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
105-2 
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
3.0 
全/半年
半年 
必/選修
選修 
上課時間
星期二7,8,9(14:20~17:20) 
上課地點
應233 
備註
本課程以英語授課。
總人數上限:54人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1052AM7008_ 
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課程概述

THIS IS THE FIRST COURSE IN NUMERICAL ANALYSIS FOR GRADUATE STUDENTS. THE MAIN OBJECTIVES OF THIS COURSE INCLUDE:
(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;
 

課程目標
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

 
課程要求
HOMEWORKS (60%); FINAL EXAM (%40) 
預期每週課後學習時數
 
Office Hours
 
參考書目
PARVIZ MOIN “FUNDAMENTALS OF ENGINEERING NUMERICAL ANALYSIS”, CAMBRIDGE UNIVERSITY PRESS

 
指定閱讀
 
評量方式
(僅供參考)
   
課程進度
週次
日期
單元主題
第1週
2/21  Interpolation 
第3週
3/07  Numerical differentiation 
第4週
3/14  Numerical integration 
第5週
3/21  Numerical Integration 
第6週
3/28  Numerical solution of ODE 
第8週
4/11  Numerical solution of ODE 
第9週
4/18  Numerical solution of ODE 
第10週
4/25  Numerical solution of ODE 
第12週
5/09  Numerical solution of PDE 
第13週
5/16  Numerical solution of PDE 
第14週
5/23  Numerical solution of PDE