第 1 章綜觀 MATLAB

112/04/22 Puff! The magic dragon, live by the sea.

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第 1章綜觀 MATLAB


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Text book

• Introduction to Matlab 6 for Engineering• William J. Palm III• Mc Graw Hill

• Matlab 6 在工程上的應用 -Matlab 6.5 Update• 呂明和黃逸群譯• 普林斯頓國際有限公司 CG 001


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Program Langage

• Matlab ( 大小寫是有區分的 !)• Fortran• C++• Virtual Basic• Cobol• Pascal• …

user:


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windows

• Launch pad window 啟動台視窗• Command window 命令視窗• Command history window 命令記錄視窗• Editor/Debugger window• Graph window• Tool bar• Current directory


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Order of precedence

• P.10 examples• P.11 T1.1-1


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P.11 T1.1-1

• (a) 6+10/13+18/(5*7)+5*9^2• (b) 6*(35^(1/4))+14^0.35


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• format short• 1/7• format long• 1/7

• help• demo


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The assignment operator ( 指定運算子 ) or replacement operator ( 替換運算子 )

• x=3 ~ x3• x=x+2 ~ xx+2

• Error expression 6=x• x=6 is the right expression

• What about x=5+y ~ x5+y


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國中應用問題 p.12

• pie=3.1416;• r=8;• h=15;• V=pie*r^2*h;• V=V+0.20*V;• r=sqrt(V/(pie*h))• ans=


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Variable names

• <32 characters; begin with alpha..• e.g.

right expression: speed_12345wrong expression: 1aaaaa


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whos ( 暫存變數 )

• x=2; y=6+x; x=y+7• x=2; x=2, y=8; x=15, y=8

• who• whos • whos x• Exist (‘var1’) ~ 1 in use, 0 not exist


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Long statement …

• See (p.13)


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for previous statement modification

, , tab


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Smart recall

• volume=3*5• vol +


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editing

• Del, backspace• Ctrl+k, Esc ~ clear all line• Clear ~ clear all variables• Clear var1, var2,.. ~ clear the 2 variables• Kill


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Complex operation

• P.16,

s=3+7i; w=5-9i;w+sw*sw/s


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Menus & the toolbar

• The desktop menus• The File Menu in Matlab 6

set path• The Edit Menu in Matlab 6


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Computing with Matlab

• Arrays 內建函數 sin(x), cos(x), log(x), log10(x), exp(x), asin(x).


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Computing with Matlab

• x=[0 1 3 6]; y=[6 3 1 0];z=x+y=[6 4 4 6]

• u=[0:.1:10]; w=5*sin(u);u(7)w(7)length(w)length(u)


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Polynomial roots

• a=[1 –7 40 –34];roots(a)

• r=[1, 3+5i, 3-5i];poly(r)

• or poly([1, 3+5i, 3-5i])• See also fzero(.)


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Self testing

• u=[cos(0): 0.02: log10(100)]length(u)u(25)

• a=[1 6 -11 290]r=roots(a)b=poly(r)

• Check a & b, are they the same?


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Working with files

• I/O• Set path… /homework/• problem1.m1. Is ‘problem1’ a variable?2. Is ‘problem1’ a pre-constructed command?3. Is problem1.m in the present directory?4. Find it in the search path directory!


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Show the present working directory & *.m files

• pwd• dir C:\MATLAB\BIN• what C:\MATLAB\BIN

• pathtool• add path• rmpath


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Relational operators

• x=[6 3 9]• y=[14 2 9]• z=(x<y)• z=(x～ =y)• z=(x==y)• z=x(x>8)

• Boolean operator (‘yes’=1, ‘no’=0)


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Relational operators

• x=[6 3 9 11]• y=[14 2 9 13]• z=x(x<y)• 找出陣列 x 中每一個小於陣列 y 中相對元素所的相對元素 , 所得的陣列 z=[6, 11]


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找出陣列中不為零的元素的索引值• x=[-2, 0, 4]• y=find(x)

• y=[1 3]


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比較• x=[6 3 9 11]; y=[14 2 9 13]• z1=x(x<y); z2=y(x<y); z3=find(x<y); • z1• z2• z3• Length(z3) • z1, z2 give the values; while z3 give the

indices


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Example p.26

• A=[55, 62, 60, 61, 63, 65, 62, 59, 58, 56];• B=[54, 59, 62, 64, 68, 68, 62, 59, 57, 53];• when=find(A>60)• how_many1=length(when)• above=A(A>B)• how_many1=length(above)


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Self testing p.27

• Test by your own, not by computer!


