MA8019: ADVANCED NUMERICAL ANALYSIS I, Fall 2024

Instructor: Prof. Suh-Yuh Yang (楊肅煜)

• Office: M315, Hong-Jing Hall 

• Phone: 03-4227151 ext. 65130

• E-mail address: syyang@math.ncu.edu.tw

• Homepage: http://www.math.ncu.edu.tw/~syyang/

Office Hours: Tuesday 10:00~12:00 am or by appointment, no teaching assistant! 

Prerequisites: Calculus, Linear Algebra and some knowledge of a high-level programming language (Fortran/C/C++), or software package Matlab: https://portal.ncu.edu.tw/ 校園授權軟體服務網裡面有關於Matlab的下載方式說明!       

Textbook: David Kincaid and Ward Cheney, Numerical Analysis: Mathematics of Scientific Computing, Third Edition, 2002, Brooks/Cole.

      http://www.ma.utexas.edu/CNA/NA3/index.html

Course Objective: This course introduces students with diverse backgrounds to the various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with careful proofs and scientific background.

General Information: This course will cover the following topics

• Mathematical preliminaries (Chapter 1)

• Computer arithmetic (Chapter 2)

• Solution of nonlinear equations (Chapter 3)

• Solving systems of linear equations (Chapter 4)

• Solving eigenvalue problems (Chapter 5)

Assignments: approximately every two weeks, will consist of theoretical problems or computer projects.

Course Transparency Set: (in PDF)

• syllabus and introduction

• mathematical preliminaries (taylor.m)

• computer arithmetic 

• nonlinear equations (polyzeros.m, functiongraph1.m, bisection.m, newton.m, comparisonnewton.m, comparisonFDnewton.m, comparisonsecant.m, homotopynewton.m) 

• linear equations

• eigenvalue problems