25 doan code ve hinh BTL giai tich2 2015

clc clf hold on grid on % ve mat cau phan tren phi=linspace(0,2pi,30); theta=linspace(0,pi4,30); p t=meshgrid(phi,theta); x=sqrt(2)sin(t).cos(p); y=sqrt(2)sin(t).sin(p); z=sqrt(2)cos(t); mesh(x,y,z,FaceColor,c,FaceAlpha,0.5,EdgeColor,non); % ve mat cau phan duoi theta=linspace(3pi4,pi,30); p t=meshgrid(phi,theta); x=sqrt(2)sin(t).cos(p); y=sqrt(2)sin(t).sin(p); z=sqrt(2)cos(t); mesh(x,y,z,FaceColor,c,FaceAlpha,0.5,EdgeColor,non);

(CODE) BTL MatLab môn giải tích 2- HK152 2.2 Vẽ hình của một trong các vật thể dưới đây

V 1: x2 + y2 ≤ 1,x2 + y2 + z2 ≤ 2

clc

clf

% ve mat cau phan tren

phi=linspace(0,2*pi,30);

theta=linspace(0,pi/4,30);

[p t]=meshgrid(phi,theta);

x=sqrt(2)*sin(t).*cos(p);

y=sqrt(2)*sin(t).*sin(p);

z=sqrt(2)*cos(t);

% ve mat cau phan duoi

theta=linspace(3*pi/4,pi,30);

[p t]=meshgrid(phi,theta);

x=sqrt(2)*sin(t).*cos(p);

y=sqrt(2)*sin(t).*sin(p);

z=sqrt(2)*cos(t);

% ve mat tru

z=linspace(-1,1,30);

[z phi]=meshgrid(z,phi);

r=1;

x=r.*cos(phi);y=r.*sin(phi);

% ve giao tuyen

title('x^2+y^2<=1, x^2+y^2+z^2<=2')

V 2: 0 ≤ z ≤px2 + y2,x2 + y2 + z2 ≤ 2

clc

clf

title('x^2+y^2+z^2<=2,0=<z<=sqrt(x^2+y^2)')

%Ve non z=sqrt(x^2+y^2) phan nam trong mat cau

phi=linspace(0,2*pi,30);

r=linspace(0,1,30);

[r phi]=meshgrid(r,phi);

x=r.*cos(phi);

z=sqrt(x.^2+y.^2);

%Ve mat Cau dung toa do cau

phi=linspace(0,2*pi,30);

theta=linspace(pi/4,pi/2,30);

[p t]=meshgrid(phi,theta);

x=sqrt(2)*sin(t).*cos(p);

y=sqrt(2)*sin(t).*sin(p);

z=sqrt(2)*cos(t);

%Ve 2 giao tuyen trong 2 mp z=0, z=1

V 3: x2 + y2 ≤ 2y,x2 + y2 + z2 ≤ 4

clc

clf

phi=linspace(0,2*pi,50);

r=linspace(0,1,50);

[r ph]=meshgrid(r,phi);

% Phan mat cau

x=r.*cos(ph);

y=r.*sin(ph)+1;

z1=sqrt(4-x.^2-y.^2);z2=-sqrt(4-x.^2-y.^2)

%Phan mat tru

x=cos(ph);y=sin(ph)+1;z1=r.*sqrt(2-2*sin(ph));z2=-r.*sqrt(2-2*sin(ph));

xlabel('x')

ylabel('y')

zlabel('z')

view(105,20)

V 4: y = 5,y = 1 + x2,z = 0,z + x = 2

√ √

clc

clf

% ve mat z=0 va z=2-x

x=linspace(-2,2,200);

y=linspace(1,5,200);

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

z1=0*x;z2=2-x;

for j=1:length(y)

z1(i,j)=NaN;z2(i,j)=NaN;

end

end

% ve mat y=5 va y=1+x^2

x=linspace(-2,2,200);

z=linspace(0,4,200);

[x z]=meshgrid(x,z);

y1=5+0*x;

y2=1+x.^2;

y1(i,j)=NaN;y2(i,j)=NaN;

end

% ve giao tuyen

x=linspace(-2,2,200);

y=linspace(1,5,200);

y1=1+x.^2;

z1=0*x;z2=2-x;

