MATLAB³ÌÐòÉè¼ÆÓëÓ¦Ó㨵ڶþ°æ£©

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%ʵÑéÒ» MATLABÔËËã»ù%µÚËÄÌâ %(1):

A=100:999; B=rem(A,21);

´¡

%µÚÒ»Ìâ %£¨1£©

z1=2*sin(85*pi/180)/(1+exp(2)) %£¨2£©

x=[2,1+2i;-0.45,5];

z2=0.5*log(x+sqrt(1+x.^2)) %(3)

a=-3.0:0.1:3.0;

z3=(exp(0.3*a)-exp(-0.3*a))/2.*sin(a+0.3)+log((0.3+a)/2) %(4)

t=0:0.5:2.5;

z4=t.^2.*(t>=0&t<1)+(t.^2-1).*(t>=1&t<2)+(t.^2-2*t+1).*(t>=2&t<3)

%µÚ¶þÌâ

A=[12 34 -4;34 7 87;3 65 7]; B=[1 3 -1;2 0 3;3 -2 7]; A+6*B

A-B+eye(size(A)) A*B A.*B A^3 A.^3 A/B B\\A [A,B]

[A([1,3],:);B^2]

%µÚÈýÌâ

A=[1 2 3 4 5;6 7 8 9 10;11 12 13 14 15;16 17 18 19 20;21 22 23 24 25]

B=[3 0 16;17 -6 9;0 23 -4;9 7 0;4 13 11] C=A*B

F=size(C)

D=C(F(1)-2:F(1),F(2)-1:F(2)) whos

C=length(find(B==0)) %(2):

A='lsdhKSDLKklsdkl'; k=find(A>='A'&A<='Z'); A(k)=[]

%ʵÑé¶þ MATLAB¾ØÕó·ÖÎöÓë´¦Àí

%µÚÒ»Ìâ

E=eye(3); R=rand(3,2); O=zeros(2,3); S=diag([2,3]); A=[E,R;O,S]; A^2

B=[E,(R+R*S);O,S^2]

%µÚ¶þÌâ

H=hilb(5) P=pascal(5) Hh=det(H) Hp=det(P) Th=cond(H) Tp=cond(P)

%µÚÈýÌâ:

A=fix(10*rand(5)) H=det(A) Trace=trace(A) Rank=rank(A) Norm=norm(A)

%µÚËÄÌâ:

A=[-29,6,18;20,5,12;-8,8,5] [V,D]=eig(A) %ÊýѧÒâÒåÂÔ

%µÚÎåÌâ·½·¨Ò»:

%(1):

A=[1/2,1/3,1/4;1/3,1/4,1/5;1/4,1/5,1/6];

b=[0.95,0.67,0.52]'; x=inv(A)*b

1

%(2):

B=[0.95,0.67,0.53]'; x=inv(A)*B %(3): cond(A)

0];

y=[]; %½¨Á¢´æ·ÅËùÓÐyÖµµÄ¾ØÕó for x0=x

if x0<0&x0~=-3

y=[y,x0*x0+x0-6]; elseif

x0>=0&x0<5&x0~=2&x0~=3

y=[y,x0*x0-5*x0+6]; else

y=[y,x0*x0-x0-1]; end end

x %Êä³öËùÓÐx

y %Êä³öËùÓÐy

%µÚÒ»Ìâ³ÌÐò¶þ

x=[-5,-3,1,2,2.5,3,5]; y=[];

for a=1:7

if x(a)<0&x(a)~=-3

y=[y,(x(a))^2+x(a)-6]; elseif

x(a)>=0&x(a)<5&x(a)~=2&x(a)~=3 y=[y,(x(a))^2-5*x(a)+6]; else

y=[y,x(a)*x(a)-x(a)-1]; end end

%µÚ¶þÌâ³ÌÐòÒ»:

score=input('ÇëÊäÈëÒ»¸ö·ÖÊý:'); if score<0&score>100 disp('ÊäÈëµÄ·ÖÊý²»ºÏÀí'); else

if score>=90&score<=100 disp('µÈ¼¶Îª:A');

elseif score>=80&score<=89 disp('µÈ¼¶Îª:B');

elseif score>=70&score<=79 disp('µÈ¼¶Îª:C');

elseif score>=60&score<=69 disp('µÈ¼¶Îª:D'); else

%µÚÎåÌâ·½·¨¶þ:

