Cao V¨n ChÝnh_B1K52

T ng h p code các bài th c hành Matlabổ ợ ựBai 1clc x=-2:0.01:2 y=exp(-0.3.*x.^2- 0.5.*x +1).*cos(20.*x) subplot(2,1,1)% lenh subplot nay chia man%hinh do thi theo 2 hang 1 cot vi tri 1 plot(x,y,'m')%lenh nay ve do thi vao phan%hinh minh chia ra vào subplot 1

%hinhcon 2 subplot(2,1,2)% ve dang ham nay thi khai bao truc tiep ham trong dau '' fplot('exp(-0.3.*x.^2- 0.5.*x+1).*cos(20.*x)',[-2 2])title('do thi ham so ')% lenh nay dien %tieu de cho do thi xlabel('truc x')% ghi tieu de cho truc x xlabel('truc y')% ghi tieu de cho truc yBai 2%hinh con 1 x=0:0.05:4;y=3.*sin(pi.*x);y1=exp(-0.2.*x) subplot(2,1,1);plot(x,y,'r',x,y1,'b') gtext('giao diem 1')% gan chu thich vao %cac giao diem giua 2 do thi gtext('giao diem 2') gtext('giao diem 3') gtext('giao diem 4') % hinh con 2& 3 x1=0:0.05:10;y2=exp(-0.2.*x1).*cos(x1) subplot(2,2,3);bar(x1,y2)% ve do thi dang cot subplot(2,2,4);stairs(x1,y2)%ve do thi dang bac thang --------------------------------------------------------------------------------------------Bai 3% Chu y ham function o day chi chay dc tren Window thui,voi may tinh tren truong thi khong chay duoc dau!!!%cau afunction tong=bai3a(n,x) s=0; for k=1:n s=s+((-1).^k./k).*((-(x-1).^k).*(x>0 & x<1)+((1./x-1).^k).*(x>=1)); end tong=s % bai3b function tong=bai3b(x) ak=1; ss=1e-6; s1=0; k=0; while any(abs(ak)>ss) k=k+1 ak=((-1).^k./k).*((-(x-1).^k).*(x>0 & x<1)+((1./x-1).^k).*(x>=1)); s1=s1+ak; end tong=s1 %bai 3c x=0.1:0.1:10; plot(x,bai3a(1,x),'r');hold on; plot(x,bai3a(5,x),'c');hold on; plot(x,bai3a(10,x),'b');hold on; plot(x,bai3b(x),'m');hold on; legend('s1','s5','s10','s') gtext('s1') ;gtext('s5') gtext('s10') ;gtext('s')

Bai 4

Cao V¨n ChÝnh_B1K52[x,y]=meshgrid(-2:.1:2); z=2.*x.*y./(x.^2 +y.^2 +1); subplot(2,2,1);mesh(x,y,z);% do thi mesh title('mesh')% gan chu thich mesh subplot(2,2,2);surf(x,y,z)% do thi surf title('surf') subplot(2,2,3);contour(x,y,z) title('contour')%do thi duong dong muc contour subplot(2,2,4);contour3(x,y,z) title('contour3')%do thi duong dong muc 3chieu Bai 5% Cau a subplot(2,2,1); [teta,phi]=meshgrid(0:pi/30:pi, 0:pi/30:2*pi); x0=0;y0=0;z01=-1;z02=1;r=1; x1=x0+r*cos(phi).*sin(teta); y1=x0+r*sin(phi).*sin(teta); z11=z01+r*cos(teta); z12=z02+r*cos(teta); mesh(x1,y1,z11);hold on mesh(x1,y1,z12); % Cau b subplot(2,2,2);R=2;r=0.25; [teta,phi]=meshgrid(0:pi/30:2*pi);x=(R+r*cos(teta)).*cos(phi) y=(R+r*cos(teta)).*sin(phi) z=r*sin(teta);mesh(x,y,z); % Cau c subplot(2,1,2); a1=[0,1/sqrt(3),-1/2*sqrt(3)]; b1=[0,0,1/2];c1=[sqrt(2/3),0,0]; fill3(a1,b1,c1,'r');hold on; a2=[1/sqrt(3),-1/2*sqrt(3),-1/2*sqrt(3)]; b2=[0,1/2,-1/2];c2=[0,0,0]; fill3(a2,b2,c2,'y'); a3=[-1/2*sqrt(3),-1/2*sqrt(3),0]; b3=[1/2,-1/2,0];c3=[0,0,sqrt(2/3)]; fill3(a3,b3,c3,'g'); a4=[-1/2*sqrt(3),0,1/sqrt(3)]; b4=[-1/2,0,0];c4=[0,sqrt(2/3),0]; fill3(a4,b4,c4,'r'); Bai 6:function t=bai6(n,x)if (n<0)|(n~=round(n))% n khac gia tri da lam tron cua nfprintf('So n nhap vao khong phai la so nguyen duong')elseif n==0 t=1;elseif n==1 t=x;else t=2.*x.*bai6(n-1,x)-bai6(n-2,x);end% Cau b;x=-1:0.01:1t0=bai6(0,x)% tinh gia tri T0;plot(x,t0);hold ont1=bai6(1,x);plot(x,t1,'r');hold ont2=bai6(2,x);plot(x,t2,'d');hold ont3=bai6(3,x);plot(x,t3,'y');hold on %den day ko chay dc???t4=bai6(4,x);plot(x,t4,'b');hold ont5=bai6(5,x);plot(x,t5,'g');hold off;legend('t0','t2','t3','t4','t5')% gan nha~n cua do thi% Cau cfigure(2) % Cau cx=linspace(-1,1);

Cao V¨n ChÝnh_B1K52plot(x,bai6(4,x));ylim([-1.5 1.5])%gioi han do thi[x0,y0]=ginput;% lay toa do = cach click chuotf=inline('bai6(4,x)','x');% de y vao ham nay khi tim khong diemfor k=1:length(x0);%do rong cua khong diem [xn(k) fxn(k)]=fzero(f,x0(k));%ham tim khong diem thuc fzero text(xn(k),fxn(k),'< 0 diem')% end% Tim cac max[x1,y1]=ginput;f1=inline('(-1)*bai6(4,x)','x');for i=1:length(x1); [xn(i) fxn(i)]=fminsearch(f1,x1(i)); text(xn(i),(-1)*fxn(i),'< max')%chu y co -1end% Tim cac min[x1,y1]=ginput;f1=inline('bai6(4,x)','x');for i=1:length(x1); [xn(i) fxn(i)]=fminsearch(f1,x1(i));% ham tim cuc tieu text(xn(i),fxn(i),'< min')endBai 7function [x0,fx0,n,xn,fxn]=bai7(a,b,fx,dfx,tol);%tol la nhap so lieu dang sai so %thay vi lap dao ham cua fx ta tinh luon dfx fx=inline(fx);dfx=inline(dfx);%inline la %1 ham moi ma minh tu dat no dang nhu 1 %function hoac @ ham xi=linspace(a,b,100); yi=subs(fx,'x',xi);%ham dao bien plot(xi,yi,'r');grid on [x0,fx0]=ginput(5); for i=1:length(x0) xn(i)=x0(i);%dau ra xn n(i)=0; k(i)=fx(x0(i))./dfx(x0(i));%chu y chuyen ve while abs(k(i))<= tol%dieu kien cua tri tuyet doi xn(i)=xn(i)-k(i); k(i)=fx(xn(i))./dfx(xn(i)); n(i)=n(i)+1;% n dau ra thu i end; fxn(i)=fx(xn(i));%dau ra fxn thu i end %Phan b ra cua so window command de goi an % cau b [x0,fx0,n,xn,fxn]=bai7(0,3,'x-sin(x)-1','1-cos(x)',10^(-10)) [x0,fx0,n,xn,fxn]=bai7(1,5,'(log(x))^2-x^2 + 2*x + 3 ','2*log(x)/x - 2*x + 2',10^(-10)) [x0,fx0,n,xn,fxn]=bai7(0,5,'exp(-x)-sin(x^2)-0.5','-exp(-x)-2*cos(x^2)*x',1e-10) Bai 8close all;clc [x,y]=meshgrid(-2:.2:2,0:.2:2); z1=(x.^2).*sin(y)+cos(2*x).*y-0.5; z2=(2.^x).*y-x.*(y.^2)-1; contour(x,y,z1,[0 0],'r');hold on contour(x,y,z2,[0 0],'b') f=inline('[(x(1)^2)*sin(x(2))+cos(2*x(1))*x(2)-0.5;(2^x(1))*x(2)-x(1)*(x(2)^2)-1]','x');%x(1)=x;x(2)=y,ham f lay chuan hoa [x0 y0]=ginput;;%ginput la ham truy nhap bang chuot lay ket qua tu do thi for k=1:length(x0)%ham fsolve la ham lay chinh xac nghiem [xn,yn]=fsolve(f,[x0(k) y0(k)]);endfprintf(' Cac cap nghiem cua phuong trinh 1 la:\n');%fprintf la ham hien thi ra man hinh comand window xn,yn% Cau b %luu sang editor khac

Cao V¨n ChÝnh_B1K52figure(2) [x,y]=meshgrid(-2:.2:2); z=x+i*y;%z la bieu thuc phuc f=z.^2+cos(log(abs(z)+1)+3)-2.^z-i; contour(x,y,real(f),[0 0],'r');hold on% ve theo phan thuc contour(x,y,imag(f),[0 0],'b');hold off% ve theo phan ao [x0,y0]=ginput; z0=x0+i*y0; fz=inline('z^2+cos(log(abs(z)+1)+3)-2^z-i','z'); for k=1:length(z0) [zn,fzn]=fsolve(fz,z0(k)) end fprintf(' Cac cap nghiem cua phuong trinh 2 la:\n'); zn fznBai 9% phan a clear all R=1 r=R.*sin(pi/10)./cos(pi/5) k=0:9; x=R.*sin(k.*pi./5).*((-1).^k==1)+r.*sin(k.*pi./5).*((-1).^k==-1); y=R.*cos(k.*pi./5).*((-1).^k==1)+r.*cos(k.*pi./5).*((-1).^k==-1); disp('Toa do dinh ngoai') k=1:2:9;% cho k chay tu 1 toi 9 voi buoc nhay la 2 xt=x(k)% toa do theo truc x yt=y(k)%toa do theo truc y disp('Toa do dinh trong') k=1:2:9; xt=x(k+1)yt=y(k+1) % Muon ve hinh tron p=linspace(0,2*pi,300); R=1 x1=R.*cos(p); y1=R.*sin(p); figure(1) fill(x1,y1,'r') hold on fill(x,y,'y') axis equal % ve quoc ky figure(2) fill([2.5 -2.5 -2.5 2.5],[2 2 -2 -2],'r')hold on fill(x,y,'y') Bai 10clear i w=linspace(1e+3,1e+5)% tan so goc w R=10 C1=1e-6 C2=0.1e-6 L=1e-3 ZL=L*2*pi*w*i ZC1=1./(2*pi*w*C1)*i ZC2=1./(2*pi*w*C2)*i ZLC2=ZL.*ZC2./(ZL+ZC2) G=ZLC2./(R+ZC1+ZLC2) subplot(2,2,1);plot(w,real(G));legend('Dothi Re(G)');%ve theo w va phan thuc subplot(2,2,2);plot(w,imag(G));legend('Dothi Im(G)');%ve theo w va phan ao subplot(2,2,3);plot(w,abs(G));legend('Do thi |G|');%ve theo w va tri tuyet doi subplot(2,2,4);plot(w,angle(G));legend('Do thi Arg(G)');%ve theo w va goc pha Bai 11L p bi u th c tính Pn: còn tính t P0-ậ ể ứ ừ P5 làm t ng t nh bài 6bươ ự ư ởfunction t=bai11a(n,x)if (n<0)|n~=round(n)