V 5: y = x,y = 2 x,z = 0,x + z = 6

% vat gioi han boi y=sqrt(x), y=2*sqrt(x), z=0, x+z=6

clc

clf

%Ve mat y=sqrt(x), y=2*sqrt(x)

x=linspace(0,6,300);z=linspace(0,6,300);

[x z]=meshgrid(x,z);

y1=sqrt(x); y2=2*sqrt(x);

y1(i,j)=NaN;y2(i,j)=NaN;

end

%Ve mat z=0, x+z=6

x=linspace(0,6,300);y=linspace(0,2*sqrt(6),300);

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

z1=0*x; z2=6-x;

z1(i,j)=NaN;z2(i,j)=NaN;

end

% ve giao tuyen

x=linspace(0,6,300);

y1=sqrt(x);y2=2*sqrt(x);

z1=0*x;z2=6-x;

V 6: y = x,y = x2,x2 + y2 = z,x2 + y2 = 2z

% ve mat gioi han boi y=x, y=x^2,x^2+y^2=z,x^2+y^2=2z

clc

clf

%Ve mat y=x, y=x.^2

x=linspace(0,1,200);z=linspace(0,2,200);

[x z]=meshgrid(x,z);

y1=x;

y1(i,j)=NaN;

end

y2=x.^2;

y2(i,j)=NaN;

end

% ve mat z=x^2+y^2,z=(x.^2+y.^2)/2;

x=linspace(0,1,200);

y=linspace(0,1,200);

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

z1=x.^2+y.^2; z2=(x.^2+y.^2)/2;

for j=1:length(y)

z1(i,j)=NaN;z2(i,j)=NaN;

end

% ve duong giao tuyen

x=linspace(0,1,1000);z=linspace(0,2,1000);y=linspace(0,1,1000);

x1=1+0.*x;

y1=x; y2=x.^2; y3=1+0.*x;

z1=x.^2+y1.^2; z2=(x.^2+y1.^2)/2;z3=x.^2+y2.^2; z4=(x.^2+y2.^2)/2; z5=x.^2+y3.^3;

V 7: z = 0,z = x2 + y2,x2 + y2 = 1

% vat gioi han boi z=0,x^+y^1=1,z=x^2+y^2;

clc

clf

%Ve mat z=0, z=x^2+y^2;

phi=linspace(0,2*pi,30);

r=linspace(0,1,30);

[r phi]=meshgrid(r,phi);

x=r.*cos(phi);

y=r.*sin(phi);

z1=0*x; z2=x.^2+y.^2;

% ve mat tru x^2+y^2=1

phi=linspace(0,2*pi,30);z=linspace(0,1,30);

[phi z]=meshgrid(phi,z);

x=cos(phi);y=sin(phi);

hold on;

phi=linspace(0,2*pi,30);

V 8: z = 0,z = px2 + y2,x2 + y2 = 4

% vat gioi han boi z=0,x^+y^4=1,z=sqrt(x^2+y^2);

clc

%Ve mat z=0, z=sqrt(x^2+y^2);

phi=linspace(0,2*pi,30);

r=linspace(0,2,30);

[r phi]=meshgrid(r,phi);

x=r.*cos(phi);

y=r.*sin(phi);

z1=0*x; z2=sqrt(x.^2+y.^2);

% ve mat tru x^2+y^2=4

phi=linspace(0,2*pi,30);z=linspace(0,2,30);

[phi z]=meshgrid(phi,z);

x=2*cos(phi);y=2*sin(phi);

% ve giao tuyen

phi=linspace(0,2*pi,30);

V 9: z = 0,y = x2,y + z = 4

√

% vat gioi han boi z=0,y+z=4,y=x^2;

clc

clf

%Ve mat z=0, y+z=4;

x=linspace(-2,2,200);

y=linspace(0,4,200);

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

z1=0*x;z2=4-y;

if y(i,j)<x(i,j)^2

z1(i,j)=NaN;z2(i,j)=NaN;

end

end

% ve mat y=x^2;

x=linspace(-2,2,200);

z=linspace(0,4,200);