A=hilb(4) A(:,1)=[] A(4,:)=[]

B=[0.95,0.67,0.52]'; X=inv(A)*B

B1=[0.95,0.67,0.53]'; X1=inv(A)*B1 N=cond(B) N1=cond(B1)

Na=cond(A) %¾ØÕóAΪ²¡Ì¬¾ØÕó

%µÚÁùÌâ

A=[1,4,9;16,25,36;49,64,81] B=sqrtm(A)

C=sqrt(A) %sqrtmº¯ÊýÊÇÒÔ¾ØÕóΪµ¥Î»½øÐмÆË㣬sqrtº¯ÊýÊÇÒÔ¾ØÕóÖеÄÔªËؽøÐмÆËã

%ʵÑéÈý Ñ¡Ôñ³ÌÐò½á¹¹Éè¼Æ

%µÚÒ»Ìâ³ÌÐòÒ»

x=[-5.0,-3.0,1.0,2.0,2.5,3.0,5.0]; y=[]; for x0=x

if x0<0&x0~=-3

y=[y,x0*x0+x0-6];

elseif x0>=0&x0<5&x0~=2&x0~=3 y=[y,x0*x0-5*x0+6]; else

y=[y,x0*x0-x0-1]; end end x

y

x=[-5.0,-3.0,1.0,2.0,2.5,3.0,5.

2

disp('µÈ¼¶Îª:E'); end end

x=input('ÇëÊäÈëÒ»¸ö°Ù·ÖÖƳɼ¨£º'); if x>100|x<0

disp('ÄúÊäÈëµÄ³É¼¨²»ÊÇ°Ù·ÖÖƳɼ¨£¬s=input('ÇëÊäÈëÒ»¸ö³É¼¨£¨0·Öµ½100·ÖÖ®¼ä£©£º'); %sÓÃÓÚ´æ·Å³É¼¨ while

1 %ÅжÏÊäÈë³É¼¨µÄºÏÀíÐÔ if s<0|s>100

disp('ÊäÈëµÄ³É¼¨ÐèÔÚ0µ½100Ö®¼ä£¬ÇëÖØÐÂÊäÈ룺')

s=input('ÇëÊäÈëÒ»¸ö³É¼¨£¨0ÇëÖØÐÂÊäÈë¡£'); else

if x<=100&x>=90 disp('A');

elseif x<=89&x>=80 disp('B');

elseif x<=79&x>=70 disp('C');

elseif x<=69&x>60 disp('D'); else

disp('E'); end end

%µÚ¶þÌâ³ÌÐò¶þ£º

score=input('ÇëÊäÈëÒ»¸ö·ÖÊý:'); if score<0&score>100 disp('ÊäÈëµÄ·ÖÊý²»ºÏÀí'); else

switch fix(score/10) case {9,10} disp('A'); case {8}

disp('B'); case {7}

disp('C'); case {6}

disp('D'); otherwise

disp('E'); end end

·Öµ½100·ÖÖ®¼ä£©£º'); else

break; end end switch

fix(s/10) %¶Ô³É¼¨×ö³öµÈ¼¶ÅÐ¶Ï case {9,10} disp('A') case 8

disp('B') case 7

disp('C') case 6

disp('D') otherwise disp('E') end

%µÚÈýÌâ

a=input('¹¤ºÅ:'); b=input('¹¤Ê±:'); if b>120

c=120*84+(b-120)*84*(1+0.15); elseif b<60 c=84*b-700; else

c=84*b; end

disp(['¹¤ºÅΪ',num2str(a),'µÄÔ±¹¤µÄ¹¤×ÊΪ',num2str(c)]);

3

n=input('ÇëÊäÈëÔ±¹¤¹¤ºÅ£º'); h=input('¸ÃÔ±¹¤¹¤×÷ʱÊýÊÇ£º'); if h>120

x=(h-120)*84*(1+0.15)+120*84; elseif h<60 x=h*84-700; else

x=h*84; end

disp([num2str(n),'ºÅÔ±¹¤','µÄÓ¦·¢¹¤×ÊΪ',num2str(x)]);

