計算數學

Computational Mathematics

學期

108-1

學分

0 學分

當期課號

0907

永久課號

DAM3201

開課單位

自主學習課程

授課教師

林得勝

類別

必修

概述

To have basic knowledge of numerical analysis, algorithm and programming skills. 試讀:https://youtu.be/iyiJ7eZY2PU

先修科目

Calculus; Linear algebra

備註

無備註

教學方式

線下測驗時間: 2019/10/19 (六), 2019/12/21(六), 2020/2/22(六), 2020/5/16(六), 2020/7/18(六)

評分方式

線上 quizzes (10%) 線下: 1st Exam[Ch1-4] (45%) 2nd Exam[Ch5-7] (45%) 線下的 1st and 2nd exam 均允許多次測驗, 各取測驗分數的平均值.

課程大綱

Solution of nonlinear equations

Bisection, Newton's, Secant methods and fixed point iteration.
Solving system of linear equations

LU and Cholesky factorization; Gaussian elimination; Solution of equations by iterative methods; Steepest descent and conjugate gradient methods.
Selected topics in numerical linear algebra

Matrix eigenvalue problem: Power method
Approximating Functions

Polynomial interpolation; Hermite interpolation; Spline interpolation; Best approximation: Least-square and Chebyshev theory.
Numerical Integration

Numerical integration based on interpolation; Gaussian quadrature.
Mathematical Preliminaries

Taylor's Theorem; Order of convergence.

週次計畫

教師未提供此項資料

教科書

Numerical Analysis: Mathematics of Scientific Computing (3rd Edition) by David Kincaid and Ward Cheney

Office Hours