1

Scilab

The Application of Scilab

2554

Scilab

The Application of Scilab

1. 5133562323 2. 5133576123

2301499 SENIOR PROJECT

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Scilab

Scilab

Scilab

Scilab

Abstract Scilab is a software program used for mathematical calculations such as addition, subtraction,

multiplication, and division, which is based on preliminary calculations, i.e. determine the limit of a

function, determine differentiation, find the integral, drawing the graph, find the specific Eigenvectors and

Eigenvalues and find value of statistics. The Scilab application with matrix, calculus and statistics It can

be calculated at the command directly, to calculate the value you are looking for. And use the theory to

help, the Scilab can help to determining some stage for easily and quickly, such as drawing graph, find the

eigenvectors. We write to explain how to use Scilab basic and applied calculus, matrices, and statistics in

detail can be understood by yourself.

Scilab

1 Scilab

1.1 1 1.2 1 1.3 1 1.4 2 1.5 2 1.6 2 1.7 3 1.8 5 1.9 5 1.10 5 1.11 6 1.12 6 1.13 6 1.14 7 1.15 7 1.16 7 1.17 7 1.18 ... 8 1.19 ... 8

1

2 Scilab 2.1 Scilab 9 2.2 Scilab 11 2.3 12 2.4 12 2.5 12 2.6 14 2.7 14 2.8 15

2.9 b

a

dxxf )( 15

2.10 )(xfdx

d )(xfdx

dn

n

15

2.11 16

2.12

n

i

ix1

16

2.13 17 2.14 17 2.15 f(x) = 0 17 2.16 17 2.17 rnC rnP 17 3 Scilab 3.1 2 18 3.2 19 3.3 histogram 20 3.4 21 3.5 (bar graph) 22 3.6 22 3.7 23 3.8 23

2

4 Scilab 4.1 Scilab 24 4.2 26 4.3 Scilab 27 4.4 Window Scilab 28 4.5 29 5 Scilab 5.1 35 5.2 Scilab 37 5.3 Scilab 38 5.4 40 6 Scilab 6.1 6.1.1 44 6.1.2 48 6.1.3 54 6.2 6.2.1 57 6.2.2 57 6.2.3 A A 59 6.3 6.3.1 60 6.3.2 61 6.3.3 61 6.3.4 62 6.3.5 63 6.3.6 63 6.3.7 64 6.3.8 65 6.3.9 65 6.3.10 66 6.3.11 67

3

7 7.1 68 7.2 68 7.3 68 69 2301399 Project Proposal 70 73

1

1 Scilab

Scilab Scilab Scilab 1.1 1.2

1.3

2

1.4 1.5 1.6 p(x) = x2 + 2x - 3 Scilab p = [ 1 2 -3 ] q(x) = x2 + 5x + 6 Scilab q = [ 1 5 6 ]

p + q ans = 2. 7. 3. p(x) + q(x) = 2x2 + 7x + 3

roots(p) p(x) = 0 1 , -3

3

1.7 1.7.1 f(x) = 2x + 3 [ -5, 5 ] f(x) = 2x + 3 g(x) = x2 4 [-5, 5] 1.7.2

53 156 58 165 55 162 60 170 62 165 68 173

4

1.7.3

1 15 2 35 3 40 4 10

1.7.4 r = 4cos2 1.7.5 3 f(x, y) = cos(x2)sin(y) [0, 2 ] x [0, 2 ]

5

1.7.6 1.8 Scilab

1.9 Scilab

1.10 Scilab

6

1.11 1.12 1.13 1.13.1 1.13.2

7

1.14 1.14.1 1.14.2 1.15 1.16 1.17

8

1.18 ...

1.19 ...

9

2 Scilab

2.1 Scilab 1. 2. icon Start

All Programs

10

scilab-4.1.2

scilab-4.1.2 logo Scilab logo Scilab version Scilab

11

2.2 Scilab Scilab 1. 45.25 + 17.5

-->45.25+17.5 ans =

62.75 2.

5

47

-->47/5 ans =

9.4 3. 15 32 -->15*32 ans =

480. 4. 43 e4 -->4^3 ans =

64. -->%e^4 ans =

54.59815 5. log(2), ln(2), sin(

6

), 3 , 5!

-->log10(2) ans =

0.30103 -->log(2) ans =

0.6931472 -->sin(%pi/6) ans =

0.5 -->sqrt(3) ans =

1.7320508 -->factorial(5) ans =

120. 6. -->x=4 x =

4.

12

7. b

a

dxxf )(

4

1

2 )4( dxx

-->syms x -->y=x^2+4; -->integ(y,x,1,4)

ans = 33

2.3 f(x) = x2 - 3x - 7 [-8, 8] -->x=-8:0.1:8; -->f=x^2-3*x-7; -->plot(x,f)

2.4

3212

219

155

123

-->x=[3 12;5 15;9 21;12 32] x =

3. 12. 5. 15. 9. 21. 12. 32.

2.5

A =

35

24 B = 2 51 3

-->A=[4 -2;-5 3] A =

4. - 2. - 5. 3.

-->B=[2 5;1 3] B = 2. 5. 1. 3.

13

A+B, 4A, AB, A2, A-1, AT, det(A) -->A=[4 -2;-5 3] A =

4. - 2. - 5. 3.

-->B=[2 5;1 3] B = 2. 5. 1. 3.

-->A+B ans =

6. 3. - 4. 6.

-->4*A ans =

16. - 8. - 20. 12.

-->A^2 ans =

26. - 14. - 35. 19.

-->A*B ans =

6. 14. - 7. - 16.