%µÚËÄÌ⣨»¹¿ÉÒÔÓÃswitchÓï¾äʵÏÖ£© a=input('a='); b=input('b=');

c=input('ÊäÈëÒ»¸öËÄÔòÔËËã·ûºÅ£º','s'); if c=='+' d=a+b;

elseif c=='-' d=a-b; elseif c=='*' d=a*b;

elseif c=='/' d=a/b; end

disp(['½á¹ûΪ:',num2str(d)]);

a=fix(10+(99-10)*rand(1,2)) %²úÉúÁ½¸öËæ»úÕûÊý x=a(1); y=a(2);

t=input('ÇëÊäÈëÔËËã·ûºÅ£º','s'); if t=='+' z=x+y;

elseif t=='-' z=x-y;

elseif t=='*' z=x*y;

elseif t=='/' z=x/y; end

disp([num2str(x),t,num2str(y),'=',num2str(z)]) %Êä³öÔËËã½á¹û %µÚÎåÌâ

a=rand(5,6);

n=input('Êä³ö¾ØÕóµÄµÚ¼¸ÐÐ:'); if n>5

disp(['³¬³öÁ˾ØÕóµÄÐÐÊý,Êä³ö¾ØÕóµÄ×îºóÒ»ÐÐΪ:',num2str(a(5,:))]); else

disp(['¾ØÕóµÄµÚ',num2str(n),'ÐÐΪ:',num2str(a(n,:))]); end

a=rand(5,6) %²úÉú5x6µÄËæ»ú¾ØÕó

n=input('ÇëÊäÈëÄúÒªÊä³ö¾ØÕóµÄµÚ¼¸ÐУº'); if n>5

disp('³¬³öÁ˾ØÕóµÄÐÐÊý£¬¾ØÕóµÄ×îºóÒ»ÐÐΪ£º') a(5,:) else

disp(['¾ØÕóµÄµÚ',num2str(n),'ÐÐΪ£º']) a(n,:) end

%ʵÑéËÄ Ñ­»·½á¹¹³ÌÐòÉè¼Æ

%µÚÒ»Ìâ³ÌÐòÒ» s=0;

n=input('n=?'); for i=1:n

s=s+1/i/i; end

PI=sqrt(6*s) pi

%µÚÒ»Ìâ³ÌÐò¶þ

n=input('n=?'); a=1:n;

4

b=1./a.^2;

PI=sqrt(6*sum(b)) pi

%µÚ¶þÌâ y=0; n=1;

while(y<3)

y=y+1/(2*n-1); n=n+1; end

y=y-1/(2*(n-1)-1) n=n-2

%µÚÈýÌâ

a=input('a=?'); b=input('b=?'); Xn=1;

Xn1=a/(b+Xn); n=0;

while abs(Xn1-Xn)>1e-5 Xn=Xn1;

Xn1=a/(b+Xn); n=n+1; if n==500 break; end end n Xn1

r1=(-b+sqrt(b*b+4*a))/2 r2=(-b-sqrt(b*b+4*a))/2 %µÚËÄÌâ

for i=1:100 if i==1 f(i)=1; elseif i==2 f(i)=0; elseif i==3 f(i)=1; else

f(i)=f(i-1)-2*f(i-2)+f(i-3);

end end max(f) min(f) sum(f)

length(find(f>0)) length(find(f==0)) length(find(f<0)) %µÚÎåÌ⣺ s=0;n=0; for i=2:49

b=i*(i+1)-1; m=fix(sqrt(b)); for j=2:m

if rem(b,j)==0 break end end

if j==m n=n+1; s=s+b; end end n s

%ʵÑéÎå º¯ÊýÎļþ

%µÚÒ»Ìâ

function y=mat1(x) %½¨Á¢º¯ÊýÎļþmat1.m

y=[exp(x),log(x),sin(x),cos(x)];

%ÔÚÃüÁî´°¿Úµ÷ÓÃÉÏÊöº¯ÊýÎļþ£º y=mat1(1+i)

%µÚ¶þÌâ³ÌÐòÒ» function

[a,b,N,M]=shiyanwu2(m,n,t)