[x z]=meshgrid(x,z);

y=x.^2;

y(i,j)=NaN;

end

% ve giao tuyen

x=linspace(-2,2,200);

y1=x.^2;

z1=0*x;z2=4-y1;

V 10: z = 0,y = 0,y = x,x + z = 4

clc

clf

% ve mat z=0 va z=4-x

x=linspace(0,4,200);

y=linspace(0,2,200);

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

z1=0*x;z2=4-x;

z1(i,j)=NaN;z2(i,j)=NaN;

end

end

% ve mat y=0 va y=sqrt(x)

x=linspace(0,4,200);

z=linspace(0,4,200);

[x z]=meshgrid(x,z);

y1=0*x;

y2=sqrt(x);

y1(i,j)=NaN;y2(i,j)=NaN;

end

% ve giao tuyen

x=linspace(0,4,200);

y1=sqrt(x);

z1=0*x;z2=4-x;

V 11: x = 0,y = 0,z = 0,y2 = 2z,2x + 3y = 12

clf

% ve mat z=0, 2z=y^2

x=linspace(0,6,200);

y=linspace(0,12/3,200);

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

z1=0*x;z2=y.^2/2;

z1(i,j)=NaN;z2(i,j)=NaN;

end

end

hold on;

% ve mat y=0 va y=(12-2*x)/3

x=linspace(0,6,200);

z=linspace(0,8,200);

[x z]=meshgrid(x,z);

y=(12-2.*x)/3;

y(i,j)=NaN;

end

% ve giao tuyen

x=linspace(0,6,200);

x1=0*x;

y1=(12-2*x)/3;y2=linspace(0,4,200);

z1=y1.^2/2;z2=y2.^2/2;

V 12:

% ve mat gioi han boi y^2+z^2=2*x, x^2+y^2+z^2=5/4

clc

clf

grid on

% ve mat x^2+y^2+z^2=5/4

phi=linspace(0,2*pi,1000);

theta=linspace(0,pi,1000);

[p ,t]=meshgrid(phi,theta);

x=(sqrt(5)/2)*sin(t).*cos(p);

y=(sqrt(5)/2)*sin(t).*sin(p);

z=(sqrt(5)/2)*cos(t);

z(i,j)=NaN;

end

% ve mat y^2+z^2=2*x

z=linspace(-2,2,1000);

y=linspace(-2,2,1000);

[y, z]=meshgrid(y,z);

x =(y.^2+z.^2)/2;

x(i,j)=NaN;

end

% ve duong giao tuyen

phi=linspace(0,2*pi,1000);

z=(1).*cos(phi);

y=(1).*sin(phi);

x=1/2+0.*phi;

V 13: x2 + y2 = 4,x + y + z = 2,z = 0

%Vat the gioi han boi x^2+y^2=4, x+y+z=2,z=0

clc

clf

% ve mat x^2+y^2=4;

x=linspace(-2,2,500);

z=linspace(0,2+2*sqrt(2),500);

[x z]=meshgrid(x,z);

y1=sqrt(4-x.^2);

y1(i,j)=NaN;

end

y2=-sqrt(4-x.^2);

for j=1:length(z)

y2(i,j)=NaN;

end

%ve mat z=0 va z=2-x-y

x=linspace(-2,2,500);

y=linspace(-2,2,500);

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

z1=0*x;z2=2-x-y;

z1(i,j)=NaN;z2(i,j)=NaN;

end

end

% ve giao tuyen

t=linspace(pi/2,2*pi,30);

V 14: z = −px2 + y2,z = 6 − x2 − y2

%vat the gioi han boi z=-sqrt(x^2+y^2), z=6-x^2-y^2

clc

clf

% ve mat z=6-x^2-y^2

x=linspace(-3,3,500);

y=linspace(-3,3,500);

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

z1=6-x.^2-y.^2; z2=-sqrt(x.^2+y.^2);

z2(i,j)=NaN;z1(i,j)=NaN;

end

%ve duong giao tuyen

phi=linspace(0,2*pi,500);

x = 3*cos(phi);

y = 3*sin(phi);

z = -3+0.*phi;

