Numerical Analysis (I)

數值分析

Fall 2006

*Reading  **Home Work  ***Programming  

 

Lecture 1.  1D Poisson's Equation and Finite Difference Method   (p. 1)

Lecture 2.  Gaussian Elimination 1*** (pdf*) Ax=b   (p. 4)

Lecture 3.  Jacobi’s Method (JM)***  (pdf*) Ax=b    (p. 8)

Templates for the Solution of Linear Systems   (pdf)

l          Ferng’s Lecture Notes on Iterative Methods*

Lecture 4.  Gauss-Seidel Method (GS)*** Ax=b    (p. 13)

Lecture 5.  The Successive Overrelaxation Method (SOR)*** Ax=b    (p. 16)

Lecture 6.  The Symmetric Successive Overrelaxation Method (SSOR)*** Ax=b    (p. 18)

Lecture 7.  Conjugate Gradient Method (CG)* (CG.pdf*) Ax=b    (p. 22)

l          An Introduction to the Conjugate Gradient Method Without the Agonizing Pain by Jonathan Richard Shewchuk.

Lecture 8.  Finite Element Method for 1D Poisson’s Problem*  Ax=b    (p. 39-49)

Lecture 9.  2D and 3D Poisson’s Equation

 

 

Topics Covered Above

I.                   Numerical Methods for PDEs

l          Finite Element Method (FEM)   (pdf*)

II.                Numerical Methods for Solving Ax=b

III.             Numerical Linear Algebra

IV.              Mathematical Sciences Digital Library

V.                 Appendices

l          SI-Units (Units)

l          The Greek Alphabet

l          The Free Dictionary