-->A^(-1) ans =

1.5 1. 2.5 2.

-->det(A) ans =

2. -->A' ans =

4. - 5. - 2. 3.

14

2.6

x =

15

8

7

5

3

2

-->x=[2;3;5;7;8;15] x =

2. 3. 5. 7. 8. 15.

2.7

u =

4

3 v =

2

1

-->u=[-3;4]

ans = - 3. 4.

-->v=[1;2];

ans = 1. 2.

u + v, 4u, vu , u -->u=[-3;4]

ans = - 3. 4.

-->v=[1;2]

ans = 1. 2.

-->u+v ans =

- 2. 6.

-->4*u ans =

- 12. 16.

u dot v

15

-->u'*v ans = 5.

-->norm(u) ans =

5. 2.8

10

1i

i ,

10

1

2

i

i ,

10

1

2 54i

ii

-->i=1:10; -->sum(i)

ans = 55.

-->i=1:10; -->sum(i^2)

ans = 385.

-->i=1:10; -->y=i^2-4*i-5; -->sum(y)

ans = 115.

2.9 b

a

dxxf )(

1

0

2dxx

3

3

2dxx

-->y=integrate('x^2','x',0,1) y =

0.3333333 -->y=integrate('x^2','x',-3,3) y =

18.

2.10 )(xfdx

d )(xfdx

dn

n

)(xfdx

d f(x) = x2 x = 1

-->syms x -->f=x^2; -->y=diff(f,x,1)

y = 2*x

-->x=1; -->2*x

ans = 2.

16

2.11 -->sin(30) ans =

- 0.9880316

-->sin(30*%pi/180) ans = 0.5

-->atan(1) ans = 0.7853982

2.12

n

i

ix1

x =

9

6

3

2

y =

19

14

15

12

204

1

i

ix , 604

1

i

iy , 13024

1

i

ix , 92624

1

i

iy , 3244

1

i

i

i yx

-->x=[2;3;6;9] x =

2. 3. 6. 9.

-->y=[12;15;14;19] y = 12. 15. 14. 19.

-->sum(x) ans = 20.

-->sum(y) ans = 60.

-->sum(x^2) ans = 130.

-->sum(y^2) ans = 926.

-->x.*y ans = 24. 45. 84. 171.

-->sum(x.*y) ans = 324.

17

2.13 x = 1, 2, 3, 4 f(x) = 2x + 4 -->x=[1:4]; -->f=2*x+4

f = 6. 8. 10. 12

-->x=[1:0.5:4]; -->f=2*x+4

f = 6. 7. 8. 9. 10. 11. 12.

2.14 ( 3 + 4i ) + ( 5 - 9i ) -->z=3+4*%i; -->w=5-9*%i; -->z+w

ans = 8. - 5.i

2.15 f(x) = 0 x2 2 = 0 -->x=poly(0,'x'); -->y=x^2-2; -->z=roots(y)

z = 1.4142136 - 1.4142136

2.16 2x + 3y = 8 x + y = 3 -->A=[2,3;1,1]; -->b=[8;3]; -->x=inv(A)*b

x = 1. 2.

2.17 rnC rnP

rnC = )!(!

!

rnr

n

10

)!25(!2

!52

5

C

-->factorial(5)/(factorial(2)*factorial(5-2)) ans =

10.

)!(

!

rn

nPr

n

20

)!25(

!52

5

P

-->factorial(5)/factorial(5-2) ans =

20.

18

3 Scilab

3.1 f(x) = 2x + 3 [0, 10] plot(x,y) -->x=0:0.1:10; -->y=2*x+3; -->plot(x,y)

plot(x,y) y = f(x) f(x) = 2x + 3 [ 0, 10 ] plot2d(x,y) -->x=0:0.1:10; -->y=2*x+3; -->plot2d(x,y)

plot2d(x,y) y = f(x)

19

2 -->x=0:0.1:10; -->a=2*x+1; -->b=3*x+1; -->plot(x,a,x,b) 2 -->x=0:0.1:10; -->y=0:0.1:15; -->b=3*x+1; -->c=y-1; -->plot(x,b,y,c) 3.2 -->x=[15;35;40;10]; -->plot2d2(x)

plot2d2(x) x plot2d2(x,[f(x)]) y = f(x)

No. X 1 15 2 35 3 40 4 10

20

f(x) = x2 + 1 x = 0, 0.5, 1.0, 1.5,, 10 -->x=0:0.5:10; -->plot2d2(x,[x^2+1]) 3.3 histogram 1, 4, 1, 1, 2, 2, 2, 3, 2 3 -->data=[1 4 1 1 2 2 2 3 2 3]; -->histplot(4,data,normalization=%f)

histplot(n,data,normalization=%f) x n

21

3.4 -->x=[15 35 40 10]; -->pie(x)

pie(x) x pie(x,explode) x explode = [d d d ] d = 0 d = 1 d = 1 -->x=[15 35 40 10]; -->explode=[1 0 0 0]; -->pie(x,explode)

No. X 1 15 2 35 3 40 4 10

22

3.5 (bar graph) -->score=[1 2 3 4]; -->fre=[15 35 40 10]; -->bar(score,fre)

bar(x,y) x y y -->z=[10 20 35 18]; -->bar(z) 3.6 r = 2cos(2t) -->t=0:0.1:2*%pi; -->r=2*cos(2*t); -->polarplot(t,r)

polarplot(t,r) plot

score frequency 1 15 2 35 3 40 4 10

23

3.7 -->x=[53 58 55 60 62 68]; -->y=[156 165 162 170 165 173]; -->plot(x,y,'*')

plot(x,y,'*') plot (xi, yi) plot '' plot * 3.8 2 x(t) = 80t y(t) = -16t2 + 80t 50 t -->t=0:0.05:5; -->x=80*t; -->y=-16*t^2+80*t; -->plot2d(x,y)

x y 53 156 58 165 55 162 60 170 62 165 68 173

24

4 Scilab

4.1 Scilab Scilab ( ) , [ ]

-->x=[1 2 3] x = 1. 2. 3.