Cao V¨n ChÝnh_B1K52fprintf('Hay nhap lai n nguyen duong')elseif n==0 t=1;elseif n==1 t=x;else t=(2*n-1)/n*x*bai11a(n-1,x)-(n-1)/n*bai11a(n-2,x);end%Bai11Bfunction tong=bai11b(n,x);if (n<0|n~=round(n)) disp('xin hay nhap lai so nguyen duong')elseif n==0 tong=1;elseif n==1 tong=x;else giaithua=1; for k=1:n; giaithua=giaithua*k; end tong=(1./(giaithua*2^n)).*diff((x^2-1)^n,n);end% Cau c %chua chay duoch=(1-x.^2).*diff(p1(n),x,2)-2.*x.*diff(p1(n),x)+n*(n+1)*p1(n) i=quad(p1(n).^2,-1,1)-2/2*n+1 k=quad(p1(6)*p1(n).^2,-1,1)Bai 12% Cau a% ve mat cong[x,y]=meshgrid(-5:.6:5); z=(2.*x.^2+3.*y.^2).*exp(-(x.^2+y.^2)) figure(1) subplot(2,2,1) mesh(x,y,z) % Cau b% tinh truong vecto va ve chung[dzx,dzy]=gradient(z) subplot(2,2,2) quiver(x,y,dzx,dzy) %dz=sqrt(dzx.^2+dzy.^2) %subplot(2,2,3) %quiver(x,y,dzx./dz,dzy./dz) % Cau c% tim cuc tri%Tim cuc tieu subplot(2,2,4) contour(x,y,z);shg[xo yo]=ginput f=inline('(2.*x(1).^2+3.*x(2).^2).*exp(-(x(1).^2+x(2).^2))','x') for i=1:length(xo) [ct(i,:) fct(i,:)]=fminsearch(f,[xo(i) yo(i)]) endct,fct%Tim cuc dai [x1 y1]=ginput f1=inline('(-1)*(2.*x(1).^2+3.*x(2).^2).*exp(-(x(1).^2+x(2).^2))','x') for j=1:length(x1) [cd fcd]=fminsearch(f1,[x1(j) y1(j)]) end cd,(-1)*fcd %chu y nhan -1 voi fcd Bai 13 (Chua hiu)%cau aclc A01=[19 -9 -6;25 -11 -9;17 -9 -4]; A02=[-1 4 -2;-3 4 0;-3 1 3]; A=A02;% Thay A01 bang A02 de tinh cho ma tran thu 2 [P,a]=eig(A);A,P fprintf('P^(-1)*A*P=\n');disp(inv(P)*A*P) % Cau b f=inline('5*x^2-4*x*y+8*y^2+20/sqrt(5)*x-80/sqrt(5)*y+4','x','y'); ezplot(f,[-4 4 -2 6]);shg

Cao V¨n ChÝnh_B1K52% Cau c function [A1,b1,c1,V,T]=bai13c(A,b,c) [V,A1]=eig(A); a=diag(A1); b1=b*V; c1=c; for k=1:length(a); if a(k)~=0 T(k)=-b1(k)/(2*a(k)); c1=c1-b1(k)^2/(4*a(k)); b1(k)=0; end end

% Thu lai cho cau b clc A=[5 -2;-2 8]; b=[20/sqrt(5) -80/sqrt(5)]; c=4; [A1,b1,c1,V,T]=bai13c(A,b,c); syms x y; XY=[x y]; pt=XY*A1*(XY.')+b1*(XY.')+c1;pretty(pt) ezplot(pt)

% Cau d syms T D=[T 1 1;1 T 1;1 1 T]; b=[1;T;T^2]; Dx=[b D(:,2) D(:,3)]; Dy=[D(:,1) b D(:,3)]; Dz=[D(:,1) D(:,2) b]; d=det(D); dx=det(Dx); dy=det(Dy); dz=det(Dz); ng=solve(d,T); % Don gian nghiem xx=[]; for i=1:length(ng) t=0; for j=1:length(xx) if ng(i)==xx(j); t=t+1; end end if t==0 xx=[xx ng(i)]; end end ng=xx;vd=[];vn=[]; for i=1:length(ng); if (subs(dx,'T',ng(i))==0)|(subs(dy,'T',ng(i))==0)|(subs(dz,'T',ng(i))==0) vd=[vd,ng(i)]; else vn=[vn,ng(i)]; end end fprintf('Phuong trinh vo dinh voi T='); for i=1:length(vd); disp(vd(i)) end fprintf('Phuong trinh vo nghiem voi T='); for i=1:length(vn); disp(vn(i)) end fprintf('PT co nghiem duy nhat voi T khac');disp(ng) fprintf(' x=');disp(dx/d) fprintf(' y=');disp(dy/d) fprintf(' z=');disp(dz/d) Bai 14%Cau a

Cao V¨n ChÝnh_B1K52syms z x=sqrt(5*pi/2-z).*cos(sqrt(5*pi/2-z))+pi dx=diff(x,z) f=inline('dx') l=quad(f,0,2*pi)%Tinh chieu dai cung %Cau b %Tinh dien tich xung quanh x1=x.*(sqrt(1+dx)) f1=inline('x1') s=2*pi*quad(f1,0,2*pi) %Tinh the tich xoay quanh Oz x2=x.^2 f2=inline('x2') v=pi*quad(f2,0,2*pi) %Tinh the tich xoay quanh Ox x3=z.*x f3=inline('x3') v1=2*pi*quad(f3,0,2*pi) %Cau c ezplot(x3,[0 2*pi]) Bai 15clear all;clc;close all syms x a=input('nhap a='); Io=input('nhapIo='); d=sqrt(x.^2+a^2); I=Io.*x./d.^3; dt=diff(I,x); f1=diff(I,x,2); x0=solve(dt,x) f2=subs(f1,x,x0) for k=1:length(f2) if double(f2(k))<0 xcd=x0(k); end end xcd Icd=subs(I,x,xcd) Bai 16%Cau a: Chu y luu ra 1 editor khac,luu voi ten: bai16afunction t=bai16a(n) if n==0 t=[0 1] elseif n==1 t=[1 0] else n>1 t=polyadd(2*conv([1 0],s(n-1)),-s(n-2)) end; t %Cau b: luu ra 1 editor khac lay ten la:bai16bfunction s=bai16b(a,b) na=length(a); nb=length(b); s=[zeros(1,(na-nb)),b]+[zeros(1,(nb-na)),a] %Luu doan code nay sang editor khac, ten file la gi cung dcfigure(1);x=-1:.1:1; plot(x,bai16b(bai16a(0),x),'r');hold on plot(x,bai16b(bai16a(1),x),'m');hold on %cach 2

function T=bai16(n,x); if n<0 |n~=round(n) fprintf('Nhap lai n khong am'); elseif n==0 T=1; elseif n==1

Cao V¨n ChÝnh_B1K52 T=x; else T=2.*x.*bai16(n-1,x)-bai16(n-2,x); end

clear;clc; x=linspace(-1,1,100); T0=bai16(0,x)% tinh gia tri T0 plot(x,T0);hold on T1=bai16(1,x) plot(x,T1,'r');hold on T2=bai16(2,x) plot(x,T2,'d');hold on T3=bai16(3,x) %den cho nay ko chay dc, chua hiu tai sao?????plot(x,T3,'dr');hold on T4=bai16(4,x) plot(x,T4,'b');hold off legend('T0','T2','T3','T4','T5')% gan nha~n cua do thi

Bai 17 (chua chay dc)% cau a function s=bai17(xj,t) ts=1; for k=1:length(xj) if k~=t ts=conv(polyadd([1 0],[0 -xj(k)]),ts); end end ms=polyval(ts,xj(t)); s=ts/ms %phan b xj=-2:.5:2;t=-2:.2:2; mau='rmgcbk';so='123456'; close all for i=1:5 plot(t,polyval(bai17(xj,i),t),mau(i)) text(-1.8,polyval(bai17(xj,i),-1.8),so(i));hold on end Bai 18%Doc lai bai tim tiem can cua do thi ham so close all; clear; clc; syms x; f1=abs(x.^3+x+1)-3; f2=x.^2-x-6; f=f1/f2 + x; yi=linspace(-30,30,100); ezplot(f,[-10 10]);axis ([-10 10 -30 30]);hold on; [x0,fx0]=ginput; fx=inline(char(f),'x');% cach 2 fx=inline('(abs(x.^3+x+1)-3)/(x.^2-x-6) + x','x'); for k=1:length(x0); [xn(k,:)]=fsolve(fx,x0(k)); end xn xv=solve(f2);% tim tiem can dung fprintf(['Tiem can dung cua do thi ham so:x=',char(xv(1)),' Va ','x=',char(xv(2)),'\n']); yv=limit(f,x,-inf);%tim tiem can ngang fprintf(['Tiem can ngang cua do thi ham so:y=',char(yv),'\n']); a=limit(f./x,x,inf);%tim tiem can xien b=limit(f-a*x,x,inf); fprintf(['Tiem can xien cua do thi ham so:y=',char(a),'x + ',char(b),'\n']); plot(double(xv(1)*ones(size(yi))),yi,'r');% cach 2 :plot(double(xv(1)),yi,'r') plot(double(xv(2)*ones(size(yi))),yi,'r');% cach 2 :plot(double(xv(2)),yi,'r') xi=(yi-1)/2;plot(xi,yi,'r'); plot(xi,double(-1*ones(size(xi))),'r');%

