課程大綱及進度表
開課系所
應數碩開課學年
101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，微分方程
學分數
3開課教師
侯世章電話
65139Office Hours
預約課程概述
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 Equationso Bisection Method o Newton’s Method o Secant Method
o Fixed Points and Functional Iteration
o Computing Zeros of Polynomicals
Approximationg Functions o Polynomial Interpolation
o Divided Difference o Hermite Interpolation o Spline Interpolation o Best Approximation:
Least-Squares Theory
o Best Approximation: Chebyshev Theory
o Trigonometric Interpolation o Fast Fourier Transform
Numerical Differentiation and Integration
o Numerical Differentiation and Richardson Extrapolation o Numerical Integration Based on
Interpolation o Gaussian Quadrature
Numerical Solution of Ordinary Differential Equations
o Taylor Series Method o Runge-Kutta Methods o Multistep Methods
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 Linear Differntial Equations
o Stiff Equations
參考書目
Numerical Analysis, by Kincaid andCheney
Numerical Analysis, by Burden and Faires
Elementary Numerical Analysis ，by Atkinson and Han