= ;

, ;

-->x=[1 2;3 4] x = 1. 2. 3. 4.

25

Scilab -->x=2 x = 2.

1 x

-->x=[1 2 3] x = 1. 2. 3.

x 1 3

-->x=[1,2,3] x = 1. 2. 3.

x 1 3 ,

-->x=[1;2;3] x = 1. 2. 3.

x 3 1 ;

-->x=[1 2;3 4] x = 1. 2. 3. 4.

x 2 2 ;

-->x=4:2:10 x = 4. 6. 8. 10.

x = a : d : b x x = [a, a+d, a+2d, . . . b ]

-->x=[4:2:10] x = 4. 6. 8. 10.

x = a : d : b x x = [a, a+d, a+2d, . . . b ]

26

4.2 Scilab + -->x=[1 2];y=[3 4];

-->x+y ans = 4. 6.

- -->p=[2 3 4];q=[1 1 3]; -->p-q ans = 1. 2. 1.

* -->a=3.5;b=5; -->a*b ans = 17.5

.* -->x=[2 3 -4];y=[2 2 4]; -->x.*y ans = 4. 6. - 16.

/ a / b =

b

a -->a=23;b=4; -->a/b ans = 5.75

\ a \ b = b a-1

-->a=23;b=4; -->a\b ans = 0.1739130

. / -->x=[2 3 4];y=[5 10 20]; -->x./y ans = 0.4 0.3 0.2

^ -->x=3;y=4; -->x^y ans = 81.

. ^ -->x=[2 3 4];y=[6 5 2]; -->x.^y ans = 64. 243. 16. -->x.^2 ans = 4. 9. 16.

27

4.3 Scilab Scilab %pi pi = 3.1415926 %i i = 1 %e e e = 2.7182818 %inf (infinity) %nan ( Not A

Number) %eps Scilab

%eps Scilab 0 ans

%t %T (Boolean constant) (True) %f %F (False) %s %z %io Scilab

28

4.4 Window Scilab 1. x = [1 2 3] Scilab 4.1.2 2. Graphic Window f(x) = x + 2 x = [1, 4]

-->x=[1:4]; -->f=x+2 f = 3. 4. 5. 6. -->plot(f,x)

29

4.5 abs(x) x a + bi real(a+bi) imag(a+bi)

-->[real(3+4*%i) imag(3+4*%i)] ans = 3. 4.

ceil(x) x -->ceil(2.4) ans = 3.

conj(a+bi) conjugate a + bi -->conj(3+4*%i) ans = 3. - 4.i

exp(x) ex -->exp(1) ans = 2.7182818

fix(x) x 0 -->[fix(2.5) fix(-2.99) fix(2.99)] ans = 2. - 2. 2.

floor(x) x -->floor(3.99) ans = 3.

log(x) ln(x) e -->log(2) ans = 0.6931472

log10(x) log(x) 10 -->log10(2) ans = 0.30103

modulo(x,y) x y -->modulo(12,5) ans = 2.

30

norm(u) u u=[3;4]; -->norm(u) ans = 5.

rat(x) -->[num,den]=rat(1.5) den = 2. num = 3. num den

round(x) x -->round(2.499) ans = 2.

sign(x) +1 x > 0 -1 x < 0 -->sign(-10) ans = - 1.

sqrt(x) x -->sqrt(2) ans = 1.4142136

sin(x), cos(x) tan(x), cot(x) sec(x), cosec(x)

-->[sin(%pi/6) cos(%pi/4) tan(%pi/3)] ans = 0.5 0.7071068 1.7320508 -->x=sin(%pi/6);y=cos(%pi/4);z=tan(%pi/3); -->[1/x 1/y 1/z] ans = 2. 1.4142136 0.5773503

31

asin(x), acos(x) atan(x)

-->[asin(%pi/6) acos(%pi/4) atan(%pi/3)] ans = 0.5510696 0.6674572 0.8084488

sinh(x), cosh(x) tanh(x)

-->[sinh(0) cosh(0) tanh(0)] ans = 0. 1. 0.

asinh(x), acosh(x) atanh(x)

-->[asinh(2) acosh(2) atanh(0.5)] ans = 1.4436355 1.3169579 0.5493061

zeros(n) zeros(m,n) zeros(size(A))

n n m n A -->zeros(2,3) -->zeros(2) ans = ans = 0. 0. 0. 0. 0. 0. 0.

ones(m,n) ones(size(A))

m n 1 1 A -->ones(2,3) ans = 1. 1. 1. 1. 1. 1.

eye(n,n) eye(m,n)

n n m n 1 0 -->eye(2,3) ans = 1. 0. 0. 0. 1. 0. -->eye(2,2) ans = 1. 0. 0. 1.

