計(jì)算機(jī)課件Matlab軟件

Matlab軟件(1)

?z=sqrt(4*xA2+l)+0.5457expA(-0.75*xA2-3.75*yA2-1.5x)/

(2*sin3*y-D

???z=sqrt(4*xA2+l)+0.5457expA(-0.75*xA2-3.75*yA2-1.5x)/

(2*sin3*y-D

I

Error:Missingvariableorfunction.

?z=sqrt(4.*x.A2+l)+0.5457exp.A(-0.75.*x.A2-3.75.*y.A2-1.5x)./

(2.*sin3.*y-l)

???z=sqrt(4.*x.A2+l)+0.5457exp.A(-0.75.*x.A2-3.75.*y.A2-1.5x)./

(2.*sin3.*y-l)

I

Error:Missingvariableorfunction.

?z=(sqrt(4.*x.A2+l)+0.5457exp.A(-0.75.*x.A2-3.75.*y.A2-1.5x))./

(2.*sin(3.*y)-l)

???z=(sqrt(4.*x.A2+l)+0.5457exp.A(-0.75.*x.A2-3.75.*y.A2-1.5x))./

(2.*sin(3.*y)-l)

Error:Missingvariableorfunction.

?

z=(sqrt(4*xA2+l)+0.5457*exp(-0.75*x-3.75*yA2-1.5*x))/(2*sin(3*y)-l

)

???Undefinedfunctionorvariable'x'.

?x=l;y=2;

?

z=(sqrt(4*xA2+l)+0.5457*exp(-0.75*x-3.75*yA2-1.5*x))/(2*sin(3*y)-l

)

z=

-1.4345

?x=(-l+sqrt(-5))/4

x=

-0.2500+0.5590i

?y=x+8+10i

7.7500+10.5590i

?A='她是我們班最好的學(xué)生'

???A='她是我們班最好的學(xué)生’

I

Error:Missingvariableorfunction.

?A=，她是我們班最好的學(xué)生，

A=

她是我們班最好的學(xué)生

?A=[123;-213;-321]

A=

123

-213

-32

?B=|l43;328;523]

B=

143

328

523

?A==B

ans=

101

000

010

?A<=B

ans=

?A>=B

ans=

101

000

010

?A<0

ans=

000

100

100

?A|B

ans=

?A&B

ans=

?A>2&B<5

ans=

00

000

000

?A~=B

ans=

00

101

Matlab軟件(2)

(l)x=|0:0.1:l|

Columns1through9

00.10000.20000.30000.40000.5000

0.60000.70000.8000

Columns10through11

0.90001.0000

?y=x*exp(-x)

???Errorusing==>mtimes

Innermatrixdimensionsmustagree.

?y=x*exp(-x);

???Errorusing==>mtimes

Innermatrixdimensionsmustagree.

?y=x.*exp(-x)

y=

Columns1through9

00.09050.16370.22220.26810.3033

0.32930.34760.3595

Columns10through11

0.36590.3679

?Plot(x,y)

⑵

(3)fori=l:6

a=0.5+i*0.5

t=[0:0.1:2*pi]

x=a*cos(t)

y=sqrt(25-aA2)*sin(t)

Plot(x,y)

holdon

(4)t=[0:0.1:2*pi];

x=2*(cos(t)).A3

y=2*(sin(t)).A3;

Plot(x,y)

'Z：SO：H：SO：Z-=x?(s)

z

[x,y]=meshgrid(x,y)

?z=x.A2+y.A2;

?surf(x,y,z)

(6)?clearall;closeall;

?[x,y]=meshgrid(-l.5:0.1:1.5,-2:0.1:2);

?

z=0.54*exp(-0.75*x.A2-3.75*y.A2-1.5*y).*(x+y>l)+0.7575*exp(-x.

A2-6*y.A2).*((x+y>-l)&(x+y<=l))+0.5457*exp(-0.75*x.A2-3.75*y.

A2+1.5*y).*(x+y<=-l);

>>surf(x,y,z);

Matlab(3)

(l)s=O

forn=l:20

t=l

fori=l:n

t=t*i

end

s=s+t

end

2.5613e+018

(2)s=0;i=l

whilei<=200

s=s+i

i=i+l

end

s

s=

20100

(3)?functions=yuan(r)

%求半徑為r的圓的面積

%s=yuan(r)

s=pi*rA2

?r=3

r=

3

?s=yuan(r)

28.2743

28.2743

(4)?clearall

r=input(，輸入圓的半徑，)

s=pi*rA2

輸入圓的半徑

r=

II

s=

11

?r=12

r=

12

?s=yuan(r)

452.3893

Matlab(4)

1.1?symsxn

?f=(l+x/n)An

f=

(l+x/n)An

?limit(f,n,inf)

ans=

exp(x)

1.2?symsnx

?f=(-l)An*(xAn/n)

f=

(-l)An*xAn/n

?symsum(f,n,l,inf)

ans=

-log(l+x)

