|
課程名稱 |
工程科學數值方法
Numerical Methods for Engineering Science |
|
開課學期 |
108-2 |
|
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/1082AM7008_ |
|
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 |
|
|
參考書目 |
PARVIZ MOIN “FUNDAMENTALS OF ENGINEERING NUMERICAL ANALYSIS”, CAMBRIDGE UNIVERSITY PRESS |
|
指定閱讀 |
待補 |
|
評量方式
(僅供參考) |
|
|
週次 |
日期 |
單元主題 |
|
第1週 |
3/03 |
Interpolation |
|
第2週 |
3/10 |
Numerical differentiation-Finite difference |
|
第3週 |
3/17 |
Numerical integration |
|
第4週 |
3/24 |
Numerical integration - continued |
|
第5週 |
3/31 |
Numerical solutions to ODEs |
|
第6週 |
4/07 |
Numerical solutions to ODEs |
|
第7週 |
4/14 |
Numerical solutions to ODEs |
|
第8週 |
4/21 |
Numerical solutions to PDEs |
|
第9週 |
4/28 |
No class |
|
第10週 |
5/05 |
Numerical solutions to PDEs |
|
第11週 |
5/12 |
Numerical solutions to PDEs |
|