32

A A -->A=[1 2;3 4] A = 1. 2. 3. 4.

det(A)

A -->det(A) ans = - 2.

inv(A)

A -->inv(A) ans = - 2. 1. 1.5 - 0.5

trace(A)

A -->trace(A) ans = 5.

diag(A)

A -->diag(A) ans = 1. 4.

rank(A) A -->rank(A) ans = 2.

diag(A) A -->B=[1 2 3 4]; -->diag(B) ans = 1. 0. 0. 0. 0. 2. 0. 0. 0. 0. 3. 0. 0. 0. 0. 4.

tril(A) -->C=[1 2 3; 4 5 6; 7 8 9]; -->tril(C) ans = 1. 0. 0. 4. 5. 0. 7. 8. 9.

33

triu(A) -->D=[1 2 3; 4 5 6; 7 8 9]; -->triu(D) ans = 1. 2. 3. 0. 5. 6. 0. 0. 9.

-->x=[2 4 6 5 7 2 3 5 7]

x = 2. 4. 6. 5. 7. 2. 3. 5. 7.

min(x) (minimum) x -->min(x) ans = 2.

max(x) (maximum) x -->max(x) ans = 7.

mean(x) (mean) x ( ) -->mean(x) ans = 4.5555556

median(x) (median) x -->median(x) ans = 5.

stdev(x) (standard deviation) x -->stdev(x) ans = 1.9436506

sum(x) x -->sum(x) ans = 41.

cumsum(x) (cumulative sum) x -->cumsum(x) ans = 2. 6. 12. 17. 24. 26. 29. 34. 41.

34

prod(x) x -->prod(x) ans = 352800.

cumprod(x) (cumulative product) x -->cumprod(x) ans = 2. 8. 48. 240. 1680. 3360. 10080. 50400. 352800.

sort(x) x histplot(n,x) (histogrsm) x n

variance(x) (variance) x

-->variance(x) ans = 3.7777778

geomean(x) (geometric mean) x -->geomean(x) ans = 4.1342055

harmean(x) (harmonic mean) x -->harmean(x) ans = 3.6950147

nfreq(x) (frequency) x -->nfreq(x) ans = 2. 2. 4. 1. 6. 1. 5. 2. 7. 2. 3. 1.

35

5 Scilab

Command Window Window 1 Window 2 Window

5.1

1. function y = f(x); 2. y = x.^2; y f(x) x.^2 x 3. f save File\Save f f.sci File\exec f.sci

1

2

36

f -->x=[1;2;3] x = 1. 2. 3. -->[x f(x)] ans = 1. 1. 2. 4. 3. 9.

)!(!

!

rnr

n

r

n

nCr (n, r)

37

2 b)-a 1,- b+(a = b) h(a, 22

2 h

5.2 Scilab -->score=[1 2 3 4]; -->freq=[15 35 40 10]; -->bar(score,freq)

pro_bargraph

pro_bargraph

38

pro_plotsincos

run pro_plotsincos

5.3 Scilab //

//Remark of program //Program name

input = input('') x=input(' input value x = ...') -->input value x = ...-->

disp disp(''), disp() -->disp('display text') display text -->disp(10^0.5) 3.1622777

39

printf printf(' ') %f %10.2f 10 2 %c %10.4e 10 4 %g -->printf('Text %10.2f',10^0.5) Text 3.16 -->printf('Text %20.8f',10^0.5) Text 3.16227766 -->printf('Text %g',10^0.5) Text 3.16228

if c1 1 end

c1 1 c1 end if x

40

for x = a : b : c 1 end \n

x x a c x b for x=1:0.5:2.25 printf('\n value of x %10.2f',x) end run value of x 1.00 value of x 1.50 value of x 2.00

while c1 1 end

c1 1 c1 x=1; while x

41

1 a, b, c

Scilab 1 input

run -->exec('C:\Program Files\scilab-4.1.2\Area');disp('exec done'); a = a 3 enter b = 4 c = 5 Area = 6

42

2 A

-->exec('C:\Program Files\scilab-4.1.2\Pro2');disp('exec done'); a11= -->1 a12= -->2 a21= -->3 a22= -->4 A = 1. 2. 3. 4. A inverse= ans = - 2. 1. 1.5 - 0.5 Adjoint of A= ans = 4. - 2. - 3. 1. exec done

3 3 (

1a , 1b ), ( 2a , 2b ), ( 3a , 3b )

)det()2

1(

1313

1212

bbaa

bbaa

-->exec('C:\Program Files\scilab-4.1.2\Pro3');disp('exec done'); x0= -->0 y0= -->0 x1= -->0 y1= -->4 x2= -->6 y2= -->0 area = 12. exec done

43

4 ( ox , 0y ) ax + by + c = 0

-->exec('C:\Program Files\scilab-4.1.2\Pro4');disp('exec done'); a= -->3 b= -->4 c= -->10 x0= -->2 y0= -->5 d = 7.2 exec done

5

643)( 23 xxxxf , 10 x )('

)(1

n

nnn

xf

xfxx

run -->exec('C:\Program Files\scilab-4.1.2\Pro5');disp('exec done'); root = -4.26697461340156 exec done

44

6 Scilab

Scilab 6.1 6.1.1 6.1.1.1 f : D R D R a D 1. c f(x) = c x D cxf

ax

)(lim

2. f(x) = x x D axfax

)(lim

f g D R D R Lxfax

)(lim Mxgax

)(lim

L M 1. MLxgxfxgxf

axaxax

)(lim)(lim))()((lim

2. LMxgxfxgxfaxaxax

))(lim))((lim()()(lim

3. M

L

xg

xf

xg

xf

ax

ax

ax

)(lim

)(lim

)(

)(lim M 0

4. Lxfxfaxax

)(lim)(lim

5. nnax

n

axLxfxf

)(lim)(lim n n L

Scilab : limit(expr,x,val) ; expr , x , val

45

)12(lim 21

xxx

)12(lim 2

1

xx

x = 41211lim2limlim

11

2

1

xxxxx

-->syms x -->limit(x^2+2*x+1,x,1)

-->limit(x^2+2*x+1,x,1) ans = 4 4lim 3

2

x

x

248424lim 33

2

x

x

-->syms x -->limit(sqrt(x^3-4),x,2)

-->limit(sqrt(x^3-4),x,2) ans = 2

x

x

x

164lim

0

x

x

x

164lim

0 =

0

44lim

0

x (IF.