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plot

• x=[0: 0.01:10];• y=sin(2*x);• plot(x,y), xlabel(‘x’), ylabel(‘sin(2x)’)

• Use help plot to understand the above statement! See also plot, label, title, gtext

• Graphic window


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Overlay plot 重疊繪圖• x=[0: .01: 5];• y=2*sqrt(x);• z=4*sin(3*x); • plot(x,y,x,z), xlabel('x'), gtext('y'), gtext('z')• gtext ~ 指定好游標位置按下滑鼠鍵 , 以放置 gtext 所要放置的文字• [u,v]=ginput(n) ~ 滑鼠點下的 n 個位置座標


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Overlay plot 重疊繪圖• x=[0: .01: 5];• y=2*sqrt(x);• z=4*sin(3*x); • plot(x,y,x,z), xlabel('x'), gtext('y'), gtext('z') • [u,v]=ginput(n)


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data marker

• x=[15: 2: 23];• y=[20 50 60 90 70];• plot(x,y,’+’,x,y), xlabel(‘x (seconds)’),

ylabel(‘y (volts)’)


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Plotting Polynomials

• a=[9, -5, 3, 7];• x=[-2: .01:5];• f=polyval(a,x); • plot(x,f), xlabel('x'), ylabel('f(x)'), grid

• f(x)=9x^3-5x^2+3x+7• find f(0), f(2), …,f(10)


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Self testing p.31

• Write down the statements on a blank paper, and try to use your brain & this book to ‘run’ this program!


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Linear Algebraic Equations

6x+12y+4z=707x-2y+3z=52x+8y-9z=64Ax=Bx=A\B• A=[6,12,4; 7,-2,3; 2,8,-9];• B=[70; 5; 64];• A\B• A/B


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Linear Algebraic Equations

6x+12y+4z=707x-2y+3z=52x+8y-9z=64Ax=Bx=A-1B therefore we use A\B• A=[6,12,4; 7,-2,3; 2,8,-9]; 3 by 3• B=[70; 5; 64]; 3 by 1• A\B• A/B


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Self testing p.32


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Other functions

• Statistics• Numerical analysis & Differential equations• Symbolic Processing


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Script files & the Editor/Debugger

• 1. Direct command ~ 互動模式• 2. Script files


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2 types of M-files

• 1. Script files (global variables 全域變數 )• 2. Function files (local variables 局部變數 )


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有效的使用草稿檔• P.35 1. kscript.m ~ start with alph.2. kscript should not be the same as any one of t

he the global variables in this script file.3. exist(‘kscript’)4. who5. type kscript


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除錯• 適時去除程式敘述末端的分號


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Programming style

1. Comment section• (a) filename & keywords in the 1st line• (b) date & author in the 2nd line• (c) Input/output variables definitions• (d) call functions2. Input section3. Calculation section4. Output section


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Document units of measurement

• 單位使用正確


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Using script files to store data

• % mydata.m : 儲存溫度資料• % 儲存包含華氏刻度的各種溫度之陣列 tem

p_F• temp_F=[72 68 75 77 83 79]

• temp_C=5*(temp_F-32)/9


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Conditional statements


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Conditional statements

if x>= 25y=50*sqrt(x)elseif x>=0y=10*xelsey=0end

25;50

250;100;0

xxy

xxyxy


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Loops

m=0;x(1)=10;for k=2:3:11m=m+1;x(m+1)=x(m)+k^2;

We will havex(2)=14, x(3)=39, x(4)=103, x(5)=224


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x=5;k=0;while x<25k=k+1;y(k)=3*x;x=2*x-1;

We will have x=[9 17 33]; y=[15 27 51]


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Example p.41

amount=500;k=0;while amount < 10000k=k+1;amount=amount*1.05+500;endamountk


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Self testing p.42


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The Matlab help system

1. Help browser2. Help functions ~ help, lookfor, doc3. Other resources ~ demo


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• Viewing documentation• Using the contents tab• Using the index tab• Using the search tab• Using the favorites tab


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Help functions

• help function_name• lookfor topic• doc function_name


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Problem solving methodologies


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Summary, p.58


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HW#CH1

• 1. Read the following statements, and (a) tell me what are they doing?a=1; b=2; c=3;u=[a b c];x=roots(u);(b) try to change a,b,c with other values; what happen about the x vector?


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HW#CH1

• Problems• 2, 5, 9, 20, 23, 25, 30, 31, 35

Documents

第 1 章 綜觀 MATLAB

第 1 章綜觀 MATLAB