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
102-2 
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233 
備註
總人數上限:60人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1022AM7008_ 
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
  Introduction & Interpolation 
第2週
  Numerical Differentiation-Finite Differences 
第3週
  More on Finite Differences &
Numerical Integration 
第4週
  Numerical Integration 
第5週
  No class 
第6週
  Numerical solution of ODEs 
第7週
  Numerical Solution for ODEs (continued) 
第8週
  Numerical Solution for ODEs(continued) 
第9週
  Numerical Solution for ODEs(continued) 
第10週
  Numerical Solution for ODEs(continued) 
第11週
  Numerical Solution for PDEs 
第12週
  Numerical Solution for PDEs(continued) 
第14週
  Numerical Solution for PDEs(continued) 
第15週
  Numerical Solution for PDEs(continued) -- Elliptic Equation 
第16週
  Review