2.1?symsxy

?f=((xA2)*exp(-y))

xA2*exp(-y)

?diff(f,x,2)

ans=

2*exp(-y)

2.1(2)symsxy

?f=((xA2)*exp(-y))

f=

xA2*exp(-y)

diff(f,x)

ans=

2*x*exp(-y)

?diff(f,y)

ans=

-xA2*exp(-y)

?x=l,y=2

y=

2

-xA2*exp(-y)

ans=

-0.1353

2.2?symsxlx2

?A=[(xl)*exp(x2);cos(xl)]

A=

xl*exp(x2)

cos(xl)

?jacobian(A,[xl,x2|)

ans=

[exp(x2),xl*exp(x2)|

[-sin(xl),0]

?jacobian(A,[xl,xl|)

ans=

[exp(x2),exp(x2)]

[-sin(xl),-sin(xl)]

?jacobian(A,[x2,x2|)

ans=

[xl*exp(x2),xl*exp(x2)|

I0,0|

?jacobian(A,[x2,xl|)

ans=

[xl*exp(x2),exp(x2)|

[0,-sin(xl)!

2.3?symsfx

?f=log(x)*sin(x)

f=

log(x)*sin(x)

taylor(f,5,l,x)

ans=

sin(l)*(x-l)+(cos(l)-l/2*sin(l))*(x-l)A2+(-l/6*sin(l)-l/2*cos(l))*

(x-l)A3+l/6*cos(l)*(x-l)A4

3.1symsft

?f=exp(-t)+sin(t)

f=

exp(-t)+sin(t)

?int(f,t)

ans=

-exp(-t)-cos(t)

3.2symsft

?f=exp(-t)+sin(t)

f=

exp(-t)+sin(t)

?int(f,t,O,l)

ans=

-exp(-l)-cos(l)+2

3.3symsgx

?g=3*sin(xA2)/x

g=

3*sin(xA2)/x

?int(g,x,l,4)

ans=

3/2*sinint(16)-3/2*sinint(l)

3.4symsgx

?g=exp(-xA(sin(x)))

g=

exp(-xAsin(x))

?int(g,x,O,l)

Warning:Explicitintegralcouldnotbefound.

>Inat58

ans=

int(exp(-xAsin(x)),x=0..1)

3.5?symsfxy

?f=2*sqrt(l-xA2)

f=

2*(l-xA2)A(l/2)

?int(f,y,-sqrt(l-xA2),sqrt(l-xA2))

ans=

4-4*xA2

?int(ans,x,-l,l)

ans=

16/3

3.6?symsfx

?f=exp(-x)*sin(x)

f=

exp(-x)*sin(x)

?int(f,x,l,inf)

ans=

l/2*exp(-l)*cos(l)+l/2*exp(-l)*sin(l)

Matlab(5)

(1)

?eye(4)

ans=

1000

0100

0010

0001

(2)

?rand(4,4)

ans=

0.95010.89130.82140.9218

0.23110.76210.44470.7382

0.60680.45650.61540.1763

0.48600.01850.79190.4057

(3)?A=[5756;71087;68109;57910]

A=

5756

71087

68109

57910

?A.,

ans=

5765

71087

58109

67910

?det(A)

ans=

28

?rank(A)

ans=

?inv(A)

ans=

2.4286-2.14292.4286-2.1429

-1.46431.5714-1.71431.3214

-0.60710.28570.14290.0357

0.3571-0.2857-0.14290.2143

?eig(A)

ans=

30.2769

3.7132

0.4281

0.5818

?[VD]=eig(A)

0.37940.32800.78800.7464

0.52870.6600-0.5025-0.4678

0.5522-0.2598-0.2801-0.3655

0.5212-0.62390.21920.3007

D=

30.2769000

03.713200

000.42810

0000.5818

(4)A=[21-11;121-1;1121]

A=

21

12

2

?B=[l;2;3]

B=

1

2

3

?A\B

ans=

1

0

1

0

(5)?A=[21-11;121-1;1121]

A=

2

2

12

?B=[l;2;3]

B=

2

3

?A\B

ans=

1

0

1

0

?A=[12-2;-2-24;24-2]

A=

12-2

-2-24

24-2

?[VJ]=jordan(A)

02.2127-0.2127

0.5000-0.79570.2957

0.50000.7957-0.2957

J=

2.000000

0-0.43840

00-4.5616

(6)

>A=[4-313;2-135;1-1-1-1;3-234;7-6-70|

A=

4-313

2-135

1-1-1-1

3-234

7-6-70

rref(A)

ans=

1006

0107

0010

0000

0000

例題：

A=[135;l23;542]

A=

135

123

542

Matlab(8)

例題1：?clear;N=10000;

x=unifrnd(-l,l,N,l);y=unifrnd(-l,l,N,l);z=rand(N,l);

