các bai tập mẫu matlab,lập trình c cho đại học,cao học và nghiên cứu sinh

các đề thi matlablập trình c cho học viên cao hocnghiên cứu sinh de 1 clear all;clc; %1 eq=DN1=a1N1, DN2=a1N1a2N2, DN3=a2N2; % he pt vi phan % A1: so khoi cua nguyen to 1; AV=6.022e+26; => N1(0)= AVA1; dk=N1(0)=AVA1, N2(0)=0, N3(0)=0; % dieu kien ban dau N1 N2 N3 = dsolve(eq,dk) %2 % A1=A2=A3=76 => M1 M2 M3= (A1AV)N1 N2 N3; T1=14.8;T2=16.1; syms A1 AV M1=N1A1AV; M2=simple(N2A1AV); M3=simple(N3A1AV); a1=log(2)T1;a2=log(2)T2; M1=subs(M1,a1,a1), M2=subs(M2,{a1,a2},{a1,a2}), M3=subs(M3,{a1,a2},{a1,a2}) ezplot(M1,0 200);hold on; h2=ezplot(M2,0 200); set(h2,Color,red) h3=ezplot(M3,0 200); set(h3,Color,g) legend(Kr,Br,Se); title(do thi khoi luong theo thoi gian); xlabel(Time(h));ylabel(Mass(kg));grid on de 2 clear all; clc; % y=(1+x2)2+2xy(1+x2) ;y(0)=10 dy=inline(((1+x2)2+2xy(1))(1+x2),x,y) x y=ode45(dy,0:0.1:15,10); %2,3 figure(1);title(do thi ham so);hold on; grid on; xlabel(chon Diem 0 roi nhan nut Enter,Color,red); xn,fn=sp_solve(x,y); % can file: sp_solve.m plot(xn,fn,ro); xlabel(chon Diem Cuc Tieu roi nhan nut Enter,Color,k); xm,fm=sp_min(x,y); % can file: sp_min.m plot(xm,fm,r); xlabel( ); de 3 clear all;clc; dy=DT=r(TTe); T=dsolve(dy,T(0)=T0) T=subs(T,{T0,Te,r},{85,23,0.025}) ezplot(T,0 200); grid on; xlabel(Time(s));ylabel(T(Celsius)); hold on; plot(0 200,23 23,r); %2 dy=DT=r1(TTe)r2(TTe)2; T2=dsolve(dy,T(0)=T0) T2=subs(T2,{T0,Te,r1,r2},{85,23,0.025,0.001}); T2=simple(T2) figure(2); ezplot(T2,0 200);hold on;grid on; xlabel(Time(s));ylabel(T(Celsius)); de 4 clear all;clc; %y=y(1); y=y(2);y=y(2) %he pt vi phan: y(1)=y(2);y(2)=y(2)+6y(1)2; dy=inline(y(2);y(2)+6y(1)2,x,y) %y(0)=1;y(1)=2; dy0=6:0.1:0; for k=1:length(dy0) x y=ode45(dy,0:.01:1,1;dy0(k)); yend(k)=y(end,1); end dyn,yn=sp_solve(dy0,yend2) x y=ode45(dy,0:.01:1,1;dyn); plot(x,y(:,1),r);hold on;grid on; % ve: y=f(x) plot(x,y(:,2),b); %ve: y=g(x) legend(y=f(x),dydx=g(x)); title(dk: y(0)=1;y(1)=2); %2 % y(0)=1; y(1)=1; figure(2); y0=2:0.1:0; for k=1:length(y0) x y=ode45(dy,0:.01:1,y0(k);1); dyend(k)=y(end,2); end yn,dyn=sp_solve(y0,dyend1) x y=ode45(dy,0:.01:1,yn;1); plot(x,y(:,1),r);hold on;grid on; % ve: y=f(x) plot(x,y(:,2),b); %ve: y=g(x) legend(y=f(x),dydx=g(x)); title(dk: dy(0)=1;dy(1)=1) de5 clear all;clc; % x=(km)x (muy)x; k=10;m=0.1;mu=0.01;x0=0;v0=0.1 dx=D2x=(km)x muDx; x=dsolve(dx,x(0)=x0,Dx(0)=v0) 2 