課程資訊
 課程名稱 應用數值方法Applied Numerical Methods 開課學期 107-1 授課對象 工學院  應用力學研究所 授課教師 周逸儒 課號 AM7190 課程識別碼 543 M1160 班次 學分 3.0 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109 備註 總人數上限：60人 Ceiba 課程網頁 http://ceiba.ntu.edu.tw/1071AM7190_ 課程簡介影片 核心能力關聯 核心能力與課程規劃關聯圖 課程大綱 為確保您我的權利,請尊重智慧財產權及不得非法影印 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 指定閱讀 待補 參考書目 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 Interpolation 第2週 Numerical differentiation 第3週 Numerical integration 第4週 Numerical integration 第5週 Numerical solutions of ODE 第6週 Numerical solution of ODEs 第7週 Numerical solution of ODEs 第9週 Numerical solution of PDEs 第10週 Numerical solution of PDEs 第11週 Numerical solutions for PDE