Cao V¨n ChÝnh_B1K52%cach 2 :plot(xi,-1,'r'); hold off; Bai 19% Bai tap so 19% a1=[1 2 3;4 5 6; 7 8 9]; a2=[1 1 3;4 5 6;7 8 9]; a3=[0.9999 2 3;4 5 6;7 8 9] b1=[1 1 3] b11=b1(:) b2=[1 2 3] b21=b2(:)%Dua vecto hang thanh cot % Lam vi du voi a1% det(a1)%Tim dinh thuc ma tran inv(a1)%Tim nghich dao ma tran diag(a1)%Tim duong cheo ma tran a=poly(a1)%Tim he so da thuc dac trung p=poly2sym(a)%Tim da thuc dac trung N=null(a1)%Ma tran chua n vector cuakhong gian 0 v=eig(a1)%Tim tri rieng cua ma tran [v,d]=eig(a1)%v:ma tran lam cheo; d: dang cheo a1 n=size(N,2)%So chieu cua khong gian khongrank(a1)%Tim hang ma tran %-----------------------------------------A1=[1 2 3;4 5 6;7 8 9]; A2=[1 1 3;4 5 6;7 8 9]; A3=[0.9999 2 3;4 5 6;7 8 9]; b1=[1;1;3];b2=[1;2;3]; %tinh chuan cua cac vector b1,b2 va cuacac ma tran A1,A2,A3 fprintf('Chuan cua cac vector b1 & b2 va cua cac ma tran A1,A2,A3la:\n') norb1=norm(b1) norb2=norm(b2) norA1=norm(A1) norA2=norm(A2) norA3=norm(A3) fprintf('Dinh thuc cua ma tranA1,A2,A3:\n') % Tinh dinh thuc cua ma tran dung 'det' detA1=det(A1) detA2=det(A2) detA3=det(A3) if det(A1)==0 fprintf('Dinh thuc ma tran A= 0\n'); fprintf('Do do khong co ma tran nghic dao\n') else fprintf('Dinh thuc ma tran A=');disp(det(A1)) fprintf('Ma tran nghich dao cua A\n');disp(inv(A1)); end if det(A2)==0 fprintf('Dinh thuc ma tran A= 0\n'); fprintf('Do do khong co ma tran nghic dao\n') else fprintf('Dinh thuc ma tran A=');disp(det(A2)) fprintf('Ma tran nghich dao cua A\n');disp(inv(A2)); end if det(A3)==0 fprintf('Dinh thuc ma tran A= 0\n'); fprintf('Do do khong co ma tran nghic dao\n') else fprintf('Dinh thuc ma tran A=');disp(det(A3)) fprintf('Ma tran nghich dao cuaA\n');disp(inv(A3)); end % % Tinh ma tran nghich dao dung 'inv'% fprintf('Ma tran nghich dao :\n') % invA1=inv(A1) % invA2=inv(A2) % invA3=inv(A3)

Cao V¨n ChÝnh_B1K52%Tinh tri rieng cua cac ma tran dung 'eig' [V1,d1]=eig(A1) %tri rieng d1, Vectorrieng V1 [V2,d2]=eig(A2) [V3,d3]=eig(A3) fprintf('Tri rieng d1:\n') disp(d1) fprintf('Tri rieng d2:\n') disp(d2) fprintf('Tri rieng d3:\n') disp(d3) fprintf('Vector rieng V1:\n') disp(V1) fprintf('Vector rieng V1:\n') disp(V2) fprintf('Vector rieng V1:\n') disp(V3) %Xac dinh da thuc dac trung cua cac ma tran A1,A2,A3 fprintf('Da thuc dac trung cua cac ma tran A1,A2,A3') dactrungA1=poly(A1) dactrungA2=poly(A2) dactrungA3=poly(A3) Bai 20% Lap function de giai function [ln,x]=bai20(A,b) if (rank(A)==rank([A,b]))&(rank(A)==size(A,1)) ln='Pt co nghiem duy nhat'; x=A\b ; elseif (rank(A)==rank([A,b]))&(rank(A)<size(A,1)) ln='Pt Vo so nghiem'; syms x1 c; x0=null(A);% Nghiem pt thuan nhat xc1=solve((A(1,1)+A(1,2))*x1+A(1,3)-b(1),x1); xc=[xc1 xc1 1].'; x=c*x0+xc; else ln='Pt Vo nghiem voi tua nghiem'; x=pinv(A)*b; end %sang editor moi%cau a b cclc A1=[1 2 3;4 5 6;7 8 9]; A2=[1 1 3;4 5 6;7 8 9]; A3=[0.999 2 3;4 5 6;7 8 9]; b1=[1 1 3].'; b2=[1 2 3].'; [ln,x11]=bai20(A1,b1) [ln,x12]=bai20(A1,b2) [ln,x21]=bai20(A2,b1) [ln,x22]=bai20(A2,b2) [ln,x31]=bai20(A3,b1) [ln,x32]=bai20(A3,b2) Bai 21function [t,lap]=bai21(x)s=1;k=0;mau=1;ak=1; while any(abs(ak)>1e-5); k=k+1; n=2*k; mau=(-1)*mau*(k^2); ak=(1/mau)*(x/2).^n; s=s+ak; end lap=k;t=s;%sang editor khac

Cao V¨n ChÝnh_B1K52clc;close all; x=0:0.01:10; plot(x,bai21(x));grid on[x0,y0]=ginput; f=inline('bai21(x)','x'); fprintf('Cac nghiem cua phuong trinh:') for k=1:length(x0); [xn(k) fxn(k)]=fzero(f,x0(k)); end xnfxnclc;close all; x=0:0.01:10; plot(x,bai21(x));grid on% Tim cac min f=inline('bai21(x)','x'); [x1 y1]=ginput; fprintf('Cac diem cuc tieu:') for i=1:length(x1); [xmin(i) fxmin(i)]=fminsearch(f,x1(i)); end;xminfxmin% Tim cac max [x1,y1]=ginput; fprintf('Cac diem cuc dai:') f1=inline('(-1)*bai21(x)','x'); for i=1:length(x1); [xmax(i) fxmax(i)]=fminsearch(f1,x1(i)); end;xmax-fxmaxBai 22function z=bai22(x,y) z=2./((x-1.5).^2+2*(y-1.8).^2+0.2)-1./(1.5*(x+1.8).^2+(y+2).^2+0.1); %sang editor khacclc;clear all;close all%phan a,b [x,y]=meshgrid(linspace(-4,4,41))z=2./((x-1.5).^2+2.*(y-1.8).^2+0.2)-1./(1.5.*(x+1.8).^2+(y+2).^2+0.1)%cuc dai [zmax,imax]=max(z) %tim gia tri lon nhat cua mang Z [zmax,jmax]=max(max(z)) %tim vi tri cot cua gia tri lon nhatimax=imax(jmax) %tim vi tri hang cua gia tri lon nhat%cuc tieu [zmin,imin]=min(z) [zmin,jmin]=min(min(z))imin=imin(jmin) %ve subplot(2,1,1);surf(x,y,z); subplot(2,1,2);contour(x,y,z,20);

%tim cuc tri [x0 y0]=ginput fx=inline('2./((x(1)-1.5).^2+2.*(x(2)-1.8).^2+0.2)-1./(1.5.*(x(1)+1.8).^2+(x(2)+2).^2+0.1)','x'); for k=1:length(x0); [xct(k,:) fxct(k,:)]=fminsearch(fx,[x0(k) y0(k)]); end xct fxct %======================== [x1,y1] =ginput g=inline('(-1).*(2./((x(1)-1.5).^2+2.*(x(2)-1.8).^2+0.2)-1./(1.5.*(x(1)+1.8).^2+(x(2)+2).^2+0.1))','x');

Cao V¨n ChÝnh_B1K52for k=1:length(x1); [xcd(k,:) fxcd(k,:)]=fminsearch(g,[x1(k) y1(k)]); end xcd-fxcdBai 23%cau asyms x; f1=inline('x^2-5*x*sin(x^2)-x+6.2','x'); figure(1);fplot(f1,[0 4]);grid on [x0,y0]=ginput; for k=1:length(x0); [xn(k),fxn(k)]=fzero(f1,x0(k)); end; xn,fxn%cau bfigure(2);clear all [x,y]=meshgrid(0:.1:2); z=x+i*y; f=z.^2+2.^z-1.5-3*i; contour(x,y,real(f),[0 0],'r');hold on contour(x,y,imag(f),[0 0],'b');hold off [x0,y0]=ginput z0=x0+i*y0; fz=inline('z^2+2^z-1.5+3*i','z'); for k=1:length(z0) [zn(k,:),fzn(k,:)]=fsolve(fz,z0(k,:)); end zn,fzn %cau cclear all; clc; [x y]=meshgrid(0:.1:2); f1=sin(x).^2+sin(y).^2-1; f2=4*x.*y+0.1*x+0.2*y-1; contour(x,y,f1,[0 0],'r');hold on; contour(x,y,f2,[0 0],'m');hold off; pt1='sin(x(1)).^2+sin(x(2)).^2-1'; pt2='4.*x(1).*x(2)+0.1.*x(1)+0.2.*x(2)-1'; hpt=['[',pt1,',',pt2,']']; fx=inline(hpt,'x'); [x0 y0]=ginput for k=1:length(x0); [xn(k,:),fxn(k,:)]=fsolve(fx,[x0(k) y0(k)]); end xn,fxn Bai 24xi=[0 0.2 0.4 0.6 0.8 1] yi=[2.3 2.87 3.72 5.02 7.05 10.3] Y=log(yi) h=polyfit(xi,Y,2) a=h(3) b=h(1) c=h(2) X=linspace(0,1); Y=a.*exp(b.*X.^2+c.*X); plot(xi,yi,'o');hold on; plot(X,Y,'-'); Bai 25clc;close all;clear allx1=[0 1 2 3 4 5 6 7 8]y1=[0.6 0.75 0.8 0.5 0.1 -0.5 -0.7 -0.3 0.1]plot(x1,y1,'+');hold onx2=0:0.001:8a=polyfit(x1,y1,5);sp=spline(x1,y1);

