數值分析.PDF

數值分析 Numerical Analysis 3 學分 姓名 ： 學號： 授課教師 ：吳俊概 目錄 第 0章 基礎 介紹(Preliminaries) ……………………………………………….. 2 第 1章 非線性方程式之求解(Solving Nonlinear Equations) ………………….. 10 第 2章 聯立方程式之求解(Solving Sets of Equations) ………………..………28 第 3章 內插與曲線配適 (Interpolation and Curve Fitting) ……………….…….. 53 第 4章 函數之近似(Approximation of Functions) …………………………….. 80 第 5章 數值微分與積分 (Numerical Differentiation and Integration) …………….. 96 第 6章 常微分方程式之求解 (NumericalSolutionofOrdinaryDifferentialEquation) …..…121 0 Preliminaries ‧This book teaches ( 本課程介紹) 1) how a computer can be used to solve problems that may not be solvable by the techniques that are taught in most calculus courses. (如何利用電腦來求解 以前不方 便 求解的問題) 2) how those problems that you may have solved before can be solved in a different way. (如何用不同的方式來求解以前解過的問題) 0.1 Analysis Versus Numerical Analysis (分析與數值分析之差異) ‧The word analysis (分析) in mathematics usually means to solve a problem through equations (使用方程式來求解問題的答案). The solving procedures may include algebra, calculus, differential equations, or the like. (求解過程可能用到代數 、微積分 、微分方程 式等運算工具) Numerical analysis 數值分析( ) is similar in that problems solved, but the only procedures that are used are arithmetic: add, subtract, multiply, divide and compare. (求解 過程中只用到算數運算 ：加 、減 、乘、除及比較 ) Since the arithmetic operations are exactly those that computers can do, numerical analysis and computers are intimately related.數值分析與電腦息息相關( ) ‧Differences between analytical solutions解析解( ) and numerical solutions 數值解( ): 1) An analytical solution is usually given in terms of mathematical functions. The behavior and properties