課程大綱

課程資訊

課程名稱

計算數學導論
INTRODUCTION TO COMPUTATIONAL MATHEMATICS

開課學期

97-1

授課對象

理學院數學研究所

授課教師

薛克民

課號

MATH5407

課程識別碼

221 U4280

班次

學分

全/半年

半年

必/選修

選修

上課時間

星期一7,8(14:20~16:20)星期三7,8(14:20~16:20)

上課地點

普204普502

備註

總人數上限：50人

Ceiba 課程網頁

http://ceiba.ntu.edu.tw/971cmath

課程簡介影片

核心能力關聯

本課程尚未建立核心能力關連

課程大綱

為確保您我的權利,請尊重智慧財產權及不得非法影印

課程概述

This is an elementary level of the course for computational mathematics.
The main topics we are going to discuss in this semester will include
1. Solving linear systems
2. Root finding
3. Interpolation
4. Quadrature
5. Discrete Fourier methods
6. Monte Carlo methods

課程目標

The aim of this course is to introduce some basic numerical techniques that can
be used to find approximate solutions of problems where analytical solutions do not
exist or are not readily obtainable. We will focus on the theoretical analysis as
well as on the development of practical algorithms. On the latter part,
the students are required to write their own computer programs and do experiments with it for
the numerical algorithms taught in the course.

課程要求

微積分, 線性代數

預期每週課後學習時數

Office Hours

每週二 11:00~12:00

指定閱讀

參考書目

1. Numerical Mathematics and Computing, W. Cheney and D. Kincaid, Brooks/Cole
2005
2. Numerical Computing with Matlab, C. B. Moler, SIAM 2004
3. Scientific Computing: An Introductory Survey, M. T. Heath, McGraw-Hill

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	期中考	25%	考試時間: 11/10, 2008
2.	期末考	25%	考試時間: 01/14, 2009
3.	作業	50%	指定頻率: 約每兩周一次

課程進度

週次	日期	單元主題
第1週	09/17	Exercise session (Condensed Matter Bldg. F3)
第1週	09/15	Course outline, Introduction to Matlab, Introduction to Latex
第2週	09/24	Exercise session (Condensed Matter Bldg. F3)
第2週	09/22	Source of errors
第3週	09/29	No class due to typhoon Jangmi
第3週	10/01	Linear systems solvers: Gaussian elimination & LU factorization
第4週	10/08	Exercise session (Condensed Matter Bldg. F3)
第4週	10/06	Linear systems solvers: implementation and stability issues
第5週	10/13	Stability of Gaussian elimination (cont.) & Nonlinear equations solvers: Scalar equations
第5週	10/15	Exercise session (Condensed Matter Bldg. F3)
第6週	10/22	Exercise session (Condensed Matter Bldg. F3)
第6週	10/20	Nonlinear equations solvers: System of equations
第7週	10/27	Unconstrained optimization: golden section search, Newton's, and BFGS methods
第7週	10/29	Exercise session (Condensed Matter Bldg. F3)
第8週	11/05	Exercise session (Condensed Matter Bldg. F3)
第8週	11/03	Unconstrained optimization: steepest descent method and line search
第9週	11/10	Function approximation: Polynomial interpolation
第9週	11/12	Midterm exam (computer programming): 計中312 & 凝態3F 14:20-18:00
第10週	11/17	Barycentric Lagrange interploation
第10週	11/19	Runge phenomena and Splines
第11週	11/26	Exercise session (Condensed Matter Bldg. F3): Make comments on programming issues for HW 5
第11週	11/24	Piecewise cubic Hermite interpolation polynomial
第12週	12/03	Pade approximant & Matlab demo for numerical differentiation formula
第12週	12/01	Numerical differentiation after Fornberg's work
第13週	12/08	Numerical integration: Newton-Cotes, Clenshaw-Curtis, & Gauss quadrature formulas
第13週	12/10	Exercise session (Condensed Matter Bldg. F3): HW 6 review
第14週	12/15	Gauss quadrature formula & Richardson extrapolation
第14週	12/17	Numerical ODE solvers
第15週	12/24	Exercise session (Condensed Matter Bldg. F3): HW 7 review
第15週	12/22	Numerical ODE solvers: LMM & zero stability
第16週	12/31	Fast Fourier transform
第16週	12/29	Absolute stability for LMM and Runge-Kutta method. Embedded method
第17週	01/07	BVPs for ODES & final exam. overview
第17週	01/05	Fast Fourier transform & its applications
第18週	01/14	Final exam (computer programming): 計中312 & 凝態3F 14:20-19:00