Cao V¨n ChÝnh_B1K52y=polyval(a,x2);plot(x2,y,'r');hold ony1=ppval(sp,x2);plot(x2,y1,'y');hold on%Cau b % Tim khong diem ham noi suy spline f1=inline('ppval(sp,x2)','x2','sp'); [x1,y1]=ginput for k=1:length(x1) [xn1(k),yn1(k)]=fsolve(f1,x1(k),[],sp); end xn1 yn1 % tinh cuc tri bang phuong phap noi suy spline % cuc tieu [x11,y11]=ginput; for k=1:length(x11) [xn12(k),fxn12(k)]=fminsearch(f1,x11(k),[],sp); end text(xn12,fxn12,'*'); %cuc dai f2=inline('-ppval(sp,x)','x','sp'); [x21,y21]=ginput; for k=1:length(x21) [xn21(k),fxn21(k)]=fminsearch(f2,x21(k),[],sp); end text(xn21,-fxn21,'*'); %Tim khong diem ham noi suy xap xi f3=inline('polyval(a,x2)','x2','a'); [x0,y0]=ginput for k=1:length(x0) [xn01(k),yn01(k)]=fsolve(f3,x0(k),[],a); end xn01 yn01 % TIm cuc tri ham noi suy xap xi [x10 y10]=ginput for i=1:length(x10) [xn10(i),yn10(i)]=fminsearch(f3,x10(i),[],a) end xn10 yn10 plot(xn10,yn10,'*') f4=inline('-polyval(a,x2)','x2','a') [x20 y20]=ginput for i=1:length(x20) [xn20(i), yn20(i)]=fminsearch(f4,x20(i),[],a) end xn20 -yn20Bai 26clc;close all;clear all;xi=0:0.3:3;yi=sqrt(xi+1).*cos(xi.^2+1)./(xi.^4+1);%Ve cac diem ung voi bang da cho cua xi,yifigure(1);subplot(2,2,1)plot(xi,yi,'*');hold on%Ve cac diem noi suy splinex1=0:0.001:3;sp=spline(xi,yi);y1=ppval(sp,x1)plot(x1,y1,'r')% Ve do thi ham gocsubplot(2,2,2) syms x y=sqrt(x+1).*cos(x.^2+1)./(x.^4+1);

Cao V¨n ChÝnh_B1K52 ezplot(y,[0 3]);hold on% Cau B%Tinh dao ham cap 1,2 ham noi suy spline dung "fnder" va ve do thisubplot(2,2,3) dh1=fnder(sp) y2=ppval(dh1,x1); plot(x1,y2,'y');hold on dh2=fnder(dh1) y3=ppval(dh2,x1);plot(x1,y3,'r');hold on% Tinh dao ham cap 1,2 ham goc va ve do thisubplot(2,2,4)dy1=diff(y,x)dy2=diff(dy1,x)ezplot(dy1,[0 3]);hold onezplot(dy2,[0 3]);hold on% Tinh tich phan ham noi suy spline bang "fnint" va ham goc bang "quad"tpsp=fnint(sp)tp03=ppval(tpsp,3)-ppval(tpsp,0)tphg=quad(inline(vectorize(y),'x'),0,3)% Cau C%tim ko diem,cuc tri cua ham goc thu=inline('sqrt(x+1)*cos(x^2+1)/(x^4+1)'); [x0,y0]=ginput; for k=1:length(x0) [xn(k) fxn(k)]=fsolve(thu,x0(k)) end text(xn,fxn,'<ko diem') %cuc tieu [x01,y01]=ginput; for k=1:length(x01) [xct(k) fct(k)]=fminsearch(thu,x01(k)); end text(xct,fct,'< cuc tieu') %cuc dai thu1=inline('-sqrt(x+1)*cos(x^2+1)/(x^4+1)'); [x02,y02]=ginput; for k=1:length(x02) [xcd(k) fcd(k)]=fminsearch(thu1,x02(k)) end text(xcd,-fcd,'< cuc dai') % bang phuong phap noi suy spline %tinh ko diem thang=inline('ppval(sp,x1)','x1','sp'); [x11,y11]=ginput; for k=1:length(x11) [xn11(k),fxn11(k)]=fsolve(thang,x11(k),[],sp); end text(xn11,fxn11,'*'); % cuc tieu [x12,y12]=ginput; for k=1:length(x12) [xn12(k),fxn12(k)]=fminsearch(thang,x12(k),[],sp); end text(xn12,fxn12,'*'); %cuc dai thang=inline('-ppval(sp,x1)','x1','sp'); [x21,y21]=ginput; for k=1:length(x21) [xn21(k),fxn21(k)]=fminsearch(thang,x21(k),[],sp); end text(xn21,-fxn21,'*'); Bai 27clc;clear all;close all;y1=inline('(x-1.5).^2-1');y2=inline('exp(-log(x).^2)');

Cao V¨n ChÝnh_B1K52y=inline('(x-1.5).^2-1-exp(-log(x).^2)');%hoac f=inline(vectorize(y1-y2))fplot(y1,[0 3],'r');hold onfplot(y2,[0 3],'b');% Tinh vi tri giao nhau de gioi han lai diem ve[x0,y0]=ginputfor k=1:length(x0) [xn(k),yn(k)]=fsolve(y,x0(k))endxn(1);xn(2);fplot(y1,[xn(1) xn(2)],'r')fplot(y2,[xn(1) xn(2)],'r')%Tinh dien tich ranh gioi giua 2 dung congtp=quad(y,xn(1),xn(2)) %Ve duong thang song song oy chia hinh thanh 2 phan bang nhautol=1e-3;k=xn(1);dt=0;while (abs(dt-tp/2)>tol) k=k+0.001; dt=quad(y,xn(1),k);endplot([k k],[y1(k) y2(k)],'m')%ve duong chia doi% To mau 2 phan bang nhau bang mau khac nhau%vung 1: ta lay x chay tu giao dim x=k toi xn(1) cua duong ben tren, %sau do di tip tu xn(1) toi x=k cua duong ben duoi;vay la het 1 vong di cua ½ daux1=linspace(k,xn(1));f1=y1(x1) x2=linspace(xn(1),k);f2=y2(x2)%vung 2: ta lay x chay tip tu x=k toi giao dim xn(2) cua duong ben duoi, %sau do di tip tu xn(2) tro ve x=k cua duong ben tren ; vay la het 1 vong di ½ nua tipx3=linspace(k,xn(2));f3=y1(x3) x4=linspace(xn(2),k);f4=y2(x4) fill([x1 x2],[f1,f2],'r',[x3 x4],[f3,f4],'b')

0.5 1 1.5 2 2.5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Bai 28clear all,close all,clc; f=inline('cos(t.^2)./(t+1)','t'); xi=linspace(0,1.5,50); for k=1:length(xi) yi(k)=quad(f,0,xi(k).^2+1)+0.25*xi(k)-0.8; end plot(xi,yi); grid on %cau b sp=spline(xi,yi); fx=inline('ppval(sp,x)','x','sp'); [x0,y0]=ginput for k=1:length(x0) [xn(k),fxn(k)]=fsolve(fx,x0(k),[],sp); end

Cao V¨n ChÝnh_B1K52text(xn,fxn,'*nghiem') fprintf('cac nghiem cua pt:') xn Bai 29%bai toan cauchy %caua giai hptvp voi dk ban dau [-7.69 -15.61 90.39]);dy=inline('[10*(u(2)-u(1));126.52*u(1)-u(2)-u(1)*u(3);u(1)*u(2)-8/3*u(3)]','t','u')[t,u]=ode45(dy,[0 8],[-7.69 -15.61 90.39]);subplot(2,2,1);plot(t,u(:,1),'r');title('do thi ham x(t)') subplot(2,2,2);plot(t,u(:,2),'b');title('do thi ham y(t)') subplot(2,2,3);plot(t,u(:,3),'y');title('do thi ham z(t)') %Cau b dy=inline('[y(2);(8*x^3*y(1)^3+y(2))./x]','x','y') [x,y]=ode45(dy,[1 4],[1/2 -1/2]);figure(2);subplot(2,1,1);plot(x,y(:,1),'b'); xlabel('x');ylabel('y') subplot(2,1,2);plot(x,y(:,2),'r'); xlabel('x');ylabel('y1') Bai 30%giai ptvp bang pp ban%Cau a dy=inline('[y(2);6*y(1)^2-y(2)]','x','y'); dyo=-2:.1:2; for i=1:length(dyo) [x,y]=ode45(dy,[0 1],[1 dyo(i)])%ham ode45 de giai PTVP, cho ngh thuc+phuc yend(i)=y(end,1)-2; end; f=inline('spline(dyo,yend,t)','t','dyo','yend');t=linspace(dyo(1),dyo(end),50); u=f(t,dyo,yend); figure(3) subplot(2,1,1) plot(t,u,'m'); [xo,yo]=ginput [dyon,yn]=fzero(f,xo,[],dyo,yend) [x,y]=ode45(dy,[0 1],[1 dyon]); subplot(2,2,3); plot(x,y(:,1),'b'); subplot(2,2,4) plot(x,y(:,2),'r'); %Cau b dy=inline('[y(2);6*y(1)^2-y(2)]','x','y'); yyo=-2:.1:2;%y tai cac gia tri khac nhau% for k=1:length(yyo) [x,y]=ode45(dy,[0 1],[yyo(k) 1]); %Gia tri y tai gia tri # va y'(1) dyend(k)=y(end,2)-1; end f=inline('spline(yyo,dyend,t)','t','yyo','dyend'); t=linspace(yyo(1),yyo(end),50) u=f(t,yyo,dyend); figure(2) subplot(2,1,1) plot(t,u,'m'); [xo,yo]=ginput [yn,dyon]=fzero(f,xo,[],yyo,dyend) [x,y]=ode45(dy,[0 1],[yn -1]);%Gia tri y(0)va y'(0) subplot(2,2,3); plot(x,y(:,1),'b'); xlabel('x') ylabel('y') subplot(2,2,4) plot(x,y(:,2),'r'); xlabel('x') ylabel('y1')% Cau c

Cao V¨n ChÝnh_B1K52dy=inline('[y(2);6*y(1)^2-y(2)]','x','y'); dyo=-2:.1:2; for k=1:length(dyo) [x,y]=ode45(dy,[0 1],[1 dyo(k)]); %y(0) va y'tai gia tri # dyend(k)=y(end,2)-3; end f=inline('spline(dyo,dyend,t)','t','dyo','dyend'); t=linspace(dyo(1),dyo(end),100); u=f(t,dyo,dyend); figure(2) subplot(2,1,1) plot(t,u,'g'); [xo,yo]=ginput [dyon,yn]=fzero(f,xo,[],dyo,dyend) [x,y]=ode45(dy,[0 1],[1 dyon]);%y(0) va y'(0) subplot(2,2,3); plot(x,y(:,1),'b'); subplot(2,2,4) plot(x,y(:,2),'r');

