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 3 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 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 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