A=[m*cos(t*pi/180),-m,-sin(t*pi/180),0;m*sin(t*pi/180),0,cos(t*pi/180),0;0,n,-sin(t*pi/180),0;0,0,-cos(t*pi/180),1]; B=[0,9.8*m,0,9.8*n]; C=inv(A)*B'; a=C(1);

5

b=C(2); N=C(3); M=C(4);

%ÔÚÃüÁî´°¿Úµ÷Óøú¯ÊýÎļþ: m1=input('m1='); m2=input('m2=');

theta=input('theta=');

[a1,a2,N1,N2]=shiyanwu2(m1,m2,t%µÚÎåÌâ %(1)

function f1=mat5(n) f1=n+10*log(n*n+5);

%ÔÚÃüÁî´°¿ÚÖе÷Óøú¯ÊýÎļþ£º

y=mat5(40)/(mat5(30)+mat5(20)) %(2)·½·¨Ò»

function f2=mat6(n) heta)

%µÚ¶þÌâ³ÌÐò¶þ

function X=mat2(m1,m2,t) g=9.8;

A=[m1*cos(t*pi/180),-m1,-sin(t*pi/180),0;m1*sin(t*pi/180),0,cos(t*pi/180),0;0,m2,-sin(t*pi/180),0;0,0,-cos(t*pi/180),1]; B=[0;m1*g;0;m2*g]; X=inv(A)*B;

%ÔÚÃüÁî´°¿Úµ÷Óøú¯ÊýÎļþ£º X=mat2(1,1,60)

%µÚÈýÌâ

function flag=mat3(x) flag=1;

for i=2:sqrt(x) if rem(x,i)==0 flag=0; break; end end

%ÔÚÃüÁî´°¿Úµ÷Óøú¯ÊýÎļþ£º for i=10:99

j=10*rem(i,10)+fix(i/10); if mat3(i)&mat3(j) disp(i) end end

%µÚËÄÌâ

function y=fx(x)

y=1./((x-2).^2+0.1)+1./((x-3).^4+0.01);

%ÔÚÃüÁî´°¿Úµ÷Óøú¯ÊýÎļþ£º y=fx(2)

a=[1,2;3,4]; y=fx(a)

f2=0;

for i=1:n

f2=f2+i*(i+1); end

%ÔÚÃüÁî´°¿ÚÖе÷Óøú¯ÊýÎļþÈ磺

y=mat6(40)/(mat6(30)+mat6(20)) %(2)·½·¨¶þ

function f2=mat7(n) i=1:n;

m=i.*(i+1); f2=sum(m); end

%ÔÚÃüÁî´°¿ÚÖе÷Óøú¯ÊýÎļþÈ磺

y=mat7(40)/(mat7(30)+mat7(20))

%ʵÑéÁù ¸ß²ã»æͼ²Ù×÷

%µÚÒ»Ì⣺

x=linspace(0,2*pi,101);

y=(0.5+3*sin(x)./(1+x.^2)).*cos(x);

plot(x,y)

%µÚ¶þÌ⣺ %£¨1£©

x=linspace(-2*pi,2*pi,100); y1=x.^2;

y2=cos(2*x); y3=y1.*y2;

plot(x,y1,'b-',x,y2,'r:',x,y3,'y--');

text(4,16,'\\leftarrow y1=x^2'); text(6*pi/4,-1,'\\downarrow y2=cos(2*x)');

text(-1.5*pi,-2.25*pi*pi,'\%uparrow y3=y1*y2');

%£¨2£©

x=linspace(-2*pi,2*pi,100);

6

y1=x.^2;

y2=cos(2*x); y3=y1.*y2;

subplot(1,3,1);%·ÖÇø plot(x,y1);

title('y1=x^2');%ÉèÖñêÌâ subplot(1,3,2); plot(x,y2);

title('y2=cos(2*x)'); subplot(1,3,3); plot(x,y3);

title('y3=x^2*cos(2*x)'); %£¨3£©

x=linspace(-2*pi,2*pi,20); y1=x.^2;

subplot(2,2,1);%·ÖÇø bar(x,y1);

title('y1=x^2µÄÌõÐÎͼ');%ÉèÖñêÌâ subplot(2,2,2); stairs(x,y1);