% Cach 2%cau aclear all;close all;clc; hpt='Dy1=y2,Dy2=6.*y1-y2';dkb='y1(0)=1,y1(1)=2'; dsb=dsolve(hpt,dkb,'x') y1b=simple(dsb.y1) y2b=simple(dsb.y2) figure(1); subplot(2,1,1); ezplot(y1b,[0 1]);grid on;hold on ezplot(y2b,[0 1]);%cau bdkb='y2(0)=-1,y2(1)=1'; dsb=dsolve(hpt,dkb,'x') y1b=simple(dsb.y1) y2b=simple(dsb.y2) subplot(2,1,2); ezplot(y1b,[0 1]);grid on ;hold on ezplot(y2b,[0 1]);%cau cdkb='y1(0)=1,y2(1)=1'; dsb=dsolve(hpt,dkb,'x') y1b=simple(dsb.y1) y2b=simple(dsb.y2) figure(2); subplot(2,1,1); ezplot(y1b,[0 1]);grid on;hold on ezplot(y2b,[0 1]);

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T ng h p code các đ thi Matlabổ ợ ềDe 1:clc;close all;clear all%cau a %luoi 41 chia deu [x,y]=meshgrid(linspace(-2,2,41));

Cao V¨n ChÝnh_B1K52 z=8./(x.^4+y.^4+2.*x+2.*y+4)-exp(-x.^2-y.^2+x+y+1);%cau b %tim chi so hang i, cot j, ung voi gi tri lon nhat cua Z [zmax,imax]=max(z) [zmax,jmax]=max(max(z)) i=imax(jmax) %tim chi so hang i, cot j, ung voi gi tri lon nhat cua Z [zmin,imin]=min(z) [zmin,jmin]=min(min(z)) i=imin(jmin) %ve mat cong subplot(1,2,1); surf(x,y,z) %ve 15 duong dong muc subplot(1,2,2); contour(x,y,z,15); %cau d: tinh min, max [x0 y0]=ginput f=inline('8./(x(1).^4+x(2).^4+2.*x(1)+2.*x(2)+4)-exp(-x(1).^2-x(2).^2+x(1)+x(2)+1)','x'); for k=1:length(x0) [xn(k,:),fxn(k,:)]=fminsearch(f,[x0(k) y0(k)]); end disp('cuc tieu la'); xn %cau c:tinh dao hs ham z theo huong x,y,voi cac dim chia cach deu [dzx,dzy]=gradient(z); figure(2); quiver(x,y,dzx,dzy); % ve ham vecto%tinh gia tri ham Z bang functionfunction z=de1a(x,y) z=8./(x.^4+y.^4+2.*x+2.*y+4)-exp(-x.^2-y.^2+x+y+1); end De 2%giong bai 1%thiet lap luoi chia 31x31[x,y]=meshgrid(linspace(-2,2,31)); z=(x.^2-2).*exp(-x.^2-y.^2)+2./(x.^2+y.^2-2.*(x+y)+3); %tim gia tri lon nhat cua mang Z va tim vt hang cot tuong ung[zmax,imax]=max(z) [zmax,jmax]=max(max(z)) imax=imax(jmax) [zmin,imin]=min(z) [zmin,jmin]=min(min(z)) imin=imin(jmin)%ve mat cong bang surfsubplot(1,2,1); surf(x,y,z) %Ve 15 duong dong mucsubplot(1,2,2); contour(x,y,z,15); x0=ginput f=inline('(x(1).^2-2).*exp(-x(1).^2-x(2).^2)+2./(x(1).^2+x(2).^2-2.*(x(1)+x(2))+3)','x'); for k=1:size(x0,1) [xn(k,:),fxn(k)]=fminsearch(f,x0(k,:)); end disp('cuc tieu la'); xn %tinh dao ham theo huong x,y va ve dthi truong vecto[dzx,dzy]=gradient(z); figure(2); quiver(x,y,dzx,dzy);

%tinh gia tri ham Z bang functionfunction z=de2a(x,y) z=8./(x.^4+y.^4+2.*x+2.*y+4)-exp(-x.^2-y.^2+x+y+1); end De 3%tao m file 2 bin n,x de tinh tong cua n so hang daufunction tong=de3(x,n)

Cao V¨n ChÝnh_B1K52ak=0; for k=1:n ak=ak+sin((2*n+1).*x)./(2*n+1); end tong=4./pi.*ak; %tao m file 1 bien x, sai so tol de tinh chuoifunction to=de3b(x,tol) ak=1; k=0; t=0; while any(abs(ak)>tol) ak=sin((2*k+1).*x)./(2*k+1); t=ak+t; k=k+1; end to=t; clear all;clc;%phan c x=linspace(-3*pi,3*pi); subplot(1,2,1);plot(x,de3(x,4),'r'); %ve do thi cua tong subplot(1,2,2);plot(x,de3b(x,1e-8),'b'); %ve dthi cua chuoi%phan d %ve mat ron xoay khi quay duong cong quanh truc x [x,phi]=meshgrid(0 : pi/15 : 2*pi); r=(3*sin(x)-sin(3*x))./(3*x)+0.5; y=r.*cos(phi); z=r.*sin(phi); figure(2); subplot(2,2,1);surf(x,y,r) %quanh truc y x1=x.*sin(phi); y1=r; z1=x.*cos(phi); subplot(2,2,2);surf(x1,y1,z1); %quanh truc Z x2=r.*cos(phi); y2=r.*sin(phi); z2=0.*phi;%neu thay z2=0 thi no khong hien thi hinh ve subplot(2,1,2);surf(x2,y2,z2);De 4function tong=de4(x) tol=1e-6; ak=1; k=0; s=0; while any(abs(ak)>tol); ak=(-1).^k.*x.^(2.*k+1)./factorial(2.*k); s=ak+s; k=k+1; end tong=s; %ve do thi x=linspace(0,10); figure(1); plot(x,de4(x)); %phan b,tim nghiem thuc cua pt x=linspace(0.5,10); f=de4(x)-(x+0.5)/x.^2+2 figure(2); plot(x,0,'r');hold on; %ve duong oy bang mau doplot(x,f,'b'); fx=inline('de4(x)-(x+0.5)/x.^2+2'); [x0 y0]=ginput for k=1:length(x0) [xn(k),fxn(k)]=fzero(fx,x0(k)) text(xn,fxn,'< nghiem') %chu thich cho vi tri nghiem

Cao V¨n ChÝnh_B1K52end xn fxn %phan c %cuc tieu ham dc lap bang function de4 x=linspace(0,10); f1=de4(x) figure(3); plot(x,0,'r');hold on; plot(x,g,'b'); fx1=inline('de4(x)'); [x1 y1]=ginput for k=1:length(x1) [xct(k),yct(k)]=fminsearch(fx1,x1(k)) text(xct,yct,'< cuc tieu') %chu thich cho vi tri cuc tieuend xct yct %cuc daif2=inline('(-1).*de4(x)'); [x2 y2]=ginput for k=1:length(x2) [xcd(k),ycd(k)]=fminsearch(f2,x2(k)) text(xcd,(-1).*ycd,'< cuc dai') end xcd-ycd %cau d %ve mat tron xoay khi quay duong cong quanh truc x [x,phi]=meshgrid(0 : pi/15 : 2*pi); r=de4(x); y=r.*cos(phi); z=r.*sin(phi); figure(2); subplot(2,2,1);surf(x,y,r) %quanh truc y x1=x.*sin(phi); y1=r; z1=x.*cos(phi); subplot(2,2,2);surf(x1,y1,z1); %quanh truc Z x2=r.*cos(phi); y2=r.*sin(phi); z2=0.*x;%neu thay z2=0 thi no khong hien thi hinh ve subplot(2,1,2);surf(x2,y2,z2);

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De 5%phan a,b [x,y]=meshgrid(linspace(-0.5,0.5),linspace(-2,2)); f1=cos(x.^2) +3.*y.*sin(2.*x)-2.*x-0.3; f2=x.^4+2.*x.*y+y.^2+8.*x+y-2; contour(x,y,f1,[0 0],'r');hold on; contour(x,y,f2,[0 0],'b'); pt1='cos(x(1).^2) +3.*x(2).*sin(2.*x(1))-2.*x(1)-0.3';

Cao V¨n ChÝnh_B1K52pt2='x(1).^4+2.*x(1).*x(2)+x(2).^2+8.*x(1)+x(2)-2'; hpt=['[',pt1,',',pt2,']']; fx=inline(hpt,'x'); [x0 y0]=ginput; for k=1:length(x0); [xn(k,:),fxn(k,:)]=fsolve(fx,[x0(k,:) y0(k,:)]); endxn,fxnfprintf('nghiem cua he phuong trinh la:\n'); disp(' x , y'); disp(xn); xlabel('truc x') ylabel('truc y') %cau 3:ve mat cong[x,y]=meshgrid(linspace(-0.2,0.2),linspace(-2,2)); z1=cos(x.^2)+3.*y.*sin(2.*x)-2.*x; z2=x.*4+2.*x.*y+y.^2+8.*x+y; subplot(1,2,1);surf(x,y,z1); subplot(1,2,2);surf(x,y,z2); De 6%phan a,b clear all;close all;clc; [x,y]=meshgrid(linspace(-0.3,0.3),linspace(-1,1)); f1=x.^2-10.*x.*y-4.*y.^4; f2=x.^4+2.*x.*y+y.^2+8.*x+y-0.1; figure(1); contour(x,y,f1,[0 0],'r'); hold on; contour(x,y,f2,[0 0],'b'); pt1='x(1).^2-10.*x(1).*x(2)-4.*x(2).^4'; pt2='x(1).^4+2.*x(1).*x(2)+x(2).^2+8.*x(1)+x(2)-0.1'; hpt=['[',pt1,',',pt2,']']; fx=inline(hpt,'x'); [x0 y0]=ginput for k=1:length(x0); [xn(k,:),fxn(k,:)]=fsolve(fx,[x0(k,:) y0(k,:)]); end text(xn(k,1),xn(k,2),'*'); xn fxn legend('do thi ham so'); xlabel('truc x') ylabel('truc y') %phan c ve mat cong [x,y]=meshgrid(linspace(-0.2,0.2),linspace(-2,2)); z1=x.^2-10.*x.*y-4.*y.^4; z2=x.^4+2.*x.*y+y.^2+8.*x+y-0.1; figure(2); subplot(1,2,1);surf(x,y,z1); subplot(1,2,2);surf(x,y,z2); De 7%ve do thi phan thuc va phan aoclear all,close all [x,y]=meshgrid(linspace(-2,2)); z=x+i.*y; u=z.^2-(1+i.*sqrt(3)).*z-1+i.*sqrt(3); subplot(2,1,1);plot(x,real(u)); subplot(2,1,2);plot(y,imag(u)); %phan b,c %tim nghiem gan dungfigure(2); contour(x,y,real(u),[0 0],'r');hold on contour(x,y,imag(u),[0 0],'b'); [x0,y0]=ginput; z0=x0+i.*y0; %tim nghiem chinh xac