x2=subs(x,{k,m,mu,x0,v0},{k,m,mu,x0,v0}); x2=simple(x2) v=diff(x2); t=0:0.01:6; x2=subs(x2,t); v=subs(v,t); title(toa do,van toc theo thoi gian);hold on; grid on; plot(t,x2,r); plot(t,v); legend(toa do,van toc); figure(2);title(khong gian pha) ;hold on; grid on; plot(x2,v); figure(3); title(nang luong);hold on; grid on; Ed=mv.22; Et=k(x2).22; E=Ed+Et; plot(t,Ed); plot(t,Et,g); plot(t,E,r); legend(dong nang,the nang,co nang); sp_min function xn,fxn=sp_min(xi,yi,lim); if nargin z = 1y = a0x+a1 xi=0 0.2 0.4 0.6 0.9 1.2 1.4 1.8 2 yi=0.97 0.69 0.57 0.456 0.36 0.31 0.265 0.2 0.196; a=polyfit(xi,yi.1,1); a0=a(1), a1=a(2) %b) plot(xi,yi,ro); hold on; grid on; x=0:0.01:2; z=polyval(a,x); plot(x,z.1); ĐỀ 13 clear all;clc; xi=0 13 24 36 40 51 63 74 82 85; yi=0 15 34 49 27 11 19 61 37 0; sp=spline(xi,yi); x=0:0.5:85; y=ppval(sp,x); plot(x,y);hold on;grid on; %b) sp2=spline(xi,yi); xlabel(chon Diem xa bo nhat roi Enter,Color,r); xm ym=ginput(1); f=inline(ppval(sp,x),x,sp) xm ym= fminsearch(f,xm,,sp2); plot(xm,ym,r); diem_xa_bo_nhat=xm ym %c) I=0; for i=1:length(x)1 r=x(i+1)x(i), y(i+1)y(i); I=I+norm(r); end quang_duong=I Đề 14 clear all;clc; ti=0:2:46; Ti=68.8 64.8 62.1 59.9 57.7 55.9 45.9 44.8 43.7 42.6 41.7 40.8,... 53.9 52.3 50.8 49.5 48.1 46.8 39.9 39.3 38.6 37.7 37.0 36.4; T=dsolve(DT=r(T17),T(0)=68.8); Tend=subs(T,t,ti(end)); % nhiet do cuoi:tai t=46s r=solve(TendTi(end),r); % tinh so bo he so r r=subs(r); r=linspace(r2,r2,50); %phuong phap ban: for k=1:length(r) Tk=subs(T,r,r(k)); Ss=subs(Tk,ti)Ti ; % Vector gia tri sai so nhiet do tai cac thoi gian ti Bp(k)=dot(Ss,Ss); % tong binh phuong sai so nhiet do end %phuong phap sai so binh phuong cuc tieu: xlabel(chon Diem Cuc Tieu roi Enter,Color,r);hold on; rr bp=sp_min(r,Bp); r=rr, %gia tri r de tong binh phuong sai so cuc tieu %b) T=subs(T,r,r) pl_min function xn,fn=pl_min(xi,yi); p=polyfit(xi,yi,length(xi)1); f=inline(polyval(p,x),x,p); x=linspace(xi(1),xi(end),100); y=f(x,p); xlabel(chon Cac cuc tieu roi Enter,Color,k);hold on;grid on; plot(x,y,b); x0,y0=ginput; for k=1:length(x0); xn(k),fn(k)=fminsearch(f,x0(k),,p); end; pl_solve function xn,fn=pl_solve(xi,yi); p=polyfit(xi,yi,length(xi)1); f=inline(polyval(p,x),x,p); x=linspace(xi(1),xi(end),100); y=f(x,p); xlabel(chon Cac diem 0 roi Enter,Color,r);hold on;grid on; plot(x,y,r); x0,y0=ginput; for k=1:length(x0); xn(k),fn(k)=fsolve(f,x0(k),,p); end; đề 6_1 clear all;clc % x= y(1); y=y(2); z=y(3) dy=inline(10(y(2)y(1));126.52y(1)y(2)y(1)y(3);y(1)y(2)8y(3)3,t,y); t y=ode45(dy,0 8,7.69 ;15.61;90.39); plot(t,y(:,1),r); hold on;grid on plot(t,y(:,2),g);plot(t,y(:,3)); legend(x(t),y(t),z(t)); %b) % y=y(1); y=y(2); y=(y+8x3y3))x; dy=inline(y(2); (y(2)+8x3y(1)3)x,x,y); x y=ode45(dy,1 4,12;12); figure(2); plot(x,y(:,1),r); hold on; grid on; plot(x,y(:,2),g); legend(y(x),dydx); Đề 7_1 clear all;clc; % bai nay giong De 2 dy=inline((1+x2)+ 2xy(1+x2),x,y); x,y=ode45(dy,0 15,10); %2 xlabel(Chon diem 0 roi Enter,Color,r); hold on;grid on; x0 y0=sp_solve(x,y); plot(x0,y0,ro); %3 xlabel(Chon cuc tieu roi Enter,Color,k); xm ym=sp_min(x,y); plot(xm,ym,r); xlabel( ); Đề 8_1 clear all;clc; % bai nay giong De 2 % y(0)=0.3; y(0)=0; dy=inline(y(2);0.2y(2)10sin(y(1)),x,y); x,y=ode45(dy,0 10,0.3;0); %2 xlabel(Chon tat ca Cac diem 0 roi Enter,Color,r); hold on;grid on; plot(x,y(:,1));plot(x,y(:,2),g);legend(y(x),dydx); x0 y0=sp_solve(x,y(:,1)); plot(x0,y0,ro); %3 xlabel(Chon Cac cuc tieu roi Enter,Color,k); xm ym=sp_min(x,y(:,1)); plot(xm,ym,r); xlabel( ); Đề 9_1 clear all;clc xi=0:8; yi=.6 .75 .8 .5 .1 .5 .7 .3 .1; a=polyfit(xi,yi,8); sp=spline(xi,yi); x=0:0.05:8; y=polyval(a,x); plot(x,y,r); hold on; grid on; ys=ppval(sp,x); plot(x,ys,y); legend(da thuc,spline); plot(xi,yi,k+); %2 figure(2); xn yn=pl_solve(xi,yi); xm ym=pl_min(xi,yi); figure(3); xlabel(chon Cac diem 0 roi Enter,Color,r);hold on; xn2 yn2=sp_solve(xi,yi); xlabel(chon Cac diem cuc tieu roi Enter,Color,k); xm2 ym2=sp_min(xi,yi); figure(1); plot(xn xn2,yn yn2,ro); plot(xm xm2,ym ym2,r); Đề 10_1 clear all;clc; % y=aexp(bx2+cx) =>ln(y)=ln(a)+bx2+cx; xi=0:0.2:1; yi=2.3 2.87 3.72 5.02 7.05 10.3; p=polyfit(xi,log(yi),2); a=exp(p(3)), b=p(1), c=p(2) %b) plot(xi,yi,ro); hold on; grid on; x=0:0.01:1; z=polyval(p,x); y=exp(z); plot(x,y); Đề 11_1 clear all;clc la=0.589 0.55 0.486 0.443 0.402; n=1.628 1.64 1.652 1.668 1.679; LA=la.2; % LA= 1la2; a=polyfit(LA,n,2); A=a(3),B=a(2),C=a(1) %2 lai=0.4:0.01:0.75; ni=polyval(a,lai.2); plot(la,n,r);hold on;grid on plot(lai,ni); xlabel(lambda(106m));ylabel(n); %3 lado=0.72; n_do=polyval(a,lado2) Đề 12_1 clear all;clc % y=1(a0x+a1) => z = 1y = a0x+a1 xi=0 0.2 0.4 0.6 0.9 1.2 1.4 1.8 2 yi=0.97 0.69 0.57 0.456 0.36 0.31 0.265 0.2 0.196; a=polyfit(xi,yi.1,1); a0=a(1), a1=a(2) %b) plot(xi,yi,ro); hold on; grid on; x=0:0.01:2; z=polyval(a,x); plot(x,z.1);