title('y1=x^2µÄ½×ÌÝͼ'); subplot(2,2,3); stem(x,y1);

title('y1=x^2µÄ¸Ëͼ'); subplot(2,2,4);

fill(x,y1,'r');%Èç¹ûÉÙÁË'r'Ôò»á³ö´í

title('y1=x^2µÄÌî³äͼ'); %ÆäËûµÄº¯ÊýÕÕÑù×ö¡£ %µÚÈýÌâ

x=-5:0.01:5;

y=[];%ÆðʼÉèyΪ¿ÕÏòÁ¿ for x0=x

if x0<=0 %²»ÄÜд³Éx0=<0

y=[y,(x0+sqrt(pi))/exp(2)]; %½«x¶ÔÓ¦µÄº¯ÊýÖµ·Åµ½yÖÐ else

y=[y,0.5*log(x0+sqrt(1+x0^2))]; end end

plot(x,y) %µÚËÄÌ⣺

a=input('a=');

b=input('b='); n=input('n=');

t=-2*pi:0.01:2*pi; r=a*sin(b+n*t); polar(t,r)

%µÚÎåÌâ

x=linspace(-5,5,21); y=linspace(0,10,31);

[x,y]=meshgrid(x,y);%ÔÚ[-5,5]*[0,10]µÄ·¶Î§ÄÚÉú³ÉÍø¸ñ×ø±ê z=cos(x).*cos(y).*exp(-sqrt(x.^2+y.^2)/4);

subplot(2,1,1); surf(x,y,z); subplot(2,1,2);

contour3(x,y,z,50);%ÆäÖÐ50Ϊ¸ß¶ÈµÄµÈ¼¶Êý£¬Ô½´óÔ½ÃÜ %µÚÁùÌâ

ezsurf('cos(s)*cos(t)','cos(s)*sin(t)','sin(s)',[0,0.5*pi,0,1.5*pi]); %ÀûÓÃezsurfÒþº¯Êý

shading interp %½øÐвåÖµ×ÅÉ«´¦Àí

%ʵÑéÆß µÍ²ã»æͼ²Ù×÷

%µÚÒ»Ìâ

h=figure('MenuBar','figure','color','r','WindowButtonDownFcn','disp(''Left Button Pressed'')') %µÚ¶þÌâ

x=-2:0.01:2;

y=x.^2.*exp(2*x); h=line(x,y);

set(h,'color','r','linestyle',':','linewidth',2)

text(1,exp(2),'y=x^2*exp(2*x)') %µÚÈýÌâ

t=0:0.00001:0.001; [t,x]=meshgrid(t);

v=10*exp(-0.01*x).*sin(2000*pi*t-0.2*x+pi);

axes('view',[-37.5,30]); h=surface(t,x,v);

title('v=10*exp(-0.01*x).*sin(2000*pi*t-0.2*x+pi)');

7

xlabel(Ct'),ylabel('x'),zlabel('v')

%µÚËÄÌâ

x=0:0.01:2*pi; y1=sin(x); y2=cos(x); y3=tan(x); y4=cot(x);

subplot(2,2,1); plot(x,y1);

subplot(2,2,2); plot(x,y2);

subplot(2,2,3); plot(x,y3);

subplot(2,2,4); plot(x,y4);

%µÚÎåÌâ

cylinder(5);

light('Position',[0,1,1]); material shiny

%ʵÑé°Ë Êý¾Ý´¦ÀíÓë¶àÏîʽÔËËã

%µÚÒ»Ìâ %(1)

A=rand(1,30000); b=mean(A) std(A,0,2) %(2) max(A) min(A) %(3) n=0;

for i=1:30000 if A(i)>0.5 n=n+1; end end

p=n/30000

%µÚ¶þÌâ %(1)

A=45+51*rand(100,5); [Y,U]=max(A)

[a,b]=min(A) %(2)

m=mean(A) s=std(A) %(3)

sum(A,2)

[Y,U]=max(ans) [a,b]=min(ans) %(4)