V 15: x2 + 4y2 = 4,z = 0,x + z = 2

%Vat the gioi han boi x^2+4*y^2=4, x+z=2,z=0

clc

clf

% ve mat x^2+4y^2=4;

x=linspace(-2,2,200);

z=linspace(0,4,200);

[x z]=meshgrid(x,z);

y1=sqrt(4-x.^2)/2;y2=-sqrt(4-x.^2)/2;

y1(i,j)=NaN;y2(i,j)=NaN;

end

%ve mat z=0 va z=2-x

x=linspace(-2,2,200);

y=linspace(-1,1,200);

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

z1=0*x;z2=2-x;

z1(i,j)=NaN;z2(i,j)=NaN;

end

end

% ve giao tuyen

t=linspace(0,2*pi,100);

V 16: x = 0,y = 0,3x + y = 3,3x + 2y = 6,x + y + z = 3

√

%Vat the gioi han boi x=0, y=0, 3*x+y=3, 3*x+2*y=6, x+y+z=3

clc

clf

% ve mat y=0, 3*x+y=3, 3*x+2*y=6

x=linspace(0,2,500);

z=linspace(0,4,500);

[x, z]=meshgrid(x,z);

y1=0.*x; y2=3-3.*x; y3=(6-3.*x)/2;

y1(i,j)=NaN;

y2(i,j)=NaN;

y3(i,j)=NaN;

end

% ve mat x=0

z=linspace(0,4,500); x=linspace(0,2,500);

[x, z]=meshgrid(x,z);

y2=3-3.*x; x1=0.*x;

y2(i,j)=NaN;

end

% ve mat x+y+z=3

x=linspace(0,2,500);y=linspace(0,3,500);

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

z1=3-x-y; z2=0.*x;

z1(i,j)=NaN;z2(i,j)=NaN;

end

V 17: x2 + y2 + z2 = 4,y = x,y = x 3 phần ứng với x ≥ 0,y ≥ 0

%Vat the gioi han boi x^2+y^2+x^2=4, y=x,y=sqrt(3).x

clc

clf

% ve mat y=x,y=sqrt(3)*x

x=linspace(0,2,200);

z=linspace(-2,2,200);

[x z]=meshgrid(x,z);

y1(i,j)=NaN;

end

y2=sqrt(3)*x;

y2(i,j)=NaN;

end

%ve mat x^2+y^2+z^2=4

phi=linspace(pi/4,pi/3,30);

theta=linspace(0,pi,30);

[p t]=meshgrid(phi,theta);

x=2*sin(t).*cos(p);

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

z=2*cos(t);

% ve giao tuyen

x1=linspace(0,sqrt(2),200);x2=linspace(0,1,200);

y1=x1;y2=sqrt(3)*x2

z1=sqrt(4-x1.^2-y1.^2);z2=sqrt(4-x2.^2-y2.^2);z3=-sqrt(4-x1.^2-y1.^2);z4=-sqrt(4-x2.^2-y2.^2);

%Vat the gioi han boi z=0,z=4-x^2-y^2;y=x,y=x/sqrt(3)

clc

clf

% ve mat y=x,y=x/sqrt(3)

x=linspace(0,2,300);

z=linspace(0,4,300);

[x z]=meshgrid(x,z);

y1=x;

y1(i,j)=NaN;

end

y2=x/sqrt(3);

for j=1:length(z)

y2(i,j)=NaN;

end

%ve mat z=4-x^2+y^2

x=linspace(0,2,300);

y=linspace(0,2,300);

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

z1=0*x;

z1(i,j)=NaN;

end

z2=4-x.^2-y.^2;

z2(i,j)=NaN;

end

% ve giao tuyen

x1=linspace(0,sqrt(2),200);x2=linspace(0,sqrt(3),200);

y1=x1;y2=x2/sqrt(3);

z1=4-x1.^2-y1.^2;z2=4-x2.^2-y2.^2;

p=linspace(pi/6,pi/4,30);

V 19: z = 0,z = x2,x2 + y2 = 4

% vat the gioi han boi z = 0, z = x2, x2 + y2 = 4

clc

clf

% ve mat x^2+y^2<=1

r=linspace(0,4,30);

phi=linspace(0,2*pi,30);

[r, phi]= meshgrid(r,phi);

x = 2*cos(phi);

y = 2*sin(phi);

z = r ;