các đề thi matlab-lập trình c cho học viên cao hoc-nghiên cứu sinh

de 1

clear all;clc;

% -1

eq='DN1=-a1*N1, DN2=a1*N1-a2*N2, DN3=a2*N2'; % he pt vi phan

% A1: so khoi cua nguyen to 1; AV=6.022e+26; => N1(0)= AV/A1;

dk='N1(0)=AV/A1, N2(0)=0, N3(0)=0'; % dieu kien ban dau

[N1 N2 N3] = dsolve(eq,dk)

% -2

% A1=A2=A3=76 => [M1 M2 M3]= (A1/AV)*[N1 N2 N3];

T1=14.8;T2=16.1;

syms A1 AV

M1=N1*A1/AV; M2=simple(N2*A1/AV); M3=simple(N3*A1/AV);

a1=log(2)/T1;a2=log(2)/T2;

M1=subs(M1,'a1',a1),

M2=subs(M2,{'a1','a2'},{a1,a2}),

M3=subs(M3,{'a1','a2'},{a1,a2})

ezplot(M1,[0 200]);hold on;

h2=ezplot(M2,[0 200]); set(h2,'Color','red')

h3=ezplot(M3,[0 200]); set(h3,'Color','g')

legend('Kr','Br','Se'); title('do thi khoi luong theo thoi gian');

xlabel('Time(h)');ylabel('Mass(kg)');grid on

de 2

clear all; clc;

% y'=[(1+x^2)^2+2xy]/(1+x^2) ;y(0)=-10

dy=inline('((1+x^2)^2+2*x*y(1))/(1+x^2)','x','y')

[x y]=ode45(dy,[0:0.1:15],-10);

% -2,3

figure(1);title('do thi ham so');hold on; grid on;

xlabel('chon Diem 0 roi nhan nut Enter','Color','red');

[xn,fn]=sp_solve(x,y); % can file: sp_solve.m

plot(xn,fn,'ro');

xlabel('chon Diem Cuc Tieu roi nhan nut Enter','Color','k'); [xm,fm]=sp_min(x,y); % can file: sp_min.m

plot(xm,fm,'r*');

xlabel(' ');

de 3

clear all;clc;

dy='DT=-r*(T-Te)';

T=dsolve(dy,'T(0)=T0')

T=subs(T,{'T0','Te','r'},{85,23,0.025})

ezplot(T,[0 200]); grid on; xlabel('Time(s)');ylabel('T(Celsius)'); hold on; plot([0 200],[23 23],'r-');

% -2

dy='DT=-r1*(T-Te)-r2*(T-Te)^2';

T2=dsolve(dy,'T(0)=T0')

T2=subs(T2,{'T0','Te','r1','r2'},{85,23,0.025,0.001});

T2=simple(T2)

figure(2);

ezplot(T2,[0 200]);hold on;grid on;

xlabel('Time(s)');ylabel('T(Celsius)');

de 4

clear all;clc;

%y=y(1); y'=y(2);y"=y(2)'

%he pt vi phan: y(1)'=y(2);y(2)'=-y(2)+6*y(1)^2;

dy=inline('[y(2);-y(2)+6*y(1)^2]','x','y')

dy0=-6:0.1:0;

for k=1:length(dy0)

[x y]=ode45(dy,[0:.01:1],[1;dy0(k)]);

yend(k)=y(end,1);

end

[dyn,yn]=sp_solve(dy0,yend-2)

[x y]=ode45(dy,[0:.01:1],[1;dyn]);

plot(x,y(:,1),'r');hold on;grid on; % ve: y=f(x)

plot(x,y(:,2),'b'); %ve: y'=g(x)

legend('y=f(x)','dy/dx=g(x)'); title('dk: y(0)=1;y(1)=2');

% -2

% y'(0)=-1; y'(1)=1;

figure(2);

y0=-2:0.1:0;

for k=1:length(y0)

[x y]=ode45(dy,[0:.01:1],[y0(k);-1]);

dyend(k)=y(end,2);

end

[yn,dyn]=sp_solve(y0,dyend-1)

[x y]=ode45(dy,[0:.01:1],[yn;-1]);

plot(x,y(:,1),'r');hold on;grid on; % ve: y=f(x)

plot(x,y(:,2),'b'); %ve: y'=g(x)

legend('y=f(x)','dy/dx=g(x)'); title('dk: dy(0)=-1;dy(1)=1')

de5

clear all;clc;