[zcj,xsxh]=sort(ans) %µÚÈýÌâ h=6:2:18;

x=6.5:2:17.5;

t1=[18,20,22,25,30,28,24]; t2=[15,19,24,28,34,32,30]; T1=spline(h,t1,x) T2=spline(h,t2,x) %µÚËÄÌâ

x=1:0.1:101; y1=log10(x);

p=polyfit(x,y1,5) y2=polyval(p,x);

plot(x,y1,':',x,y2,'-') %µÚÎåÌâ %(1)

p1=[1,2,4,0,5]; p2=[1,2]; p3=[1,2,3];

p=p1+[0,conv(p2,p3)] %ΪʹÁ½ÏòÁ¿´óСÏàͬ£¬ËùÒÔ²¹0 %(2)

A=roots(p) %(3)

A=[-1,1.2,-1.4;0.75,2,3.5;0,5,2.5];

polyval(p,A) %(4)

polyvalm(p,A)

ʵÑéÊ®

³ÌÐò£º

x=sym('6'); y=sym('5');

z=(x+1)/(sqrt(3+x)-sqrt(y))

8

1¡¢ ·Ö½âÒòʽ £¨1£© ³ÌÐò£º syms x y; A=x^4-y^4; factor(A) £¨2£© ³ÌÐò£º

factor(sym('5135')) 3¡¢»¯¼ò±í´ïʽ £¨1£© ³ÌÐò£º

syms beta1 beta2

y=sin(beta1)*cos(beta2)-cos(beta1)*sin(beta2) simple(y) £¨2£© ³ÌÐò£º

syms x

y=(4*x^2+8*x+3)/(2*x+1) simple(y)

5¡¢Ó÷ûºÅ·½·¨ÇóÏÂÁм«ÏÞ»òµ¼Êý £¨1£© ³ÌÐò£º

syms x

f=(x*(exp(sin(x))+1)-2*(exp(tan(x))-1))/(sin(x)) limit(f) £¨2£© ³ÌÐò£º

syms x

y=(sqrt(pi)-sqrt(acos(x)))/(sqrt(x+1));

limit(f,x,-1,'right') £¨3£© ³ÌÐò£º

syms x

y=(1-cos(2*x))/x; y1=diff(y) y2=diff(y,x,2)

6¡¢Ó÷ûºÅ·½·¨ÇóÏÂÁлý·Ö £¨1£© ³ÌÐò£º syms x

f=1/(1+x^4+x^8) int(f) £¨2£© ³ÌÐò£º

syms x

f=1/(((asin(x))^2)*sqrt(1-x^2)) int(f) £¨3£© ³ÌÐò£º

syms x

f=(x^2+1)/(x^4+1) int(f,x,0,inf) £¨4£© ³ÌÐò£º

syms x

f=exp(x)*(1+exp(x))^2 y=int(f,x,0,log(2)) double(y)

ʵÑéʮһ ¼¶ÊýÓë·½³Ì·ûºÅÇó½â 1. ¼¶Êý·ûºÅÇóºÍ¡£ (1) ¼ÆËã ¡£

(2) Çó¼¶Êý µÄºÍº¯Êý£¬²¢Çó Ö®ºÍ¡£ ½â£º

MÎļþ£º clear all;clc;

n=sym('n');x=sym('x');

S1=symsum(1/(2*n-1),n,1,10) S2=symsum(n^2*x^(n-1),n,1,inf)

S3=symsum(n^2/5^n,n,1,inf) %vpa(S3)¿ÉÒÔת»¯³ÉСÊý ÔËÐнá¹û£º S1 =

31037876/14549535 S2 =

piecewise([abs(x) < 1, -(x^2 + x)/(x*(x - 1)^3)]) S3 = 15/32

2. ½«lnxÔÚx=1´¦°´5´Î¶àÏîʽչ¿ªÎªÌ©ÀÕ¼¶Êý¡£ ½â£º

MÎļþ£º clear all;clc; x=sym('x');

9

f=log(x); clear all;clc; taylor(f,x,6,1) dsolve('D2y+4*Dy+29*y','y(0)=0','Dy(0)=15','

x') ÔËÐнá¹û£º

ans = x - (x - 1)^2/2 + (x - 1)^3/3 - (x - 1)^4/4 + (x - ÔËÐнá¹û£º 1)^5/5 - 1 ans =

