同济大学数值计算课件

3.numerical computing of random quantities Monte Carlo methods and simulation
四、How ห้องสมุดไป่ตู้o learn?



Mathematics is classified into three categories: Baby mathematics + Cemetery mathematics + Church mathematics Baby mathematics emphasizes on new ideas Cemetery mathematics emphasizes on proof Church mathematics emphasizes on comment
high performance computer platform (Jun.18, 2012) --- status quo

No.1 in globe(1) Sequoia(红杉) US 16.32 Pflops/s（
10
）
15

No.1 in China (5) Tianhe-1A(天河) 2.56 Pflops/s
1.
Matlab: Matrix Laboratory, 1970s Variables （变量） Variables name: start with a letter and can have a length of up to 31 characters. Type: matrices.
2. Arrays and Matrices （数组和矩阵） Row vector:



Design: using CAD software to design to outer curve of car or plane. The two preliminary factor: beautiful smaller drag force Computing: using computational air dynamics, obtaining the drag force of car or plane. Judgement: if the computed drag force > the required drag force, then repeat step (1),(2); else exit from the iteration loop, stop.
A [1 2 3]
Column vector:
A [1 2 3]

Column vector:
A [1; 2;3]
A [1 2 3]'

Matrix:
1 2 3 A 4 5 6 7 8 9
A [1 2 3 456 7 8 9]
一、The position of scientific computing
1.


In scientific research The third eye of the modern scientific research. The three methods of the modern scientific research: Theory Experiment Scientific computing
C A B
C A* B
C A.* B
C A \ B (C=A B)
-1
6. Functions in Matlab
C sqrt ( x)
C sin( x)
C log( x)
7. M-files
Two kinds of commands: an interactive mode, ( by typing each command from the keyboard---extended calculator) A Matlab program, a script file, or M-file.
Numerical method and computer algorithm
陈素琴 同济大学数学系
References:
1. Applied Numerical Methods for Engineering and Scientists, Singiresu S.Rao, Prentice Hall, Upper Saddle River, NJ07458, 2002. 2. Numerical Analysis, David Kincaid, Ward Cheney, Brooks/Cole Publishing Company, 1996.
2. In engineering and industrial application ----becoming wider.
The conclusion comes from IT TOP 500.
二、The future of scientific computing

is beautiful but the path is full of difficulties
References:
3. MATLAB循序渐进,主编李胡锡,姜红, 上海交通大学出版社,1997. 4.精通MATLAB 6，[美]D.Hanselman, B.Littlefield 著，张航， 黄攀，译， 清华大学出版社，2002。
What is it?
The course involves the two parts: 1. Algorithms: ideas for obtaining numerical solutions to various mathematical problems; 2. The computer program: to communicate the algorithms to computer, FORTRAN(C), or Matlab.

I can compute traces of planets, but I can‟t imagine madness of human being. ---------------Newton
三、outline of the course

1.
the three preliminary problems of numerical computing: the problem of representing functions within a computer Interpolation (4) 插值 Approximation by Spline Functions (7) 样条 近似 Smoothing of Data and the method of least squares (10) 数据光滑和最小二乘方法
二、The future of scientific computing

Sep. 1996, America DOE proposed “ASCI” plan（加速战略计算创新） The object of ASCI: In computer platform with 1014 Flop/s （ 100万亿次/秒）, 3D complete physics processing, complete scalable, high precision scientific simulation computing will be done.
Importance of scientific computing:


Foreign university, since 1970. Chinese university, since 1990. Tongji University, since 1999.
一、The position of scientific computing
四、How to learn?

The teaching style: idea + practice Point policy : exam + three projects 70 points + 30 points
五、Relation between Matlab and Numerical method
Climate Prediction
The three kernel problems in scientific computing:

suitable mathematical modeling high efficiency numerical method high performance computer platform http://www.top500.org

No.1 in Shanghai(94) Magic cubic( 魔方) 0.18 Pflops/s
high performance computer platform --- Histoty


Top1 (Jun.18, 1993)-------60GFlops Top1 (Jun.18, 2012)-------16,324,751GFlops 19 years--------2.7e5

Let us image the style of scientific research after “ASCI” plan is finished: (As an example, car‟s or plane‟s outer curve design)
An iterative process with three steps
3.Arrays with Special Structure
A 1:10
A 2: 0.5: 4
4. Special Matrices
A eye(3)
A ones(3, 4)
A zeros(2, 4)
5. Matrix Operations
C A B
二、The future of scientific computing

Origin: scientific computing method will take place experiment method in scientific research.
二、The future of scientific computing
M-file Example
%m-file to compute Fibonacci numbers f=[1 1]; i=1; While f(i)+f(i+1)<1000 f(i+2)=f(i)+f(i+1); i=i+1; end
8. Plotting of Graphs
x=0:0.2:3; y=x.^2+1; plot(x,y,‟g*--„)

Relation between Calculator and the basic arithmetic operations addition, subtraction, multiplication, division.
Ax b
x A\b
Chapter 1 Basics of Matlab
2. numerical computing of certain quantities
Differentiation (4) 微分 Integration (5) 积分 Ordinary Differential Equations (8) 常微分方程 Systems of Linear Equations (6) 线性方程组 Locating roots of equations (3)方程求根