% x''=-(k/m)*x - (muy)*x';

k=10;m=0.1;mu=0.01;x0=0;v0=0.1

dx='D2x=-(k/m)*x -mu*Dx';

x=dsolve(dx,'x(0)=x0','Dx(0)=v0')

-2

x2=subs(x,{'k','m','mu','x0','v0'},{k,m,mu,x0,v0}); x2=simple(x2)

v=diff(x2);

t=0:0.01:6;

x2=subs(x2,t); v=subs(v,t);

title('toa do,van toc theo thoi gian');hold on; grid on; plot(t,x2,'r'); plot(t,v); legend('toa do','van toc');

figure(2);title('khong gian pha') ;hold on; grid on; plot(x2,v);

figure(3); title('nang luong');hold on; grid on; Ed=m*v.^2/2; Et=k*(x2).^2/2; E=Ed+Et;

plot(t,Ed); plot(t,Et,'g'); plot(t,E,'r');

legend('dong nang','the nang','co nang');

sp_min

function [xn,fxn]=sp_min(xi,yi,lim);

if nargin<3

lim=[xi(1),xi(end)];

end;

sp=spline(xi,yi);

f=inline('ppval(sp,x)','x','sp');

fnplt(sp,lim);grid on;

[x0,y0]=ginput;

for k=1:length(x0);

[xn(k),fxn(k)]=fminsearch(f,x0(k),[],sp);

end;

sp_sole

function [xn,fxn]=sp_solve(xi,yi,lim);

if nargin<3

lim=[xi(1),xi(end)];

end;

sp=spline(xi,yi);

f=inline('ppval(sp,x)','x','sp');

fnplt(sp,lim);grid on;

[x0,y0]=ginput;

for k=1:length(x0);

[xn(k),fxn(k)]=fsolve(f,x0(k),[],sp);

end;

Đề 4b

clear all;clc;

%y=y(1); y'=y(2);y"=y(2)'

%he pt vi phan: y(1)'=y(2);y(2)'=-y(2)+6*y(1)^2; dy=inline('[y(2);-y(2)+6*y(1)^2]','x','y')

%y(0)=1;y(1)=2title('khong gian pha');hold on; grid on;

dy0=-6:0.1:0;

for k=1:length(dy0)

[x y]=ode45(dy,[0:.01:1],[1;dy0(k)]);

yend(k)=y(end,1);

end

xlabel('Chon diem 0 roi Enter','Color','r'); hold on;

[dyn,yn]=sp_solve(dy0,yend-2); hold off;

[x y]=ode45(dy,[0:.01:1],[1;dyn]);

plot(x,y(:,1),'r');hold on;grid on; % ve: y=f(x)

plot(x,y(:,2),'b'); %ve: y'=g(x)

legend('y=f(x)','dy/dx=g(x)'); title('dk: y(0)=1;y(1)=2');

% -2

% y'(0)=-1; y'(1)=1;

figure(2);

y0=-2:0.1:0;

for k=1:length(y0)

[x y]=ode45(dy,[0:.01:1],[y0(k);-1]);

dyend(k)=y(end,2);

end

xlabel('Chon diem 0 roi Enter','Color','r'); hold on;

[yn,dyn]=sp_solve(y0,dyend-1); hold off;

[x y]=ode45(dy,[0:.01:1],[yn;-1]);

plot(x,y(:,1),'r');hold on;grid on; % ve: y=f(x)

plot(x,y(:,2),'b'); %ve: y'=g(x)

legend('y=f(x)','dy/dx=g(x)'); title('dk: dy(0)=-1;dy(1)=1')

ĐỀ 6

clear all;clc

% x= y(1); y=y(2); z=y(3)

dy=inline('[10*(y(2)-y(1));126.52*y(1)-y(2)-y(1)*y(3);y(1)*y(2)-8*y(3)/3]','t','y'); [t y]=ode45(dy,[0 8],[-7.69 ;-15.61;90.39]);

plot(t,y(:,1),'r'); hold on;grid on

plot(t,y(:,2),'g');plot(t,y(:,3)); legend('x(t)','y(t)','z(t)');

% -b)

% y=y(1); y'=y(2); y"=(y'+8x^3y^3))/x;

dy=inline('[y(2); (y(2)+8*x^3*y(1)^3)/x]','x','y');

