課程大綱及進度表
開課系所 應數碩
開課學年
98
開課學期
1
課程名稱(中文) 數值分析(一)
課程名稱（英文）
NUMERICAL ANALYSIS(1)
課程碼
L150710
分班碼
先修科目或先備能力 微積分，線性代數，高等微積分
學分數
3
開課教師 侯世章
e-mail [email protected]
電話
65139
Office Hours By Appointment
課程概述 這個課程主要是從數學的觀點來 探討科學計算碰到的演算法。
教學目標 讓學生理解各個數值方法背後的 數學理論
授課課程大綱明細 Solution of Nonlinear Equations
o (第一週)
o Bisection Method o Newton’s Method o (第二週)
o Secant Method
o Fixed Points and Functional Iteration
o (第四週)
o Computing Zeros of Polynomicals
Approximationg Functions o Polynomial Interpolation o (第六週)
o Divided Difference o Hermite Interpolation o Spline Interpolation o (第九週)
o Best Approximation:
Least-Squares Theory o (第十週)
o Best Approximation: Chebyshev Theory
o (第十一週)
o Trigonometric Interpolation o Fast Fourier Transform
Numerical Differentiation and Integration
o (第十二週)
o Numerical Differentiation and Richardson Extrapolation o Numerical Integration Based on
Interpolation o Gaussian Quadrature
Numerical Solution of Ordinary Differential Equations
o (第十四週)
o Taylor Series Method o Runge-Kutta Methods o Multistep Methods
o (第十六週)
o Local and Global Errors:
Stability
o Boundary Value Problems:
Shooting Methods
o Boundary Value Prolems: Finite Difference Methods
o Boundary Value Problems:
Collocation Methods o (第十八週)
o Linear Differntial Equations o Stiff Equations
參考書目 Numerical Analysis, by Kincaid and
Cheney
Elementary Numerical Analysis ，by Atkinson and Han
課程要求
評量方式 期中和期末考各佔 5%
課程網址 助教資訊 備註
