix Algebra
Reading ‐> S.C.: pp. 182~199, 209~225
Distribute: HW4
Due: HW3 |
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第8週 |
4/13 |
Gauss Elimination and LU Factorization
Reading ‐> S.C.: pp. 229~250, 254~266 |
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第9週 |
4/20 |
Midterm
Due: HW4 (Sunday night) |
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第10週 |
4/27 |
Matrix Condition and Iterative Methods
Reading ‐> S.C.: pp. 268~280, 284~293
Distribute: HW5 |
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第11週 |
5/04 |
Newton‐Raphson Method and Eigenvalues
Reading ‐> S.C.: pp. 293~300, 303~316
Distribute: HW6 |
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第12週 |
5/11 |
Linear Regression and Polynomial Regression
Reading ‐> S.C.: pp. 324~356, 361~365
Distribute: HW7
Due: HW5 |
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第13週 |
5/18 |
General Linear Least Squares and Interpolation
Reading ‐> S.C.: pp. 365~375, 405~417
Due: HW6 |
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第14週 |
5/25 |
Lagrange Interpolation and Piecewise Interpolation
Reading ‐> S.C.: pp. 417~425, 429~440
Distribute: HW8
Due: HW7 |
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第15週 |
6/01 |
Natural Cubic Splines and Numerical Integration
Reading ‐> S.C.: pp. 440~456, 462~482 |
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第16週 |
6/08 |
Numerical Integration of Functions
Reading ‐> S.C.: pp. 482~492, 497~
Due: HW8 |
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第17週 |
6/15 |
Numerical Differentiation |
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第18週 |
06/22 |
Final |
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