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

các đề thi matlab-lập trình c cho học viên cao hocnghiên 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')


%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,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];


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
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);


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*(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);


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));126.52*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');


%-----------------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);-0.2*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+');


%---------------------------------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=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