Cao V¨n ChÝnh_B1K52f=inline('z.^2-(1+i.*sqrt(3)).*z-1+i.*sqrt(3)','z'); for k=1:size(z0,1) [zn(k,:),fzn(k,:)]=fsolve(f,z0(k,:)); end znfznplot(zn,fzn,'*')De 8%ve phan thuc va phan ao[x,y]=meshgrid(linspace(-2,2)); %bo di cung dcz=x+i.*y; u=(cos(z).^2-2).^2+6.^z+4-10.*i; subplot(2,1,1);plot(x,real(u)); subplot(2,1,2);plot(y,imag(u)); %phan b,c tim nghiem gan dung va chinh xac nghiem figure(2); contour(x,y,real(u),[0 0],'r');hold on contour(x,y,imag(u),[0 0],'b'); [x0,y0]=ginput; z0=x0+i.*y0; f=inline('(cos(z).^2-2).^2+6.^z+4-10.*i','z'); for k=1:size(z0,1) [zn(k,:),fzn(k,:)]=fsolve(f,z0(k,:)); end zn,fzn De 9% tinh cac duong tiem can clear all;close all;clc; syms x; f1=abs(x^3+5*x+3); f2=5-2*x-x^2; f=f1/f2; fprintf('Cac giao diem voi truc hoanh\n') x0=double(solve(f,x)); disp(x0); fprintf('Cac tiem can dung\n'); xtcd=solve(f2); for k=1:length(xtcd); fprintf(' x='); disp(xtcd(k)); end fprintf('Tiem can ngang ben trai\n'); xtcnt=limit(f,-inf); fprintf(' yt='); disp(xtcnt); fprintf('Tiem can ngang ben phai\n'); xtcnp=limit(f,inf); fprintf(' yp='); disp(xtcnp); fprintf('Tiem can xien\n'); a1=limit(f/x,-inf); b1=limit(f-a1*x,-inf); tcx1=a1*x+b1; fprintf(' y='); disp(tcx1); a2=limit(f/x,+inf); b2=limit(f-a2*x,+inf); tcx2=a2*x+b2; fprintf(' y=');disp(tcx2); %ve cac duong tiem can ezplot(f,[-15,15]); ylim([-30 30]); hold on % giao voi ox plot(x0,subs(f,x,x0),'ro'); % Ve tiem can dung ycd=[-30 30]; xcd1=double(xtcd(1)*ones(size(ycd)));

Cao V¨n ChÝnh_B1K52xcd2=double(xtcd(2)*ones(size(ycd))); plot(xcd1,ycd,'g',xcd2,ycd,'g') % Ve tiem can ngang %tiem can ngang ko xd % Ve tiem can xien xcx1=linspace(-15,double(xtcd(2))); ycx1=subs(tcx1,x,xcx1); plot(xcx1,ycx1,'k') xcx2=linspace(double(xtcd(1)),15); ycx2=subs(tcx2,x,xcx2); plot(xcx2,ycx2,'k') x11=linspace(-15,15); plot(x11,0); legend('Do thi ham f(x)','Giao voi Ox','Tiem can dung 1','Tiem can dung 2','Tiem can xien',0)

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De10%phan a,b clear all;close all,clc; xi=-0.4:0.2:1.6;yi=[0.86,0.92,0.95,0.93,0.86,0.76,0.64,0.53,0.44,0.36,0.30]; heso=polyfit(xi,1./asin(yi),2); a=heso(1) b=heso(2) c=heso(3) x1=-1:0.01:2; y1=sin(1./polyval(heso,x1)); plot(xi,yi,'*r',x1,y1); legend('diem thuc nghiem','ham noi suy') %phan c f=inline('-sin(1./polyval(heso,x))','x','heso'); [x0,y0]=ginput; for k=1:length(x0) [xn(k),fxn(k)]=fminsearch(f,x0(k),[],heso); end text(xn,-fxn,'<cuc dai') xn fxn

Cao V¨n ChÝnh_B1K52

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De11%phan a,b %tim he so va ve hinh clear all;close all;clc; xi=0:0.2:1.6; yi=[1.00,1.13,1.16,1.14,1.12,1.11,1.12,1.14,1.17]; hs=polyfit(xi.^2,(exp(xi)./yi).^2,2); a=hs(1),b=hs(2),c=hs(3), x1=0:0.01:2; y1=exp(x1)./sqrt(polyval(hs,x1.^2)); plot(xi,yi,'*r',x1,y1);ylim([1,2]); legend('diem thuc nghiem','ham noi suy') %phan c %cuc dai f=inline('-exp(x)./sqrt(polyval(hs,x.^2))','x','hs'); [x0,y0]=ginput; for k=1:length(x0) [xn(k),fxn(k)]=fminsearch(f,x0(k),[],hs); end text(xn,-fxn,'<cuc dai') xn fxn %cuc tieu f1=inline('exp(x)./sqrt(polyval(hs,x.^2))','x','hs'); [x11,y11]=ginput; for k=1:length(x11) [xn1(k),fxn1(k)]=fminsearch(f1,x11(k),[],hs); end text(xn1,fxn1,'<cuc tieu') xn1 fxn1

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Cao V¨n ChÝnh_B1K52De 12clear all,close all,clc %phan a,b %tim he so va ve hinh xi=-.2:.2:1.2; yi=[-.54 -.33 -.16 -.01 .11 .23 .41 2.61]; hs=polyfit(xi,yi.*(2.*xi.^2-3)./cos(xi)+0.2.*exp(xi),2); a=hs(1),b=hs(2),c=hs(3), x1=-0.2:0.01:1.2; y1=(polyval(hs,x1)-0.2.*exp(x1)).*cos(x1)./(2.*x1.^2-3); plot(xi,yi,'*r',x1,y1);hold on plot(x1,0); legend('diem thuc nghiem','ham noi suy') %phan c %tim ko diem f=inline('(polyval(hs,x)-0.2.*exp(x)).*cos(x)./(2.*x.^2-3)','x','hs'); [x0,y0]=ginput; for k=1:length(x0) [xn(k),fxn(k)]=fsolve(f,x0(k),[],hs); end text(xn,fxn,'<khong diem') xn fxn

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De 13clear all,close all,clc %noi suy da thuc va noi suy spline xi=1.5:0.25:3.5; yi=[0.52 0.05 -0.38 -0.42 -0.01 0.35 0.14 -0.28 -0.09]; x1=linspace(1,4); spl=spline(xi,yi); y1=ppval(spl,x1) hs=polyfit(xi,yi,5); y2=polyval(hs,x1) plot(xi,yi,'+m',x1,y1,'r',x1,y2,'b');hold on plot(x1,0);ylim([-0.52,1]); legend('diem thuc nghiem','noi suy spline','noi suy da thuc'); %phan b %tinh ko diem,cuc tri bang ham noi suy spline %tinh ko diem f11=inline('ppval(spl,x)','x','spl'); [x01,y01]=ginput; for k=1:length(x01) [xn11(k),fxn11(k)]=fsolve(f11,x01(k),[],spl); end text(xn11,fxn11,'*'); % tinh cuc tri bang phuong phap noi suy spline % cuc tieu [x11,y11]=ginput; for k=1:length(x11)

Cao V¨n ChÝnh_B1K52 [xn12(k),fxn12(k)]=fminsearch(f11,x11(k),[],spl); end text(xn12,fxn12,'o'); %cuc dai f12=inline('-ppval(spl,x)','x','spl'); [x21,y21]=ginput; for k=1:length(x21) [xn21(k),fxn21(k)]=fminsearch(f12,x21(k),[],spl); end text(xn21,-fxn21,'<'); %phan c %tinh tich phan cua ham noi suy spline sp=fnint(spl); I2=ppval(sp,3.5)-ppval(sp,1.5)

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De14clear all;close all;clc %dung noi suy da thuc va noi suy spline xi=0:4:44; yi=[82.3 74.3 67.6 62.5 58.1 54.3 51.2 48.6 46.1 43.9 41.9 40.1]; spl=spline(xi,yi); hs=polyfit(xi,yi,5); x1=linspace(0,44); plot(xi,yi,'+r',x1,ppval(spl,x1),'r',x1,polyval(hs,x1),'y'); %tinh dien tich theo noi suy da thuc va spline trong khoang [0 44] ff=inline(vectorize(poly2sym(hs))); %poly2sym(heso,bien) de chuyen doi dang bieu dien cua x sang sym de tinh TP %tinh dt theo noi suy da thuc (xap xi) s2=quad(ff,0,44) %cach2 cho ham la ham goc: sym xi;s2=quad(inline(vectorize(y),'x',0,44)) %tinh dt theo noi suy spline sp=fnint(spl);%tinh tp s1=ppval(sp,44)-ppval(sp,0)%thay can vao sp de tinh gt tich phan %tim nghiem bang pp spline ham y(x)=55.7 figure(2) plot(x1,ppval(spl,x1)-55.7);hold on plot(x1,0); f=inline('ppval(spl,x)-55.7','x','spl'); [x0,y0]=ginput; for k=1:length(x0) [xn(k),fxn(k)]=fsolve(f,x0(k),[],spl); end text(xn,fxn,'o') fprintf('nghiem cua no la\n'); disp(xn)

De 15

Cao V¨n ChÝnh_B1K52%giong bai27, phan cac bai thuc tap% ve danh gioi va tinh dien tich. clear all,close all;clc syms x; y1=30.*sin(x.^2-0.25); y2=(x.^4+1)./log(x+1)-10; f=inline(vectorize(y1-y2)); figure(1); ezplot(y1,[0,2]);hold on %ve ranh gioi ezplot(y2,[0 2]);ylim([-30,30]) [x0,y0]=ginput; %tim nghiem chinh xac cua pt f=0 de tinh dt for i=1:length(x0) [xn(i),fxn(i)]=fsolve(f,x0(i)); end xn(1) xn(2) s=abs(quad(f,xn(1),xn(2))) %tinh dien tich voi can xn(1),xn(2)%phan b % Ve doan thang dk=2;%diu kin ban dau dat raxm=1.15;%duong chia ranh gioi lay bat kiss=1e-4; while (dk==2) xm=xm+ss; s1=quad(f,xn(1),xm); if (abs(s/2)-abs(s1))<=ss; dk=0; %den khi bang 0 thi suat ra gia tri xm chia doi hinh end end fprintf('Duong chia hinh thanh 2 phan co S bang nhau x='); disp(xm) %gt xm duoc suat ras1=quad(f,xn(1),xm) %tinh dt 2 nua, de tim sai sos2=quad(f,xm,xn(2)) fprintf(' Sai so S2-S1='); disp(s2-s1) %gioi han lai hinh, chi trong khoang tu giao dim xn(1) den xn(2) figure(2); ezplot(y1,[xn(1) xn(2)]);hold on ezplot(y2,[xn(1) xn(2)]);ylim([-30,30]);hold on yi=-2:0.01:2; plot(xm,yi,'k')%ve duong chia doi xm % % To mau vung 1,2 %vung 1: ta lay x chay tu giao dim x1 toi xm cua duong ben tren, %sau do quay lai tu xm tro ve x1 cua duong ben duoi;het 1/2 vongx1=linspace(xn(1),xm,20); y1=30.*sin(x1.^2-0.25); x2=linspace(xm,xn(1),20); y2=(x2.^4+1)./log(x2+1)-10; %vung 2: ta lay x chay tu xm toi giao dim x2 cua duong ben tren, %sau do quay lai tu x2 tro ve xm cua duong ben duoix3=linspace(xm,xn(2),20); y3=30.*sin(x3.^2-0.25); x4=linspace(xn(2),xm,20); y4=(x4.^4+1)./log(x4+1)-10; fill([x1,x2],[y1,y2],'r',[x3,x4],[y3,y4],'b')