(3*sin(5*x))/exp(2*x) 3. ÇóÏÂÁз½³ÌµÄ·ûºÅ½â¡£

½â£º 5. Çó΢·Ö·½³Ì×éµÄͨ½â¡£ MÎļþ£º ½â£º clear all;clc; MÎļþ£º x1=solve('log(x+1)-5/(1+sin(x))=2') clear all;clc; x2=solve('x^2+9*sqrt(x+1)-1') [x y z]=dsolve('Dx=2*x-3*y+3*z',... x3=solve('3*x*exp(x)+5*sin(x)-78.5') 'Dy=4*x-5*y+3*z','Dz=4*x-4*y+2*z','t') [x4 ÔËÐнá¹û£º y4]=solve('sqrt(x^2+y^2)-100','3*x+5*y-8') x =

C1/exp(t) + C2*exp(2*t) ÔËÐнá¹û£º

x1 = y = 521.67926389905839979437366649258 C1/exp(t) + C2*exp(2*t) + C3/exp(2*t) x2 = z =

C2*exp(2*t) + C3/exp(2*t) -1 ʵÑé¾Å Êýֵ΢»ý·ÖÓë·½³ÌÊýÖµÇó½â (3^(1/2)*i*(4/(9*(6465^(1/2)/2 + 1. Çóº¯ÊýÔÚÖ¸¶¨µãµÄÊýÖµµ¼Êý¡£ 2171/54)^(1/3)) - (1/2*6465^(1/2) + ½â£ºMÎļþ£º 2171/54)^(1/3)))/2 - (6465^(1/2)/2 + clc;clear; 2171/54)^(1/3)/2 - 2/(9*(6465^(1/2)/2 + x=1; 2171/54)^(1/3)) + 1/3 i=1; 1/3 - (6465^(1/2)/2 + 2171/54)^(1/3)/2 - f=inline('det([x x^2 x^3;1 2*x 3*x^2;0 2 (3^(1/2)*i*(4/(9*(6465^(1/2)/2 + 6*x])'); 2171/54)^(1/3)) - (1/2*6465^(1/2) + while x<=3.01 2171/54)^(1/3)))/2 - 2/(9*(6465^(1/2)/2 + g(i)=f(x); 2171/54)^(1/3)) i=i+1; x3 = x=x+0.01; %ÒÔ0.01µÄ²½2.3599419584772910151699327715486 ³¤Ôö¼Ó£¬¿ÉÔÙËõС²½³¤Ìá¸ß¾«¶È x4 = end 12/17 - (10*21246^(1/2))/17 g; (10*21246^(1/2))/17 + 12/17 t=1:0.01:3.01; y4 = dx=diff(g)/0.01; %²î·Ö·¨½üËÆÇóµ¼ (6*21246^(1/2))/17 + 20/17 f1=dx(1) %x=1µÄÊýÖµµ¹Êý 20/17 - (6*21246^(1/2))/17 f2=dx(101) %x=2µÄÊýÖµµ¹Êý 4. Çó΢·Ö·½³Ì³õÖµÎÊÌâµÄ·ûºÅ½â£¬²¢ÓëÊýÖµf3=dx(length(g)-1) %x=3µÄÊýÖµµ¹Êý ½â½øÐбȽϡ£ ÔËÐнá¹û£º f1 =

6.0602 ½â£º

f2 = MÎļþ£º

10

24.1202 f3 =

54.1802

2. ÓÃÊýÖµ·½·¨Ç󶨻ý·Ö¡£ (1) µÄ½üËÆÖµ¡£ (2)

½â£ºMÎļþ£º clc;clear;

f=inline('sqrt(cos(t.^2)+4*sin(2*t).^2+1)'); I1=quad(f,0,2*pi)

g=inline('log(1+x)./(1+x.^2)'); I2=quad(g,0,2*pi) ÔËÐнá¹û£º

3. ·Ö±ðÓÃ3ÖÖ²»Í¬µÄÊýÖµ·½·¨½âÏßÐÔ·½³Ì×é¡£

½â£ºMÎļþ£º clc;clear;