Cl=(x.A2+y.A2)<l;C2=(x.A2+z.A2)<l;

Nc=sum(Cl&C2);I=(Nc/N)*4

2.6508

?clear;N=10000;

x=unifrnd(-l,l,N,l);y=unifrnd(-l,l,N,l);z=rand(N,l);

Cl=(x.A2+y.A2)<l;C2=(x.A2+z.A2)<l;

Nc=sum(Cl&C2);I=(Nc/N)*4

2.6864

?clear;N=10000;

x=unifrnd(-l,l,N,l);y=unifrnd(-l,l,N,l);z=rand(N,l);

Cl=(x.A2+y.A2)<l;C2=(x.A2+z.A2)<l;

Nc=sum(Cl&C2);I=(Nc/N)*4

2.6340

例題2：clear;close;x=linspace(-2.*pi,2.*pi,300000)

f=(l-x.A3).*sin(3.*x)

plot(x,f)

fun=inline(T)

x=fminbnd(fun,-2.*pi,2.*pi),f=feval(fun,x);

x=unifrnd(-2.*pi,2.*pi,300000,1)

f=-min(feval(fun,x))

Matlab(6)

例題：

l.?dsolve(,Du=l+uA2,)

ans=

tan(t+Cl)

2.?dsolve(,D2y+4*Dy+29*y,；y(0)=0,,,Dy(0)=15,,,x,)

ans=

3*exp(-2*x)*sin(5*x)

3.?

dsolve(,Dx=2*x-3*y+3*z*,,Dy=4*x-5*y+3*z*,,Dz=4*x-4*y+2*z,,*t,)

ans=

x:|lxlsym|C2*exp(-t)+C3*exp(2*t)

y:[1x1sym]C2*exp(-t)+C3*exp(2*t)+exp(-2*t)*Cl

z:[1x1sym]C3*exp(2*t)+exp(-2*t)*Cl

4.functiondy=my2011(t,y)

dy=zeros(2,l)；

dy⑴=y(2);

dy(2)=1000*(l-y(l)^2)*y(2)-y(l)

Odel5s(@my2011,[03000],[20])

1500

0

-1000

-15001-----------------1-----------------1------------------1-----------------?-----------------1-----------------

050010001500200025003000

5.functiondy=my2012(t,y)

dy=zeros(3,l)

dy(l)=y(2)*y(3);

dy(2)=-y(l)*y(2);

dy(3)=-0.51*y(l)*y(2);

ode45(@my2012,|01000|,[011|)

1.4

12

0.

0.6

0端

02

-0.2

01002003004006007008009001000

練習(xí)：1(a),?dsolve(*Dy=(x+y)*(x-y),,,x,)

ans=

-x*(-Cl*besseli(-3/4,l/2*xA2)+besselk(3/4,l/2*xA2))/(Cl*besseli(l/4,l/2

*xA2)+besselk(l/4,l/2*xA2))

1(b)?dsolve(,x*Dy=y*tan(y/x),,,y(10)=r,,x,)

???Errorusing==>dsolve

Error,(indsolve/IC)The?implicit*optionisnotavailablewhengiving

InitialConditions.

1(c)dsolve(,Dy=-x*sin(x)/cos(y),,,y(2)=r,,x,)

ans=

asin(-sin(x)+x*cos(x)+sin(2)-2*cos(2)+sin(l))

2,dsolve(,Df=f+2*g',,Dg=f+4,)

ans=

f:|lxlsym]-exp(-t)*C2+2*exp(2*t)*C1-4

g:[1x1sym]exp(-t)*C2+exp(2*t)*Cl+2

3.方法1?dsolve('Df=f+g,,,Dg=-f+g,,,f(0)=2,,,g(0)=5,)

ans=

f:|lxlsym]exp(t)*(5*sin(t)+2*cos(t))

g:[1x1sym]-exp(t)*(-5*cos(t)+2*sin(t))

方法2：

?functiondy=love(t,y)

dy=zeros(2,l);

dy(l)=y(l)+y(2);

dy(2)=-y(l)+y(2);

ode45(@love,[03000],[25])

s307

X10

500WOO150020003000

Matlab(7)

例題：1、f=[-4;-5;-6];A=[l,-l,l;3,2,4;3,2,0]

A=

1-11

324

320

?b=[20;42;30];b=zeros(3,l)

0

0

0

[x,feval]=linprog(f,A,b,[],[],b)

Optimizationterminated.

X=

1.0e-011*

0.0000

0.1418

0.0820

feval=

-1.2010e-011

練習(xí)題：

1、f=[l1-4000]

11-4000

?Aeq=[l12100;11-1010;-l11006]

Aeq=

112100

11-1010

-111006

?Aeq=[l121001-1010;-l11006]

Aeq=

112100

11-1010

-111006

?Aeq=[l12100;1-1010;-l11001]

Aeq=

11210