[x y]=ode45(dy,[1 4],[1/2;-1/2]);

figure(2);

plot(x,y(:,1),'r'); hold on; grid on;

plot(x,y(:,2),'g'); legend('y(x)','dy/dx');

ĐỀ 7

clear all;clc; % bai nay giong De 2

dy=inline('(1+x^2)+ 2*x*y/(1+x^2)','x','y');

[x,y]=ode45(dy,[0 15],-10);

% -2

xlabel('Chon diem 0 roi Enter','Color','r'); hold on;grid on;

[x0 y0]=sp_solve(x,y);

plot(x0,y0,'ro');

% -3

xlabel('Chon cuc tieu roi Enter','Color','k');

[xm ym]=sp_min(x,y);

plot(xm,ym,'r*');

xlabel(' ');

đề 8

clear all;clc; % bai nay giong De 2

% y(0)=0.3; y'(0)=0;

dy=inline('[y(2);-0.2*y(2)-10*sin(y(1))]','x','y');

[x,y]=ode45(dy,[0 10],[0.3;0]);

% -2

xlabel('Chon tat ca Cac diem 0 roi Enter','Color','r'); hold on;grid on; plot(x,y(:,1));plot(x,y(:,2),'g');legend('y(x)','dy/dx');

[x0 y0]=sp_solve(x,y(:,1));

plot(x0,y0,'ro');

% -3

xlabel('Chon Cac cuc tieu roi Enter','Color','k');

[xm ym]=sp_min(x,y(:,1));

plot(xm,ym,'r*');

xlabel(' ');

Đề 9

clear all;clc

xi=0:8; yi=[.6 75 8 5 1 -.5 -.7 -.3 1];

a=polyfit(xi,yi,8);

sp=spline(xi,yi);

x=0:0.05:8; y=polyval(a,x);

plot(x,y,'r'); hold on; grid on;

ys=ppval(sp,x);

plot(x,ys,'y'); legend('da thuc','spline');

plot(xi,yi,'k+');

% -2

figure(2);

[xn yn]=pl_solve(xi,yi); [xm ym]=pl_min(xi,yi);

figure(3);

xlabel('chon Cac diem 0 roi Enter','Color','r');hold on; [xn2 yn2]=sp_solve(xi,yi);

xlabel('chon Cac diem cuc tieu roi Enter','Color','k'); [xm2 ym2]=sp_min(xi,yi);

figure(1);

plot([xn xn2],[yn yn2],'ro'); plot([xm xm2],[ym ym2],'r*');

ĐỀ 10

clear all;clc;

% y=a*exp(b*x^2+c*x) =>ln(y)=ln(a)+b*x^2+c*x; xi=0:0.2:1; yi=[2.3 2.87 3.72 5.02 7.05 10.3];

a=exp(p(3)), b=p(1), c=p(2)

% -b)

plot(xi,yi,'ro'); hold on; grid on;

x=0:0.01:1; z=polyval(p,x); y=exp(z);

plot(x,y);

Đề 11

clear all;clc

la=[0.589 0.55 0.486 0.443 0.402];

n=[1.628 1.64 1.652 1.668 1.679];

LA=la.^-2; % LA= 1/la^2;

a=polyfit(LA,n,2);

A=a(3),B=a(2),C=a(1)

% -2

lai=0.4:0.01:0.75; ni=polyval(a,lai.^-2);

plot(la,n,'r*');hold on;grid on

plot(lai,ni); xlabel('lambda(10^-6m)');ylabel('n');

% -3

lado=0.72;

n_do=polyval(a,lado^-2)

ĐỀ 12

clear all;clc

% y=1/(a0*x+a1) => z = 1/y = a0*x+a1

xi=[0 0.2 0.4 0.6 0.9 1.2 1.4 1.8 2]

yi=[0.97 0.69 0.57 0.456 0.36 0.31 0.265 0.2 0.196]; a=polyfit(xi,yi.^-1,1);

a0=a(1), a1=a(2)

% -b)

plot(xi,yi,'ro'); hold on; grid on;

x=0:0.01:2; z=polyval(a,x);

ĐỀ 13

clear all;clc;

xi=[0 13 24 36 40 51 63 74 82 85];

yi=[0 15 34 49 27 11 19 61 37 0];

sp=spline(xi,yi);

x=0:0.5:85; y=ppval(sp,x);

plot(x,y);hold on;grid on;