0

0 )

= x

x

x

x

x

164

164164lim

0

= )164(

)16(16lim

0 xx

x

x

= )164(

lim0 xx

x

x

= )164(

1lim

0 xx

= )0164(

1

= 8

1

46

-->syms x -->limit((4-sqrt(16+x))/x,x,0)

-->limit((4-sqrt(16+x))/x,x,0) ans = -1/8

xx

1lim

0

xx

1lim

0 =

0

1lim

0x =

-->syms x

-->limit(1/x,x,0) -->limit(1/x,x,0) ans = und 6.1.1.2 1. 0sinlim

x

ax

2. 1coslim

xax

3. axax

sinsinlim

4. axax

coscoslim

5. 1sinlim0

x

x

x

6. 0cos1lim0

x

x

x

47

)(2

2sinlim

x

x

x

)(2

2sinlim

x

x

x =

)(2

2sinlim

x

(IF. 0

0 )

= )(2

)22sin(lim

x

x

x

=

22

)22sin(lim

x

x

x

= 1 -->syms x

-->limit((sin(2*x))/(2*(x-%pi)),x,%pi) -->limit((sin(2*x))/(2*(x-%pi)),x,%pi) ans = 1

30

sintanlim

x

xx

x

0x 33

sincos

sin

sintan

x

xx

x

x

xx

xx

xx

cos

)cos1)((sin3

xx

xx

cos

)2

sin2)((sin

3

2

)cos

2()

2

2sin

)(sin

)(4

1( 2

xx

x

x

x

2

1)

1

2)(1)(1)(

4

1(

sintanlim 2

30

x

xx

x

-->syms x -->limit((tan(x)-sin(x))/x^3,x,0)

-->limit((tan(x)-sin(x))/x^3,x,0) ans =

48

6.1.2 6.1.2.1 u = f(x) v = g(x) x c r

1. 0dx

dc

2. 1dx

dx

3. 1 rr

rxdx

dx

4. dx

duccu

dx

d)(

5. dx

dv

dx

duvu

dx

d )(

6. dx

duv

dx

dvuuv

dx

d)(

7. 2

)(v

dx

dvu

dx

duv

v

u

dx

d

v 0

8. dx

duru

dx

du rr

1

Scilab : diff(expr,x,n) ; expr , x , n 4)( 2 xxxf )(' xf

42 xx = 21

2 4 xx

)4()4(2

1)(' 22

1

2

xxdx

dxxxf

42

12

2

xx

x

-->syms x -->fx=sqrt(x^2-x+4); -->diff(fx,x)

-->syms x -->fx=sqrt(x^2-x+4); -->diff(fx,x) ans = (2*x-1)/(2*sqrt(x^2-x+4))

49

f(x) = (1 + 2x3)(x - 4)5 )(' xf

2543 6)4()4(5)21()(' xxxxxf 4 3 5 25( 4) (2 1) 6( 4)x x x x -->syms x

-->diff((1+2*x^3)*(x-4)^5,x,1) -->syms x -->diff((1+2*x^3)*(x-4)^5,x,1) ans = 5*(x-4)^4*(2*x^3+1)+6*(x-4)^5*x^2 6.1.2.2 )(' xf f x )(' xf

f x )('' xf 2y 2

2

dx

yd

n n f )()( xf n )(ny

n

n

dx

yd

f(x) = (x3 + 1)4 )('' xf )1(''f )3()1(4)(' 233 xxxf 332 )1(12 xx xxxxxxf 24)1(3)1(312)('' 332232 xxxx 24)1()1(108 33234 3 3 4 3 224 ( 1) 108 ( 1)x x x x 6248)24()4(108)1('' f

-->syms x -->diff((x^3+1)^4,x,1)

ans = 12*x^2*(x^3+1)^3 -->diff((x^3+1)^4,x,2) ans = 24*x*(x^3+1)^3+108*x^4*(x^3+1)^2 -->x=1;

-->24*x*(x^3+1)^3+108*x^4*(x^3+1)^2 ans = 624.

50

6.1.2.3 u x

1. dx

duuu

dx

dcossin

2. dx

duuu

dx

dsincos

3. dx

duuu

dx

d 2sectan

4. dx

duuecu

dx

d 2coscot

5. dx

duuuu

dx

dtansecsec

6. dx

duuecuecu

dx

dcotcoscos

f(x) = xcosx 3sin5x )5)(5(cos3cos)sin()(' xxxxxf

xxxx 5cos15cossin 15cos5 sin cosx x x x -->syms x

-->diff(x*cos(x)-3*sin(5*x),x,1) -->syms x -->diff(x*cos(x)-3*sin(5*x),x,1) ans = -15*cos(5*x)-x*sin(x)+cos(x)

xx

xxf

cossin

2tan)(

2

2

)cos(sin

)sin(cos2tan))2(sec2)(cos(sin)('

xx

xxxxxxxf

2

2

2sec 2 (cos sin ) tan 2

sin cos (sin cos )

x x x x

x x x x

-->syms x -->diff(tan(2*x)/(sin(x)+cos(x)),x,1)

