課程資訊
課程名稱
工程科學數值方法
Numerical Methods for Engineering Science 
開課學期
101-1 
授課對象
工學院  應用力學研究所  
授課教師
周逸儒 
課號
AM7008 
課程識別碼
543EM1110 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期二6,7,8(13:20~16:20) 
上課地點
應111 
備註
本課程以英語授課。
總人數上限:98人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1011Numerical_Method 
課程簡介影片
 
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課程概述

Course outline:
1. Interpolation (3 hrs)
(1) Lagrange Polynomials
(2) Polynomial interpolations; Splines

2. Numerical Differentiation (4 hrs)
(1) Construction of finite difference scheme, order of accuracy
(2) Modified wavenumber as a measure of accuracy
(3) Pade approximation
(4) Matrix representation of finite difference schemes

3. Numerical Integration (8 hrs)
(1) Trapezoidal rule; Simpson’s rule; error analysis and mid-point rule
(2) Romberg integration and Richardson’s extrapolation
(3) Adaptive quadrature; Gauss quadrature

4. Numerical Solution of Ordinary Differential Equations (10 hrs)
(1) Initial value problems; numerical stability analysis, model equation
(2) Accuracy; phase and amplitude errors
(3) Runge-Kutta type formulas, multi-step methods; implicit methods
(4) System of differential equations; stiffness
(5) Linearization for implicit solution of non-linear differential equations
(6) Boundary value problems, shooting, direct methods, non-uniform grids, eigenvalue problems

5. Partial Differential Equations (10 hrs)
(1) Finite-difference solution of partial differential equations
(2) Modified wavenumber and Von Neumann stability analysis, modified equations analysis
(3) Alternating direction implicit methods; non-linear equations; iterative methods for elliptic PDE’s
 

課程目標
(1) Development and applications of numerical methods when analytical techniques are not available;
(2) Development of a conceptual framework for analysis of methods to fix the problem;
(3) Discrete calculus and approximations;
(4) Tradeoffs between accuracy and computational cost;
 
課程要求
Homeworks (70%); Final exam (%30)  
預期每週課後學習時數
 
Office Hours
 
參考書目
 
指定閱讀
Parviz Moin “Fundamentals of Engineering Numerical Analysis”, Cambridge University press 
評量方式
(僅供參考)
   
課程進度
週次
日期
單元主題
第1週
9/11  Introduction & Interpolation 
第2週
9/18  Numerical Differentiation-Finite Differences 
第3週
9/25  More on Finite Differences &
Numerical Integration 
第4週
10/02  Numerical Integration 
第5週
10/09  Numerical Integration & Solving ODEs 
第6週
10/16  No class 
第7週
10/23  Numerical Solution for ODEs 
第8週
10/30  Numerical Solution for ODEs(continued) 
第9週
11/06  Numerical Solution for ODEs(continued) 
第10週
11/13  Numerical Solution for ODEs(continued) 
第11週
11/20  Numerical Solution for PDEs 
第12週
11/27  Numerical Solution for PDEs(continued) 
第14週
12/11  Numerical Solution for PDEs(continued) 
第15週
12/18  Numerical Solution for PDEs(continued) -- Elliptic Equation 
第16週
12/25  Review