% -b)

sp2=spline(xi,-yi);

xlabel('chon Diem xa bo nhat roi Enter','Color','r');

[xm ym]=ginput(1);

f=inline('ppval(sp,x)','x','sp')

[xm ym]= fminsearch(f,xm,[],sp2);

plot(xm,-ym,'r*');

diem_xa_bo_nhat=[xm -ym]

% -c)

I=0;

for i=1:length(x)-1

r=[x(i+1)-x(i), y(i+1)-y(i)];

I=I+norm(r);

end

quang_duong=I

Đề 14

clear all;clc;

ti=0:2:46;

Ti=[68.8 64.8 62.1 59.9 57.7 55.9 45.9 44.8 43.7 42.6 41.7 40.8, 53.9 52.3 50.8 49.5 48.1 46.8 39.9 39.3 38.6 37.7 37.0 36.4]; T=dsolve('DT=-r*(T-17)','T(0)=68.8');

Tend=subs(T,'t',ti(end)); % nhiet do cuoi:tai t=46s

r=solve(Tend-Ti(end),'r'); % tinh so bo he so r

r=subs(r);

r=linspace(r/2,r*2,50); %phuong phap ban:

for k=1:length(r)

Tk=subs(T,'r',r(k));

Ss=subs(Tk,ti)-Ti ; % Vector gia tri sai so nhiet do tai cac thoi gian ti Bp(k)=dot(Ss,Ss); % tong binh phuong sai so nhiet do

end

%phuong phap sai so binh phuong cuc tieu:

xlabel('chon Diem Cuc Tieu roi Enter','Color','r');hold on;

[rr bp]=sp_min(r,Bp);

r=rr, %gia tri r de tong binh phuong sai so cuc tieu

% -b)

T=subs(T,'r',r)

pl_min

function [xn,fn]=pl_min(xi,yi);

p=polyfit(xi,yi,length(xi)-1);

f=inline('polyval(p,x)','x','p');

x=linspace(xi(1),xi(end),100); y=f(x,p);

xlabel('chon Cac cuc tieu roi Enter','Color','k');hold on;grid on;

plot(x,y,'b');

[x0,y0]=ginput;

for k=1:length(x0);

[xn(k),fn(k)]=fminsearch(f,x0(k),[],p);

end;

pl_solve

function [xn,fn]=pl_solve(xi,yi);

p=polyfit(xi,yi,length(xi)-1);

x=linspace(xi(1),xi(end),100); y=f(x,p);

xlabel('chon Cac diem 0 roi Enter','Color','r');hold on;grid on;

plot(x,y,'r');

[x0,y0]=ginput;

for k=1:length(x0);

[xn(k),fn(k)]=fsolve(f,x0(k),[],p);

end;

đề 6_1

clear all;clc

% x= y(1); y=y(2); z=y(3)

dy=inline('[10*(y(2)-y(1));126.52*y(1)-y(2)-y(1)*y(3);y(1)*y(2)-8*y(3)/3]','t','y'); [t y]=ode45(dy,[0 8],[-7.69 ;-15.61;90.39]);

plot(t,y(:,1),'r'); hold on;grid on

plot(t,y(:,2),'g');plot(t,y(:,3)); legend('x(t)','y(t)','z(t)');

% -b)

% y=y(1); y'=y(2); y"=(y'+8x^3y^3))/x;

dy=inline('[y(2); (y(2)+8*x^3*y(1)^3)/x]','x','y');

[x y]=ode45(dy,[1 4],[1/2;-1/2]);

figure(2);

plot(x,y(:,1),'r'); hold on; grid on;

plot(x,y(:,2),'g'); legend('y(x)','dy/dx');

Đề 7_1

clear all;clc; % bai nay giong De 2

dy=inline('(1+x^2)+ 2*x*y/(1+x^2)','x','y');

[x,y]=ode45(dy,[0 15],-10);

% -2

xlabel('Chon diem 0 roi Enter','Color','r'); hold on;grid on;

[x0 y0]=sp_solve(x,y);

plot(x0,y0,'ro');

xlabel('Chon cuc tieu roi Enter','Color','k');

[xm ym]=sp_min(x,y);

plot(xm,ym,'r*');

xlabel(' ');