De 16%de nay giong de15, bai 27, khac o cho hinh gioi han de bai cho ta %bit trc [0.7 1.2] ma ko can tin nhu bai 27 va de15,bai nay chia lam 3 phan= % ve danh gioi va tinh dien tich. clear all,close all;clc syms x; y1=-(x.^2+x+1)./(2.*x-1)+0.3; y2=(x.^4+1)./log(x+1)-10; f=inline(vectorize(y1-y2)); figure(1); ezplot(y1,[0.7 1.2]);hold on ezplot(y2,[0.7 1.2]);ylim([-10,10]) s=abs(quad(f,0.7,1.2)) %phan b

Cao V¨n ChÝnh_B1K52 % Ve doan thang 1 x=xm de chia hinh thanh 3phan = dk=1;xm=0.8;ss=1e-4; %gia su duong chia ban dau la xm=0.8 while (dk==1) xm=xm+ss; s1=quad(f,0.7,xm); if (abs(s/3)-abs(s1))<=ss; dk=0; end end fprintf('Duong chia hinh thanh 2 phan co S bang nhau x='); disp(xm)%ve doan thang 2 x=xm1 de chia hinh thanh 3 phan =dk=2;xm1=1;ss=1e-4; while (dk==2) xm1=xm1+ss; s2=quad(f,xm,xm1); if (abs(s/3)-abs(s2))<=ss; dk=0; end end fprintf('Duong chia hinh thanh 2 phan co S bang nhau x=');disp(xm1) %tinh dt 3 phan vua chia de so sanhs1=quad(f,0.7,xm) s2=quad(f,xm,xm1) s2=quad(f,xm1,1.2)%ve lai ranh gioi figure(2); ezplot(y1,[0.7 1.2]);hold on ezplot(y2,[0.7 1.2]);ylim([-10,10]);hold on %ve 2 duong thang chia hinh thanh 3 phan = yi=-8:0.01:-2; plot(xm,yi,'k',xm1,yi,'k') % % To mau vung 1,2,3 x1=linspace(0.7,xm,20); y1=-(x1.^2+x1+1)./(2.*x1-1)+0.3; x2=linspace(xm,0.7,20); y2=(x2.^4+1)./log(x2+1)-10; %vung 2x21=linspace(xm,xm1,20); y21=-(x21.^2+x21+1)./(2.*x21-1)+0.3; x22=linspace(xm1,xm,20); y22=(x22.^4+1)./log(x22+1)-10; %vung 3x3=linspace(xm1,1.2,20); y3=-(x3.^2+x3+1)./(2.*x3-1)+0.3; x4=linspace(1.2,xm1,20); y4=(x4.^4+1)./log(x4+1)-10; fill([x1,x2],[y1,y2],'r',[x21 x22],[y21 y22],'c',[x3,x4],[y3,y4],'b')

0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2-10

-8

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(x4+1)/log(x+1)-10

De 17%phan a:tinh va ve do thi

Cao V¨n ChÝnh_B1K52%chu y trong khoang gioi han bai ra ta ko thay cuc tieu dau,kaka!!!%nhung bai nay ta cu viet code de tim cuc tieu, ke no,okok !!!clear all,close all,clc; f=inline('(cos(t)+1)./(t.^2+1)','t'); xi=linspace(0,1.5); for k=1:length(xi) yi(k)=sin(2.*xi(k)).*quad(f,0,xi(k).^2+1)-xi(k).^2-0.2; end plot(xi,yi); grid on; %cau b,c:tim nghiem va tinh cuc tri,ve %tim nghiem sp=spline(xi,yi); fx=inline('ppval(sp,x)','x','sp'); [x0,y0]=ginput for k=1:length(x0) [xn(k),fxn(k)]=fsolve(fx,x0(k),[],sp); end text(xn,fxn,'o') fprintf('cac nghiem cua pt:'); disp(xn) %cuc tieu[x01,y01]=ginput for k=1:length(x01) [xct(k),fct(k)]=fminsearch(fx,x01(k),[],sp); end text(xct,fct,'*') xct%cuc daifx1=inline('-ppval(sp,x)','x','sp'); [x02,y02]=ginput for k=1:length(x02) [xcd(k),fcd(k)]=fminsearch(fx1,x02(k),[],sp); end text(xcd,-fcd,'*') %phan d syms a t xi=linspace(0,1.5); for k=1:length(xi) a=xi(k); %dat cai nay la do trong de co an a f1=inline(vectorize((cos(t)+1)./(t.^2+a.^2+1))); %tinh lan luot cac gt cua ham ung voi tung gt xi yi1(k)=quad(f1,0,xi(k).^2+1)-xi(k).^2-0.2; end figure(2); plot(xi,yi1);

De 18%phan a:tinh va ve do thi clear all,close all,clc; f=inline('(cos(t)+1)./(t.^2+1)','t'); xi=linspace(0,2); for k=1:length(xi) yi(k)=cos(2.*xi(k)).*quad(f,0,xi(k).^2+1)-xi(k).^2-0.8; end plot(xi,yi); grid on; %cau b,c:tim nghiem va tinh cuc tri,ve %tim nghiem sp=spline(xi,yi); fx=inline('ppval(sp,x)','x','sp'); [x0,y0]=ginput for k=1:length(x0) [xn(k),fxn(k)]=fsolve(fx,x0(k),[],sp); end text(xn,fxn,'o')

Cao V¨n ChÝnh_B1K52fprintf('cac nghiem cua pt:'); disp(xn) %cuc dai fx1=inline('-ppval(sp,x)','x','sp'); [x01,y01]=ginput for k=1:length(x01) [xcd(k),fcd(k)]=fminsearch(fx1,x0(k),[],sp); end text(xcd,-fcd,'*')%phan d syms a t xi=linspace(0,2); for k=1:length(xi) a=xi(k); %dat cai nay la do trong de co a f1=inline(vectorize((cos(t)+1)./(t.^2+a.^2+1))); yi1(k)=quad(f1,0,xi(k).^2+1)-xi(k).^2-0.2; end figure(2); plot(xi,yi1);grid on;

De 19%bai toan cauchy %caua: giai ptvp va ve dthi D=inline('[2*u(2)-u(1);3*u(1)+u(3)-u(1)*u(3);4*u(1)*u(2)-u(3)]','t','u'); [t,u]=ode45(D,[0 5],[-5 10 0]) %[0 5] ung voi dk doi so vao t;[-5 10 0] ung voi dk ban dau: %x(0),y(0),z(0) plot(t,u(:,1),'r',t,u(:,2),'b',t,u(:,3),'y');shg; legend('x(t)','y(t)','z(t)'); y1=u(:,1); %liet ke cac hang ung voi cot1 cua MT u, tuc la liet ke gt cua x(t),ta %dat ham x(t) do la y1%Cau b: tinh ko diem va cuc tri spl=spline(t,y1); f11=inline('ppval(spl,x)','x','spl'); [x01,y01]=ginput; for k=1:length(x01) [xn11(k),fxn11(k)]=fsolve(f11,x01(k),[],spl); end text(xn11,fxn11,'*'); % tinh cuc tri bang phuong phap noi suy spline % cuc tieu [x11,y11]=ginput; for k=1:length(x11) [xn12(k),fxn12(k)]=fminsearch(f11,x11(k),[],spl); end text(xn12,fxn12,'o'); %cuc dai f12=inline('-ppval(spl,x)','x','spl'); [x21,y21]=ginput; for k=1:length(x21) [xn21(k),fxn21(k)]=fminsearch(f12,x21(k),[],spl); end text(xn21,-fxn21,'<');

%Cau c: chu y chua lam dc

Cao V¨n ChÝnh_B1K52

De 20%cach 1%bai toan ve phuong phap ban %phan a giai ptvp tinh y(x),y'(x)f=inline('[y(2);y(1)+sin(x)*cos(x)+x^2*sin(x+pi/4)/(x^10+1)]','x','y')[x y]=ode45(f,[0 5],[0 0])%[0 0] la dk ban dau;[0 5] la gioi han cua x%cau b: ve do thi y(x) va y'(x) hay y(:,1) va y(:,2)subplot(2,1,1);plot(x,y(:,1),'r');subplot(2,1,2);plot(x,y(:,2),'b');%cau c: figure(2);plot(x,y(:,1),'y',x,y(:,2),'g');grid on%noi suy tung duong y,y'sp1=spline(x,y(:,1));gtsp1=ppval(sp1,x);sp2=spline(x,y(:,2));gtsp2=ppval(sp2,x);[x0 y0]=ginput[xn yn]=fsolve(@(x)(ppval(sp1,x)-ppval(sp2,x)),x0) %for k=1:length(x0) %[xn(:,k) yn(:,k)]=fsolve(inline('ppval(sp1,x)-ppval(sp2,x)','x'),x0(k))%tai sao khai %bao the nay thi ko chay dc??????????????? %end %xn,yn%cau c tinh dt bao boi duong bien trensp=spline(x,y(:,2)-y(:,1));tp=fnint(sp);dt=ppval(tp,xn)-ppval(tp,0)%chu y: hoi cac ban cach giai giong bai 27,de gioi han lai dc hinh ta phai%lam tnao va neu khai bao inline de chinh xac ngh thi lam tnao?????????

