一、課程說明(Course Desc<x>ription) 
<br>
<br>This is the second semester course of the Numerical Analysis.
<br>
<br>Students are assumed to have taken the course "Numerical Analysis I" and learned 
<br>the necessary knowledge.  
<br>
<br>As stated in the preface of the text book, the goal of this course is 
<br>
<br>"to introduce modern approximation techniques; 
<br> to explain how, why, and when they can be expected to work; and 
<br> to provide a foundation for further study of numerical analysis and scientific 
<br>computing" 
<br>
<br>本課程使用 atlab 講解所教授的 algorithms，強調實際解題，用電腦找出答案。修課能精進
<br>matlab的功力。
<br>
<br>
<br>二、指定用書(Text Books) 
<br>none
<br>
<br>
<br>三、參考書籍(References) 
<br>1. Burden/ Faires/ Burden, Numerical Analysis, 10th ed., CENGAGE Learning, 2016
<br>2. Gilat/Subramaniam, Numerical Methods: An Introduction with Application Using 
<br>MATLAB 2en ed., (SI ed.), John Wiley & sons, 2011
<br>3. Kincaid/ Cheney, Numerical Analysis: Mathematics of Scientific Computer 3rd 
<br>ed., American Mathematical Society, 2009
<br>
<br>
<br>四、教學方式(Teaching Method) 
<br>
<br>Three-hour lectures per week，板書上課。
<br>
<br>課程將使用 matlab 演示課堂上所學到的各種數值方法 
<br>
<br>
<br>五、教學進度(Syllabus) 
<br>
<br>1. chap 7: Iterative techniques in matrix algebra
<br>2. chap 8: Approximation theory
<br>3. chap 9: Approximating eigenvalues
<br>4. chap 10: Numerical solutions of nonlinear systems of equations
<br>5. chap 11: Boundary value problems for ordinary differential equations
<br>6. chap 12: Numerical solutions to partial differential equations
<br>
<br>詳細的課程內容及進度: 請參連結
<br>https://mx.nthu.edu.tw/~pyhsiao/2024/2024_ess415000/2024_ess415000.htm
<br>後面有 2022 授課進度。
<br>
<br>授課主題包含: steepest descent method，conjugate gradient method，power method，
<br>Schur decomposition, QR-decomposition, Householder’s reflection transformation，
<br>Singular value decomposition, fast Fourier transform，finite difference method 
<br>to solve ODE and PDE,  等等。
<br>
<br>
<br>六、成績考核(Evaluation) 
<br>
<br>Homework 30%, Midterm exam 35%, Final exam 35%, 點名(加分用)
<br>
<br>
<br>七、可連結之網頁位址 
<br>
<br>https://mx.nthu.edu.tw/~pyhsiao/2024/2024_ess415000/2024_ess415000.htm
<br>
<br>
<br>NB. 本課程無涉及AI使用