A=[6 5 -2 5;9 -1 4 -1;3 4 2 -2;3 -9 0 2]; b=[-4 13 1 11]'; x=A\\b

y=inv(A)*b [L,U]=lu(A); z=U\\(L\\b) ÔËÐнá¹û£º

4. Çó·ÇÆë´ÎÏßÐÔ·½³Ì×éµÄͨ½â¡£ ½â£ºMÎļþ

function [x,y]=line_solution(A,b) [m,n]=size(A); y=[ ];

if norm(b)>0 %·ÇÆë´Î·½³Ì×é if rank(A)==rank([A,b]) if rank(A)==n

disp('ÓÐΨһ½âx'); x=A\\b; else

disp('ÓÐÎÞÇî¸ö½â£¬Ìؽâx£¬»ù´¡½âϵy');

x=A\\b;

y=null(A,'r'); end else

disp('ÎÞ½â'); x=[ ];

11

end

else %Æë´Î·½³Ì×é disp('ÓÐÁã½âx'); x=zeros(n,1); if rank(A)

disp('ÓÐÎÞÇî¸ö½â£¬»ù´¡½âϵy'); y=null(A,'r'); end end

clc;clear; format rat

A=[2 7 3 1;3 5 2 2;9 4 1 7]; b=[6 4 2]';

[x,y]=line_solution(A,b) ÔËÐнá¹û£º

ÓÐÎÞÇî¸ö½â£¬Ìؽâx£¬»ù´¡½âϵy

Warning: Rank deficient, rank = 2, tol = 8.6112e-015.

> In line_solution at 11 x =

-2/11 10/11 0 0 y =

1/11 -9/11 -5/11 1/11 1 0 0 1 ËùÒÔÔ­·½³Ì×éµÄͨ½âÊÇ£º £¬ÆäÖРΪÈÎÒâ³£Êý¡£ 5. Çó´úÊý·½³ÌµÄÊýÖµ½â¡£

(1) 3x+sinx-ex=0ÔÚx0=1.5¸½½üµÄ¸ù¡£ (2) ÔÚ¸ø¶¨µÄ³õÖµx0=1£¬y0=1£¬z0=1Ï£¬Çó·½³Ì×éµÄÊýÖµ½â¡£ ½â£ºMÎļþ£º function g=f(x)

g=3*x+sin(x)-exp(x); clc;clear; fzero('f',1.5) ½á¹ûÊÇ£º ans =

1289/682

(2). MÎļþ£º function F=fun(X) x=X(1); y=X(2); z=X(3);

F(1)=sin(x)+y^2+log(z)-7; F(2)=3*x+2-z^3+1; F(3)=x+y+z-5;

X=fsolve('myfun',[1,1,1]',optimset('Display','off'))

ÔËÐнá¹û£º

6. Çóº¯ÊýÔÚÖ¸¶¨Çø¼äµÄ¼«Öµ¡£ (1) ÔÚ(0,1)ÄÚµÄ×îСֵ¡£

(2) ÔÚ[0,0]¸½½üµÄ×îСֵµãºÍ×îСֵ¡£ ½â£ºMÎļþ£º function f=g(u) x=u(1); y=u(2);

f=2*x.^3+4*x.*y^3-10*x.*y+y.^2; clc;clear; format long

f=inline('(x^3+cos(x)+x*log(x))/exp(x)'); [x,fmin1]=fminbnd(f,0,1)

[U,fmin2]=fminsearch('g',[0,0]) ÔËÐнá¹û

7. Çó΢·Ö·½³ÌµÄÊýÖµ½â¡£ ½â£ºMÎļþ£º

function xdot= sys( x,y) xdot=[y(2);(5*y(2)-y(1))/x]; clc;clear;

x0=1.0e-9;xf=20;

[x,y]=ode45('sys',[x0,xf],[0 0]); [x,y]

ÔËÐнá¹û£º

8. Çó΢·Ö·½³Ì×éµÄÊýÖµ½â£¬²¢»æÖƽâµÄÇúÏß¡£

½â£º Áîy1=x,y2=y,y3=z; ÕâÑù·½³Ì±äΪ: ,×Ô±äÁ¿ÊÇt MÎļþ£º

function xdot=sys(x,y)

xdot=[y(2)*y(3);-y(1)*y(3);-0.51*y(1)*y(2)]; clc;clear; t0=0;tf=8;

12

[x,y]=ode23('sys',[t0,tf],[0,1,1]) plot(x,y)