-->syms x -->diff(tan(2*x)/(sin(x)+cos(x)),x,1) ans = 2*sec(2*x)^2/(sin(x)+cos(x))-(cos(x)-sin(x))*tan(2*x)/(sin(x)+cos(x))^2

51

dx

dy )12(sec 23 xy

'y = )4)(12tan()12sec()12(sec3 2222 xxxx

= )12tan()12(sec12 223 xxx 2

4 2

12 sin(2 1)

cos (2 1)

x x

x

-->syms x -->diff(1/(cos(2*x^2+1))^3,x,1)

-->syms x -->diff(1/(cos(2*x^2+1))^3,x,1) ans = 12*x*sin(2*x^2+1)/cos(2*x^2+1)^4

dx

dy )1tancos( xy

))(sec1tan2

1)(1tansin()(' 2 x

xxxf

2sec sin( tan 1)

2 tan 1

x x

x

-->syms x -->diff(cos(sqrt(tan(x)+1)),x,1)

-->syms x -->diff(cos(sqrt(tan(x)+1)),x,1) ans = -sec(x)^2*sin(sqrt(tan(x)+1))/(2*sqrt(tan(x)+1)) u x

1. dx

du

uu

dx

d

21

1arcsin

2. dx

du

uu

dx

d

21

1arccos

3. dx

du

uu

dx

d21

1arctan

4. dx

du

uuarc

dx

d21

1cot

5. dx

du

uuuarc

dx

d

1

1sec

2

6. dx

du

uuecu

dx

d

1

1arccos

2

52

dx

dy )12arcsin(2 xxy

)12arcsin(2))12(1

1(2'

2

2

xxx

xy 2

2

22 arcsin(2 1)

1 (2 1)

xx x

x

-->syms x -->diff(x^2*asin(2*x+1),x,1)

-->syms x -->diff(x^2*asin(2*x+1),x,1) ans = 2*x*asin(2*x+1)+2*x^2/sqrt(1-(2*x+1)^2) 6.1.2.4 8543),( 224 yxyxyxf )2,1(xf )2,1(yf

)8543(),( 224

yxyx

xyxf x

xyx 812 23 40)1(8)2()1(12)2,1( 23 xf

)8543(),( 224

yxyx

yyxf y

56 4 yx 175)2()1(6)2,1( 4 yf Scilab )2,1(xf -->syms x y

-->diff(3*x^4*y^2-4*x^2+5*y-8,x) ans = 12*x^3*y^2-8*x -->x=1;y=2;

--> 12*x^3*y^2-8*x ans = 40.

53

)2,1(yf -->syms x y

-->diff(3*x^4*y^2-4*x^2+5*y-8,y) ans = 6*x^4*y+5 -->x=1;y=2;

--> 6*x^4*y+5 ans = 17. 6.1.2.5 2442 4),,( zxxyzyxzyx )2,0,1( 234 442),,( zxyzxyzyxx xzyxzyxy 44),,( 32

zxxyzyxz 424),,( ),,(),,(),,(),,( zyxzyxzyxzyx zyx 234 442 zxyzxy + xzyx 44 32 + zxxy 424

kji 4816)2,0,1( -->syms x y z

-->diff(x^2*y^4+4*x*y*z+x^4*z^2,x,1) ans = 4*x^3*z^2+4*y*z+2*x*y^4 -->diff(x^2*y^4+4*x*y*z+x^4*z^2,y,1) ans = 4*x*z+4*x^2*y^3 -->diff(x^2*y^4+4*x*y*z+x^4*z^2,z,1) ans = 2*x^4*z+4*x*y -->x=1;y=0;z=2;

-->[4*x^3*z^2+4*y*z+2*x*y^4,4*x*z+4*x^2*y^3,2*x^4*z+4*x*y] ans = 16. 8. 4.

54

6.1.3 6.1.3.1

D

dAxy 2 D ,1[ ,0[]3 ]1

1

0

3

1

22 dxdyxydAxyD

3

4

34

4

2

1

0

3

1

0

2

3

1

1

0

22

y

y

x

x

y

dyy

dyx

y

Scilab -->syms x y

-->integ(integ(x*y^2,x,1,3),y,0,1) -->syms x y -->integ(integ(x*y^2,x,1,3),y,0,1) ans = 4/3

55

6.1.3.2 1. yzxzyxf 23),,( 2 ,1[D ,2[]2 ,2[]3 ]3 f D

dydzdxyzxfdVD

2

1

3

2

3

1

2 )23( ( y, z x )

43

)]1(8)1(5[)]2(8)8(5[

]85[

)815(

)]23(8)49(3[

]83[

)86(

))19()13(3(

]3[

2

1

3

2

1

2

2

1

2

2

1

3

2

22

2

1

3

2

2

2

1

3

2

2

2

1

3

2

3

1

22

x

x

z

z

y

y

xx

dxx

dxx

dxzzx

dzdxzx

dzdxzx

dzdxyzyx

Scilab -->syms x y z

-->integ(integ(integ(3*x^2*z+2*y,y,1,3),z,2,3),x,1,2) -->syms x y z -->integ(integ(integ(3*x^2*z+2*y,y,1,3),z,2,3),x,1,2) ans = 43

56

2.