%de20 cach 2, hay hon nhieu cach1 cua Thay Chi%bai toan ve phuong phap ban %phan a giai ptvp tinh y(x),y'(x)f=inline('[y(2);y(1)+sin(x)*cos(x)+x^2*sin(x+pi/4)/(x^10+1)]','x','y')[x y]=ode45(f,[0 5],[0 0])%[0 0] la dk ban dau;[0 5] la gioi han cua x%cau b: ve do thi y(x) va y'(x) hay y(:,1) va y(:,2)subplot(2,1,1);plot(x,y(:,1),'r');subplot(2,1,2);plot(x,y(:,2),'b');%cau c: figure(2);plot(x,y(:,1),'y',x,y(:,2),'g');grid on%noi suy tung duong y'-ysp=spline(x,y(:,2)-y(:,1)); % Tim khong diem 2ham giao nhau tu ham noi suy spline sp %x2=0:.01:5 f1=inline('ppval(sp,x)','x','sp'); [x0,y0]=ginput for k=1:length(x0) %chu y vong lap for o day dung cho ham noi suy %khac voi vong for dung voi ham so!!!!bai27 [xn(k),yn(k)]=fsolve(f1,x0(k),[],sp); end xn(1) xn(2)

Cao V¨n ChÝnh_B1K52 % Tinh tich phan ham noi suy spline bang "fnint" va ham goc bang "quad"tpsp=fnint(sp)dt=abs(ppval(tpsp,xn(1))-ppval(tpsp,xn(2)))

De 21Cach 1%cau a: %giai ptvp tim y,y',y''va ve chungf=inline('[y(2);y(3);8*x-y(1)^2*y(2)-y(1)*y(3)]','x','y')[x y]=ode45(f,[0 pi/2],[0 2 5]);plot(x,y(:,1),'r',x,y(:,2),'y',x,y(:,3),'b');grid on;xlabel('x');ylabel('y(x),dy/dx,d2y/dx')legend('y(x)','dy/dx','d2y/dx');%chu thich cho cac duong da ve%cau b:tim nghiem pt:y(x)=1.5sp=spline(x,y(:,1)-1.5);%x2=linspace(0,pi/2);y=ppval(sp,x);figure(2);plot(x,y);grid on % Tim khong diem 2ham giao nhau tu ham noi suy spline sp f1=inline('ppval(sp,x)','x','sp'); [x0,y0]=ginput for k=1:length(x0) %chu y vong lap for o day dung cho ham noi suy %khac voi vong for dung voi ham so!!!!bai27 [xn(k),yn(k)]=fsolve(f1,x0(k),[],sp); endxn,ynCach 2%de21 cach 2%cau a: %giai ptvp tim y,y',y''va ve chungf=inline('[y(2);y(3);8*x-y(1)^2*y(2)-y(1)*y(3)]','x','y')[x y]=ode45(f,[0 pi/2],[0 2 5]);plot(x,y(:,1),'r',x,y(:,2),'y',x,y(:,3),'b');grid on;xlabel('x');ylabel('y(x),dy/dx,d2y/dx')legend('y(x)','dy/dx','d2y/dx');%chu thich cho cac duong da ve%cau b:tim nghiem pt:y(x)=1.5sp=spline(x,y(:,1)-1.5);y=ppval(sp,x);figure(2);plot(x,y);grid on[x0 y0]=ginput[xn yn]=fsolve(@(x)ppval(sp,x),x0)

De 22Cach 1%cach 1 nay khong chay duoc???????????

clear all;close all;clc; hpt='Dy1=y2,Dy2=-9.8*sin(y1)-y2'; dkb='y1(0)=0.5,y2(0)=0'; dsb=dsolve(hpt,dkb,'x') y11=simple(dsb.y1) y22=simple(dsb.y2) figure(1); subplot(2,1,1); ezplot(y11,[0 3]);grid on subplot(2,1,2) ezplot(y22,[0 3]);grid on

Cach 2%cach 2clear all;close all;clc; f=inline('[y(2);-y(2)-9.8*sin(y(1))]','t','y')[t y]=ode45(f,[0 3],[0.5 0])plot(t,y(:,1),'r',t,y(:,2),'b');grid on;xlabel('t');ylabel('teta');legend('teta(t)','dteta/dt')%cau b: tim 0 diem va cuc tri ham:y=teta(t)

Cao V¨n ChÝnh_B1K52sp=spline(t,y(:,1));ysp=ppval(sp,t)figure(2);plot(t,ysp)f=inline('ppval(sp,t)')[t0 y0]=ginputfor i=1:length(t0) [tn yn]=fsolve(f,t0(i),[],sp)endtn,yn %tim cuc tieu ham noi suy cua dx/dt hay ham noi suy cua y(:,1)[t1 y1]=ginputfor i=1:length(t1) [tct yct]=fminsearch(f,t1(i),[],sp)endtext(tct,yct,'<cuc tieu day ne !!!')tct,yct %tim cuc dai ham noi suy cua dx/dt hay ham noi suy cua y(:,1)f1=inline('-1*ppval(sp,t)')[t2 y2]=ginputfor i=1:length(t2) [tcd ycd]=fminsearch(f1,t2(i),[],sp)endtext(tcd,-ycd,'<cuc dai day ne!!! ')%chu y co dau tru nhe,bai nay minh thi quyen ko cho dau - vao,huhu !tcd,-ycd

De 23clear all;close all; syms x; %bien syms vi o day ta co buoc tinh dao ham%Cau a:ve do thi y=x-7/2+sqrt(4.*x.^2+2.*x+7); ezplot(y,[-6 6]);%Cau b:tim cuc tri f=inline('xi-7/2+sqrt(4.*xi.^2+2.*xi+7)','xi') [x0 y0]=ginput; for k=1:length(x0) [xn(k),fxn(k)]=fminsearch(f,x0(k)); end text(xn,fxn,'< cuc tieu'); %Cau c:Tinh va ve tiem can a1=limit(y/x,x,inf);a2=limit(y/x,x,-inf); b1=limit(y-a1*x,x,inf);b2=limit(y-a2*x,x,-inf); h1=ezplot(a1*x+b1);set(h1,'color','r') h2=ezplot(a2*x+b2);set(h2,'color','r') axis([-6 6 -3 14])%Cau d:tinh do dai cung: bang tich phan sqrt(1+dy^2) %chu y: tinh dao ham thi bien x phai o dang syms dy=diff(y,x); dyy=sqrt(1+dy^2); fdx=inline(vectorize(dyy),'x');%vectorize(hoac char):de chuyen tu sym sang vecto I=quad(fdx,-6,6) %Cau e: %quay quanh truc x figure(2); [xi phi]=meshgrid(-6:0.7:6,0:pi/10:2*pi); ri=xi-7/2+sqrt(4*xi.^2+2*xi+7); yi=ri.*cos(phi); zi=ri.*sin(phi); surf(xi,yi,zi); %tinh dien tich cua vat the xoay quanh ox %ban kinh vat the chinh la truc oy disp('dien tich xung quanh'); S=int(2*pi*y,x,-6,6); Sxq=double(S) disp('dien tich toan phan');

Cao V¨n ChÝnh_B1K52 R1=subs(y,x,-6); R2=subs(y,x,6); Stp=Sxq+pi*double(R1^2+R2^2) disp('the tich khoi tron xoay'); V=double(pi*int(y^2,x,-6,6))

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De 24Chu y: Cau b khong bit lamclear all;close all;clc %Cau a: ve do thi [x,y]=meshgrid(linspace(-10,10)); f1=x.^2+2.*y.^2-3; f2=2.*x.^2-x.*y-5.*x+1; contour(x,y,f1,[0 0],'r');hold on; contour(x,y,f2,[0 0],'b') %Cau b:lap function chuyen duong cong bac 2 ve dang chinh tac %cau b nay ko chay dc,ko hiu gi hit A=[2,-1/2;-1/2,0]; B=[-5,0]; C=1; F=de24b(A,B,C) h=ezplot(F);set(h,'color','r')%cau c%tinh chu vi va dien tich disp('dien tich '); f=inline('sqrt((3-x.^2)./2)','x') S1=quad(f,-sqrt(3),sqrt(3)); %can nay lay o dau ra nhi ??? dt=2*double(S1) %do dai cung disp('chu vi'); syms x; y1=sqrt((3-x.^2)./2); dy=diff(y1,x); dyy=sqrt(1+dy^2); fdx=inline(vectorize(dyy),'x'); %bien dyy ve dang vecto I=quad(fdx,-sqrt(3),sqrt(3)) cvi=I*2

De 25Cau b khong chay dc dau?????

clear all;close all;clc

Cao V¨n ChÝnh_B1K52%ve do thi [x,y]=meshgrid(linspace(-10,10)); f1=2.*x.^2-4.*x.*y-y.^2+8; f2=x.^2+2.*x.*y+y.^2+8.*x+y; contour(x,y,f1,[0 0],'r');hold on; contour(x,y,f2,[0 0],'b')

%Cau b:lap function chuyen duong cong bac 2 ve dang chinh tac %cau b nay ko chay dc,ko hiu gi hit

A1=[2,-2;-2,-1];B1=[0,0];C1=8F1=standardform(A1,B1,C1);figure(2);h1=ezplot(F1);grid on;hold on A2=[1,1;1,1];B2=[8,1];C2=0F2=standardform(A2,B2,C2);h2=ezplot(F2);set(h2,'color','r')

De 26Cau a: Cach 1

%bai toan ve phuong phap ban clear all;close all;clc; hpt='Dy1=y2,Dy2=sin(x)-y1-y2'; dkb='y1(pi/2)=1,y1(0)=0'; dsb=dsolve(hpt,dkb,'x') y11=simple(dsb.y1) %nghiem yy22=simple(dsb.y2) %nghiem y'figure(1); subplot(2,1,1);ezplot(y11,[0 5]);grid on %ve ham ysubplot(2,1,2);ezplot(y22,[0 5]);grid on %ve ham y'

Cau a: cach 2clear all;close all;clc; %cau a: giai ptvp voi dk ban dau va ve dthi:y,y'dy=inline('[y(2);sin(t)-y(1)-y(2)]','t','y')[t y]=ode45(dy,[0 5],[0 0]);plot(t,y(:,1),'r',t,y(:,2),'b');grid on

%cau b: giai ptvp voi dk bien

De 27R1=1;R2=1;R3=1;R4=1;R5=1;syms V%cau a dung DL Kirchoff lap hpttt va giai no

Cao V¨n ChÝnh_B1K52A=[R1 0 R3 0 0;0 R2 -R3 R4 0;0 0 0 R4 -R5;1 -1 -1 0 0;0 1 0 -1 -1];b=[V;0;0;0;0]I=A\b%cau b ve dthi dong ra Iezplot(I(5),[-5,5]);grid on

Hay xem lai cach giai PTVP nhe, chua hiu dau day !!!!!!!!!!!!!Thi tot nhe !

OK !