課程大綱及進度表
開課系所 數學三
開課學年 98
開課學期 1
課程名稱(中文) 數值分析導論
課程名稱（英文） INTRODUCTION TO NUMERICAL ANALYSIS
課程碼 C133900
分班碼
先修科目或先備能力 微積分
學分數 3
開課教師 侯世章
e-mail schou@mail.ncku.edu.tw
電話 65139
Office Hours By Appointment
課程概述 介紹一些數值分析的基本概念，並 強調 Matlab 程式寫作。
教學目標 期能對數值方法有基本的認識，並 對 Matlab 有初步的了解。
授課課程大綱明細
• (第一週)• Matlab 簡介與實作
• (第三週)
• Floating Point Numbers
• (第四週)
• Root Finding
o Bisection Method o Newton’s Method
o Secant Method o (第五週)
o Fix point Method
• Interpolation and Approximation o Polynomial Interpolation o (第六週)
o Error in Polynomial Interpolation o Spine Functions o (第七週)
o The Best Approximation o Chebyshev Polynomials o A Near-Minimax
Approximation o (第八週)
o Least Square Approximation
• Numerial Integration and Differentiation
o (第九週)
o The Trapzoidal and Simpson’s Rule o Error Formulas o Gaussian Numerical
Integration o (第十週)
o Numerical Differentiation
• Solution of Linear Equations o Matrix Arithematics o (第十一週)
o Gaussian Elimination
o (第十二週)
o The LU Factorization o Error in Solving Linear
Systerms o (第十三週)
o Iteration Methods
• Numerical Linear Alegebra o (第十四週)
o Least Square Data Fitting o The Eigenvalue Problem o (第十五週)
o Nonlinear System
• Ordinary Differential Equation o Introduction
o (第十六週) o Euler’s Method
o Convergence Analysis of Euler’s Method
o Taylor and Runge-Kutta Methods
o (第十七週)
o Multistep Methods o System of Differential
Equations o (第十八週)
o Finite Differece Method for Two-Point Boundary Value Problems
參考書目
Elementary Numerical Analysis ，by Atkinson and Han Numerical Analysis, by Kincaid and Cheney
