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課程名稱 |
應用數值方法
Applied Numerical Methods |
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開課學期 |
107-1 |
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授課對象 |
工學院 應用力學研究所 |
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授課教師 |
周逸儒 |
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課號 |
AM7190 |
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課程識別碼 |
543 M1160 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期二6,7,8(13:20~16:20) |
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上課地點 |
應109 |
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備註 |
總人數上限：60人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1071AM7190_ |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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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;
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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
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課程要求 |
HOMEWORKS (60%); FINAL EXAM (%40) |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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參考書目 |
PARVIZ MOIN “FUNDAMENTALS OF ENGINEERING NUMERICAL ANALYSIS”, CAMBRIDGE UNIVERSITY PRESS
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
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Interpolation |
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第2週 |
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Numerical differentiation |
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第3週 |
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Numerical integration |
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第4週 |
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Numerical integration |
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第5週 |
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Numerical solutions of ODE |
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第6週 |
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Numerical solution of ODEs |
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第7週 |
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Numerical solution of ODEs |
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第9週 |
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Numerical solution of PDEs |
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第10週 |
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Numerical solution of PDEs |
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第11週 |
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Numerical solutions for PDE |
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