S

xyzdV48 S 2

22x

z

z = 0, y = x y = 0

2

0 0

22

0

2

4848

x

x

S

xyzdzdydxxyzdV

32

)2(8

3)2(4)2(12

]8

3412[

)32448(

)4

24(12

)2

2(12

][)2

2(12

)2

2(24

][24

864

2

0

864

2

0

753

2

0

423

2

0

22

3

2

0

0

222

2

0 0

22

2

0 0

22

0

2

2

x

x

xy

y

x

x xz

z

xxx

dxxxx

dxx

xx

dxx

x

dxyx

x

dydxx

xy

dydxzxy

Scilab -->syms x y z

-->integ(integ(integ(48*x*y*z,z,0,2-((x^2)/2)),y,0,x),x,0,2) -->integ(integ(integ(48*x*y*z,z,0,2-((x^2)/2)),y,0,x),x,0,2) ans = 32

57

6.2 6.2.1

64

53A

86

74B

1410

127BA

7652

6142*BA

5.12

5.231A

2)det( A -->A=[3 5;4 6]

A = 3. 5. 4. 6.

-->B=[4 7;6 8] B = 4. 7. 6. 8.

-->A+B ans = 7. 12. 10. 14.

-->A*B ans = 42. 61. 52. 76.

-->A^(-1) ans = - 3. 2.5 2. - 1.5

-->det(A) ans = - 2.

6.2.2

31

04A A

31

04IA

0)det( IA

4,3

0127

00)3)(4(

2

4,3

3

01

01

331

034

01

01 ~

00

01

58

000

00

21

21

xx

xx

01 x

Rtx 2

1

00

2

1t

t

t

x

x

3

t

0 Rt

1

0

4

11

00

431

044

11

00 ~

00

11

000

0

21

21

xx

xx

21 xx

Rtx 2

1

1

2

1t

t

t

x

x

4

t

t Rt

2

12

1

-->A=[4 0;1 3] A =

4. 0. 1. 3.

-->poly(A,"x") ans = 12 - 7x + x2

-->spec(A) ans = 3. 4.

-->[V,D]=spec(A) D = 3. 0 0 4. V = 0 0.7071068 1. 0.7071068

31

04A x2 7x + 12 = 0

59

3, 4 (0, 1) (0.7071068, 0.7071068) 6.2.3 A A

987

654

321

A Guassian rank A

987

654

321

A = 13

12

7

4

1260

630

321

RR

RR

= 3

1260

210

3212

R

= 23 6000

210

321

RR

= 21 2

000

210

101 RR

rank A = 2 -->A=[1 2 3;4 5 6;7 8 9] A =

1. 2. 3. 4. 5. 6. 7. 8. 9.

-->rank(A) ans = 2.

-->rref(A) ans = 1. 0. - 1. 0. 1. 2. 0. 0. 0.

60

6.3 6.3.1 , , , x = 2, 3, 5, 7, 8, 15 x 6

= 67.66

1587532

= 62

75

=

68.46

)67.615()67.68()67.67()67.65()67.63()67.62( 222222

= 67.21)68.4( 2 x 2 x 15 -->xmean=mean(x) xmean =

6.6666667 -->xmedian=median(x) xmedian =

6. -->xlength=length(x) xlength =

6. -->xstdev=stdev(x) xstdev =

4.6761808 -->xvariance=variance(x) xvariance =

21.866667 -->xmax=max(x) xmax =

15. -->xmin=min(x) xmin =

2. xmean = x xmedian = x xstdev = () x xvariance = () x xlength = x xmax = x xmin = x

61

6.3.2 ( geomean ) N

NxxxMG ..... 21 2, 4, 8 8,4,2 321 xxx 3N

1 2

3

3

. . ...

. . (2)(4)(8)

. . 64

. . 4

NNGM x x x

GM

GM

GM

Scilab -->x=[2 4 8]; -->gm=geomean(x)

gm = 4.

6.3.3 ( harmean )

Nxxx

NMH

1...

11..

21

30, 40, 50 50,40,30 321 xxx 3N

1 2

. .1 1 1

...

3. .

1 1 1

30 40 50

3. . 38.30

47

600

N

NH M

x x x

H M

H M

Scilab -->x=[30 40 50]; -->hm=harmean(x)

hm = 38.297872

62

6.3.4

mean N

xxxx

N

xx N

...321

14, 16, 14, 17, 16, 14, 18, 17 1 14,x 2 16,x 3 14,x 4 17,x 5 16,x 6 14,x 7 18,x 8 17x 8N

75.158

126

8

1718141617141614

N

xx

Scilab -->x=[14 , 16 , 14 , 17 , 16 , 14 , 18 , 17]; -->y=mean(x)

y = 15.75

meanf

n

xfxfxfxf

N

xfx NN

ii

...332211

40 (f) x f*x 11 20

21 30

31 40

41 50

51 - 60

7

6

8

15

4

15.5

25.5

35.5

45.5

55.5

108.5

153

284

682.5

222

405

1

Nfi

i 14505

1

i

ii xf

25.3640

1450

N

xfx

ii

Scilab -->x=[15.5 25.5 35.5 45.5 55.5]; -->y=[7 6 8 15 4]; -->m=meanf(x,y)

m = 36.25

63

6.3.5 () ( 0.01 )

