Numerical Methods and Applications
數值方法與應用

2011/2 – 2012/6/21

http://www.math.nuk.edu.tw/jinnliu/teaching/cs97/J01.gif
Jinn-Liang Liu

新竹教育大學應數系

Read C++ Language Tutorial and write programs.

課程大綱 Topics

(Lecture or Reading Order: 1, 2, …, 11.)

I.            Overview
  1.  Ion Channel
      (Nervous system (0:50) (Recital), Action Potentials (3:24), Potassium Channel (1:42))

II.         Numerical Methods
  2.  1D Poisson’s Problem and Finite Difference Method 
  3.  Jacobi Method (Read Lecture 2 in 2010F數值分析(I), P4Ab.cpp, P5Ab.cpp. Do Projects 3.1 and 3.2.)
  4.  Conjugate Gradient Method (Do Project 7.1.)
  5.  Newton and Monotone Iterative Methods  (Do Project 9.1.)

III.       Mathematical Models with Fundamental Physics
  6.  Poisson’s Equation in Electrostatics  (Poisson)
  7.  Convection-Diffusion-Reaction Model  (CDR)
  8.  Poisson-Nernst-Planck (PNP) Model
  9.  VMD: 2011-VMD-Tutorial, 2009-VMD-Tutorial-KcsA, 2011-VMD-Steps-GA

 

 

Your Check List (Name:                    , ID#                   )

Assignments

Finish Dates

Signature

1.  Ion Channel    (R)

 

 

2.  Recital            (R)

 

 

3.  Lecture 1        (R)

 

 

4.  Lecture 2        (R)

 

 

5.  Lecture 3        (R)

 

 

6.  Project 3.1      (P)

 

 

7.  Project 3.2      (P)

 

 

8.  Lecture 7        (R)

 

 

9.  Project 7.1      (P)

 

 

10.  Lecture 9        (R)

 

 

11.  Project 9.1      (P)

 

 

12.  Poisson           (R)

 

 

13.  CDR               (R)

 

 

14.  PNP                (R)

 

 

15.  Report I         (W)

 

 

16.  Report II       (W)

 

 

17.  Final Report  (W)

 

 

R: Reading, P: Programming, W: Writing. jinnlliu

 

 

 

教學目標 Objectives

·        Learn basic Numerical Methods for Partial Differential Equations (PDEs)

·        Learn basic Numerical Methods for Linear Algebra

·        Learn basic Physics behind PDEs

·        Learn Programming in Scientific Computing

授課方式 Teaching Style

·        Regular Lecturing

評分標準 Grading Policy

·        Project 50% Report 50%

教科書 Texts

·        Jinn-Liang Liu, Lecture Notes on Numerical Methods for Partial Differential Equations, 2010.

·        Juan Soulie, C++ Language Tutorial, 2007.

閱讀文獻 References

·        R. J. LeVeque, Finite Difference Methods for Differential Equations, 2005.  LeVeque-FDM-2005.pdf (Chapters 1-5)

·      E. Suli, Finite Element Methods for Partial Differential Equations, 2007. Suli-FEM-2007.pdf

·      R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Donato, J. Dongarra , V. Eijkhout, R. Pozo, C. Romine, and H. Van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition, SIAM, 1994, Philadelphia, PA.  Templates for the Solution of Linear Systems (book)  

 

2011/2-2011/6

Project 2. (Due 6/7)
Project 1. (Due 3/29) Do Project 9.1 in Lecture 9.

Report 2. (Due 6/14)
Report 1. (Due 2011/4/19)
Submit all Reports and Projects via email.
(Email標題: NameR1 or NameP1 etc. )

Report

研究計畫名稱：

Numerical Simulation of Biological Ion Channel by Quantum Hydrodynamic Model

 

研究計畫內容：

(一)摘要

(二)研究動機

(三)研究問題與文獻回顧

(四)研究方法與步驟

(五)需要學習與請教之內容

(六)預期結果
(七)參考文獻