% ve? z=x^2

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

z = x.^2;

z(i,j)=NaN;

end

V 20: 1 ≤ x2 + y2 + z2 ≤ 4,x ≥ 0

% vat gioi han boi 1<=x^2+y^2+z^2<=4,x>=0

clc

clf

phi=linspace(0,2*pi,30);

theta=linspace(0,pi/2,30);

[p t]=meshgrid(phi,theta);

% ve mat x^2+y^2+z^2=4

z=2*sin(t).*cos(p);

x=2*sin(t).*sin(p);

y=2*cos(t);

%x^2+y^2+z^2=1

z=sin(t).*cos(p);

x=sin(t).*sin(p);

y=cos(t);

% ve mat day yz

phi=linspace(0,2*pi,30);

r=linspace(1,2,30);

[phi r]=meshgrid(phi,r);

x=r.*cos(phi);

z=r.*sin(phi);

y=0*phi;

% ve giao tuyen

phi=linspace(0,2*pi,30);

V 21: x2 + y2 + z2 ≤ 4,x + y le0

V 22: x = 0,y = 0,z = 0,y = 3,x + z = 2

% vat gioi han boi x=0,y=0,z=0,y=3,x+z=2;

clc

clf

%Ve mat z=0,z=2-x

x=linspace(0,2,200);

y=linspace(0,3,200);

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

z1=0*x;z2=2-x;

% ve mat y=3;y=0;x=0

x=linspace(0,2,200);

z=linspace(0,2,200);

[x z]=meshgrid(x,z);

y1=3+0*x;y2=0*x;

y1(i,j)=NaN;y2(i,j)=NaN;

end

% ve mat x=0

y=linspace(0,3,200);

z=linspace(0,2,200);

[y z]=meshgrid(y,z);

x=0*y

% ve giao tuyen

V 23: 0 ≤ z ≤p2 − x2 − y2,x2 + y2 ≥ 1

clc

clf

%Ve nua cau z=sqrt(2-x^2+y^2),z=0

phi=linspace(0,2*pi,50);

r=linspace(0,1,50);

[r ph]=meshgrid(r,phi);

% Phan mat cau

x=r.*cos(ph);

y=r.*sin(ph);

z1=sqrt(2-x.^2-y.^2);z2=0*x;

% phan mat tru

phi=linspace(0,2*pi,50);

z=linspace(0,1,50);

[phi z]=meshgrid(phi,z);

x=cos(phi);y=sin(phi);

% ve giao tuyen

phi=linspace(0,2*pi,50);

V 24: x2 + z2 = 1,x2 + y2 = 1

%Vat the gioi han boi x^2+y^2=1, x^2+z^2=1

clc

clf

r=linspace(0,1,30);phi=linspace(0,2*pi,30);

[r phi]=meshgrid(r,phi);

%Mat x^2+z^2=1

x=r.*cos(phi);y=r.*sin(phi);

z1=sqrt(1-x.^2);z2=-sqrt(1-x.^2);

%Mat x^2+y^2=1

x=r.*cos(phi);z=r.*sin(phi);

y1=sqrt(1-x.^2);y2=-sqrt(1-x.^2);

% ve duong giao tuyen

t=linspace(0,2*pi,50);

V 25: x2 + z2 = 1,x2 + z2 = 4,y = −1,y = 3

% ve x2 + z2 = 1, x2 + z2 = 4, y = ?1, y = 3

clc

clf

% ve mat x^2+y^2=1

r=linspace(-1,3,30);

phi=linspace(0,2*pi,30);

[r, phi]= meshgrid(r,phi);

x = cos(phi);

z = sin(phi);

y = r ;

% ve mat x^2+y^2=1

r=linspace(-1,3,30);

phi=linspace(0,2*pi,30);

[r, phi]= meshgrid(r,phi);

x = 2*cos(phi);

z = 2*sin(phi);

y = r ;

% y=-1;y=3

% y=3

x=linspace(-2,2,500);z=linspace(-2,2,500);

[x, z]=meshgrid(x,z);

y=3+0.*x;y1=-1+0.*x;

y(i,j)=NaN;y1(i,j)=NaN;

end