Đề 8_1

clear all;clc; % bai nay giong De 2

% y(0)=0.3; y'(0)=0;

dy=inline('[y(2);-0.2*y(2)-10*sin(y(1))]','x','y');

[x,y]=ode45(dy,[0 10],[0.3;0]);

% -2

xlabel('Chon tat ca Cac diem 0 roi Enter','Color','r'); hold on;grid on; plot(x,y(:,1));plot(x,y(:,2),'g');legend('y(x)','dy/dx');

[x0 y0]=sp_solve(x,y(:,1));

plot(x0,y0,'ro');

% -3

xlabel('Chon Cac cuc tieu roi Enter','Color','k');

[xm ym]=sp_min(x,y(:,1));

plot(xm,ym,'r*');

xlabel(' ');

Đề 9_1

clear all;clc

xi=0:8; yi=[.6 75 8 5 1 -.5 -.7 -.3 1];

a=polyfit(xi,yi,8);

sp=spline(xi,yi);

x=0:0.05:8; y=polyval(a,x);

plot(x,y,'r'); hold on; grid on;

ys=ppval(sp,x);

plot(x,ys,'y'); legend('da thuc','spline');

plot(xi,yi,'k+');

figure(2);

[xn yn]=pl_solve(xi,yi); [xm ym]=pl_min(xi,yi);

figure(3);

xlabel('chon Cac diem 0 roi Enter','Color','r');hold on; [xn2 yn2]=sp_solve(xi,yi);

xlabel('chon Cac diem cuc tieu roi Enter','Color','k'); [xm2 ym2]=sp_min(xi,yi);

figure(1);

plot([xn xn2],[yn yn2],'ro'); plot([xm xm2],[ym ym2],'r*');

Đề 10_1

clear all;clc;

% y=a*exp(b*x^2+c*x) =>ln(y)=ln(a)+b*x^2+c*x; xi=0:0.2:1; yi=[2.3 2.87 3.72 5.02 7.05 10.3];

p=polyfit(xi,log(yi),2);

a=exp(p(3)), b=p(1), c=p(2)

% -b)

plot(xi,yi,'ro'); hold on; grid on;

x=0:0.01:1; z=polyval(p,x); y=exp(z);

plot(x,y);

Đề 11_1

clear all;clc

la=[0.589 0.55 0.486 0.443 0.402];

n=[1.628 1.64 1.652 1.668 1.679];

LA=la.^-2; % LA= 1/la^2;

a=polyfit(LA,n,2);

A=a(3),B=a(2),C=a(1)

% -2

lai=0.4:0.01:0.75; ni=polyval(a,lai.^-2);

plot(la,n,'r*');hold on;grid on

plot(lai,ni); xlabel('lambda(10^-6m)');ylabel('n');

% -3

lado=0.72;

n_do=polyval(a,lado^-2)

Đề 12_1

clear all;clc

% y=1/(a0*x+a1) => z = 1/y = a0*x+a1

xi=[0 0.2 0.4 0.6 0.9 1.2 1.4 1.8 2]

yi=[0.97 0.69 0.57 0.456 0.36 0.31 0.265 0.2 0.196]; a=polyfit(xi,yi.^-1,1);

a0=a(1), a1=a(2)

% -b)

plot(xi,yi,'ro'); hold on; grid on;

x=0:0.01:2; z=polyval(a,x);

plot(x,z.^-1);

Đề 13_1

clear all;clc;

xi=[0 13 24 36 40 51 63 74 82 85];

yi=[0 15 34 49 27 11 19 61 37 0];

sp=spline(xi,yi);

x=0:0.5:85; y=ppval(sp,x);

plot(x,y);hold on;grid on;

% -b)

sp2=spline(xi,-yi);

xlabel('chon Diem xa bo nhat roi Enter','Color','r'); [xm ym]=ginput(1);

f=inline('ppval(sp,x)','x','sp')

[xm ym]= fminsearch(f,xm,[],sp2); plot(xm,-ym,'r*');

diem_xa_bo_nhat=[xm -ym]

% -c)

I=0;

for i=1:length(x)-1

r=[x(i+1)-x(i), y(i+1)-y(i)]; I=I+norm(r);

end

quang_duong=I