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課程名稱 (中文) 數值方法
(英文) Numerical Method
開課單位 化學工程學系
課程代碼 C4990
授課教師 陳泰祥
學分數 3.0 必/選修 選修 開課年級 大三
先修科目或先備能力:微積分、工程數學、程式語言、Excel軟體使用
課程概述與目標: 教導同學利用數值方法解決工程領域常見之數學問題,包括:微分,積分,線性及非線性方程式,常微分方程式,簡單篇為分方程式及最小平方法等.
本課程除介紹各種數值方法外,並注重誤差之判斷,邏輯能力訓練及程式之撰寫能力.
教科書 1.Chapra and Canale, "Numerical Methods for Engineers," 7/e, McGraw-Hill, 20152.陳友剛,數值方法,碁峰資訊
(所有學生均須有第一本教科書, 第2本自行決定是否需要)
參考教材 (1) Bilal M. Ayyub, Richard H. McCuen, “Numerical Methods for Engineers,” Prentice Hall.
(2) J. N. Sharma, “Numerical Methods for Engineers And Scientists,” Alpha Science International.
課程大綱 學生學習目標 單元學習活動 學習成效評量 備註
單元主題 內容綱要
1 Review of Programming and Software 1. Applied software
2. Excel
3. C++ programming
4. Sigmaplot
1. Applied software
2. Excel
3. C++ programming
4. Sigmaplot
 
2 Review of Programming and Software 1. Applied software
2. Excel
3. C++ programming
4. Sigmaplot
1. Applied software
2. Excel
3. C++ programming
4. Sigmaplot
 
3 Errors, Round-Off & Truncation errors 1.Error analysis
2.Significant figures
3.Round-off errors
4.Truncation errors
1.Error analysis
2.Significant figures
3.Round-off errors
4.Truncation errors
  • 作業
  •  
    4 Errors, Round-Off & Truncation errors 1.Error analysis
    2.Significant figures
    3.Round-off errors
    4.Truncation errors
    1.Error analysis
    2.Significant figures
    3.Round-off errors
    4.Truncation errors
     
    5 Roots of Equations 1.Graphical method
    2.Bisection method
    3.Newton method
    1.Graphical method
    2.Bisection method
    3.Newton method
  • 作業
  •  
    6 Roots of Equations 1.Graphical method
    2.Bisection method
    3.Newton method
    1.Graphical method
    2.Bisection method
    3.Newton method
     
    7 Roots of Equations 1.Graphical method
    2.Bisection method
    3.Newton method
    1.Graphical method
    2.Bisection method
    3.Newton method
     
    8 Linear Equations 1.Matrix inversion
    2.Gauss Elimination
    3.Special matrices
    1.Matrix inversion
    2.Gauss Elimination
    3.Special matrices
  • 上機測驗
  • 作業
  •  
    9 期中考 期中考 期中考
  • 期中考
  • 期中考 3 hr  
    10 Numerical Differentiation 1.Difference method
    2.High accuracy differentiation formula
    1.Difference method
    2.High accuracy differentiation formula
     
    11 Numerical Differentiation 1.Difference method
    2.High accuracy differentiation formula
    1.Difference method
    2.High accuracy differentiation formula
  • 作業
  •  
    12 Numerical Differentiation 1.Difference method
    2.High accuracy differentiation formula
    1.Difference method
    2.High accuracy differentiation formula
     
    13 Numerical Integration 1. Trapezoidal rule
    2. Simpson’s rule
    3. Romberg integration
    1. Trapezoidal rule
    2. Simpson’s rule
    3. Romberg integration
  • 作業
  •  
    14 Numerical Integration 1. Trapezoidal rule
    2. Simpson’s rule
    3. Romberg integration
    1. Trapezoidal rule
    2. Simpson’s rule
    3. Romberg integration
     
    15 Numerical Method for ODE 1.Euler's method
    2.Runge-Kutta method
    3.Shooting method for BVP
    1.Euler's method
    2.Runge-Kutta method
    3.Shooting method for BVP
  • 作業
  •  
    16 Numerical Method for ODE 1.Euler's method
    2.Runge-Kutta method
    3.Shooting method for BVP
    1.Euler's method
    2.Runge-Kutta method
    3.Shooting method for BVP
  • 作業
  •  
    17 Numerical Method for PDE 1.Difference method for PDE
    2.Transfer PDE to ODE system
    1.Difference method for PDE
    2.Transfer PDE to ODE system
  • 上機測驗
  • 作業
  •  
    18 期末考 期末考 期末考
  • 期末考
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    教學要點概述:
    教材編選: ■ 自編教材 ■ 教科書作者提供
    評量方法: 期末考:20%   期中考:20%   上機測驗:20%   作業:40%  
    教學資源: □ 教材電子檔 ■ 課程網站
    課程網站:網路硬碟2 社群分享 C4990
    扣考規定:http://eboard.ttu.edu.tw/ttuwebpost/showcontent-news.php?id=504