4.3 126 4.5 121 5.9 116 5.6 118 6.1 114 5.2 118 3.8 132 2.1 141 7.5 108

1. b bxay 2. a ( Y) bxay Scilab -->x=[4.3 4.5 5.9 5.6 6.1 5.2 3.8 2.1 7.5]; -->y=[126 121 116 118 114 118 132 141 108]; -->regress(x,y)

ans = 153.17549 - 6.3239875

Scilab 1. b = - 6.3239875 2. a = 153.17549 6.3.6

r

x

pnxbpnrBrXP0

),;(),;()(

80% 10 5

8.0100

80p , 2.0q , 10n

10 5

9936.00064.01)8.0,10;(1)5(1)5(4

0

x

xbXPXP

64

Scilab -->[P,Q]=cdfbin("PQ",5,10,0.8,0.2) Q =

0.9936306 P = 0.0063694

6.3.7

r

x

xprP0

);();(

5 10 10x , 5

0181.09682.09863.0)5;()5;(!10

5)5;10(

9

0

10

0

105

xx

xpxpe

p

Scilab -->[P,Q]=cdfpoi("PQ",10,5) Q =

0.0136953 P = 0.9863047

-->[P,Q]=cdfpoi("PQ",9,5) Q = 0.0318281 P = 0.9681719

-->0.9863047-0.9681719 ans = 0.0181328

65

6.3.8 2)(

2

1

2

2

1),;(

x

exn x , ...14159.3 ...71828.2e

3 0.5 2.3 X X )25.0,3;(xn

)5.0

33.2()3.2(

XPXP

0808.0

)4.1(

ZP

Scilab -->[P,Q]=cdfnor("PQ",2.3,3,0.5) Q =

0.9192433 P = 0.0807567

6.3.9

T 212

)1(

)2

(

)2

1(

)(

v

v

t

vv

v

th

df

t 5v a 90.0)( atP

a 90.0)( atP

90.0)( ataP 90.0)( 05.005.0 tttP 5v 05.0 015.205.0 t 015.2a Scilab -->[T]=cdft("T",5,0.95,0.05) T =

2.0150484

66

6.3.10

F 2

2

121

122

2

121

21

11

)1)(2

()2

(

))(2

(

vv

vv

fv

vvv

fv

vvv

0f

h(f) = 0 f F 91 v 52 v . )77.40( FP . k 05.0)( kFP 77.4)5,9(,05.0 21 vvf 95.0)77.40( FP 77.4k Scilab -->[P,Q]=cdff("PQ",4.77,9,5) Q =

0.0500515 P = 0.9499485

-->[F]=cdff("F",9,5,0.95,0.05) F = 4.7724656

67

6.3.11 )( 2 v

21

2

2 )2

(2

1xv

vex

v

x > 0

f(x) = 0 x X 5v a b 05.0)( aXP 90.0)( bXaP a 05.0)0( aXP 2 95.0 5v 145.1295.0 05.0)145.10( XP a = 1.145 2 95.0 5v 070.11205.0 95.005.01)070.110( XP )145.10()070.110()070.11145.1( XPXPXP

05.095.0 90.0 b = 11.070 Scilab -->[X]=cdfchi("X",5,0.05,0.95) X =

1.1454762 -->[X]=cdfchi("X",5,0.95,0.05) X =

11.070498

68

7

Scilab

Scilab

7.1

- Scilab

-

-

7.2

Scilab

7.3

Scilab

http://home.npru.ac.th/piya/webscilab/index.php

69

1. , ,

, 2544.

2. , Mathcad Mathematica Mathlab

Maple, , , 2546.

3. , Instat,

, , 2551.

4. , ,

, Calculus I, , , 2548.

5. http://home.npru.ac.th/piya/webscilab/download.php

70

. 2301399 Project Proposal

() : Scilab

() : The Application of Scilab

:

: 1. 5133562323

2. 5133576123

:

Mathcad, Mathematica, Matlab Maple

Scilab

:

Scilab ,

:

Scilab

71

:

Scilab

Scilab

Scilab

: 2554 2555

.. .. .. .. .. .. .. ..

Scilab

Scilab

:

Scilab

72

Scilab

Hardware

2 GB

Flash drive

CD

Software

Microsoft Windows XP Professional

Scilab

Symbolic toolbox

Microsoft Offices 2007

:

, ,

, 2544.

, Matlab, ,

, 2546

, Instat,

, , 2546

, , ,

Calculus I, , , 2548.

http://home.npru.ac.th/piya/webscilab/download.php

73

.

Mathlab Scilab = 3.141592654 pi %pi i = 1 i %i

x sqrt(x) sqrt(x) e = 2.7182818, xe exp(x) exp(x) n! factorial(n) factorial(n) f(x) f.m file f = 10 log(x) log10(x) e log10(x) log(x) sin(x) sin(x) sin(x) cos(x) cos(x) cos(x) tan(x) tan(x) tan(x) sec(x) sec(x) 1/cos(x) cosec(x) csc(x) 1/sin(x) cot(x) cot(x) 1/tan(x) arcsin(x) asin(x) asin(x) arcos(x) acos(x) acos(x) arctan(x) atan(x) atan(x) arcsec(x) asec(x) acos(1/x) arccosec(x) acsc(x) asin(1/x) arccot(x) acot(x) atan(1/x) abs(x) abs(x) z real(z) real(z) z imag(z) imag(z) z conj(z) conj(z) det(A) det(A) det(A) 1A inv(A), A^-1 inv(A)

74

Mathlab Scilab A DV , = eig(A) spec(A) A DV , = eig(A) [V,D]=spec(A) A norm(u) norm(u) u dot v dot(u, v) u*v sum, symsum sum prod prod limit limit diff diff intg integ taylor taylor laplace laplace ilaplace ilaplace gamma(x) gamma(x) bessej, bessely besselj, bessely legendre legendre XY plot, ezplot plot, plot2d polar,ezpolor polarplot 3 surf, ezsurf plot3d contour contour, ezsurf contour expand expand factor factor solve, root, fzero solve, root solve, linsolve rref