CoCalc -- week7.sagews

Week 7 of Math 211

Project: Math 211

Views: ¹⁰⁰

var('x y z')

(x, y, z)

f(x,y) = x^2+y^2-x*y;
p1 = contour_plot(f(x,y),(x,-4,4),(y,-4,4),contours=15,fill=False); p1.show();
plot3d(f(x,y),(x,-4,4),(y,-4,4))

3D rendering not yet implemented

g(x,y) = cos(x)*y-cos(y)*x; b=2*pi; c=20;
p2 = contour_plot(g(x,y),(x,-b,b),(y,-b,b),contours=c,fill=False); p2.show();
plot3d(g(x,y),(x,-b,b),(y,-b,b),plot_points=300)

3D rendering not yet implemented

j(x,y)=cos(x*y);
p = contour_plot(j(x,y), (x, -10, 5), (y, -5, 5), fill=False, contours=8, plot_points=150); p.show();
plot3d(j(x,y),(x, -10, 5), (y, -5, 5),plot_points=300)

3D rendering not yet implemented

h(x,y) = x^2-y^2; b=2; c=20;
p = contour_plot(h(x,y),(x,-b,b),(y,-b,b),contours=c,fill=False); p.show();
plot3d(h(x,y),(x,-b,b),(y,-b,b))

3D rendering not yet implemented

i(x,y) = x*y; b=2; c=20;
p = contour_plot(i(x,y),(x,-b,b),(y,-b,b),contours=c,fill=False); p.show();
plot3d(i(x,y),(x,-b,b),(y,-b,b))

3D rendering not yet implemented

k(x,y) = sin(x^2+y^2); b=pi; c=6;
p = contour_plot(k(x,y),(x,-b,b),(y,-b,b),contours=c,fill=False,plot_points=150); p.show();
plot3d(k(x,y),(x,-b,b),(y,-b,b),plot_points=300)

3D rendering not yet implemented

m(x,y) = x^3-3*x*y^2; b=2; c=20;
p = contour_plot(m(x,y),(x,-b,b),(y,-b,b),contours=c,fill=False); p.show();
plot3d(m(x,y),(x,-b,b),(y,-b,b))

3D rendering not yet implemented

l(x,y) = sin(x)^3-3*sin(x)*y^2; b=3; c=25;
p = contour_plot(l(x,y),(x,-b,b),(y,-2,2),contours=[0,0.25,0.5,1,2,3,4,5,6,7,8,9,-0.25,-0.5,-1,-2,-3,-4,-5,-6,-7,-8,-9],fill=False); p.show();
plot3d(l(x,y),(x,-b,b),(y,-2,2),plot_points=300)

3D rendering not yet implemented

E = implicit_plot3d(3*x^2+2*y^2+6*z^2==6, (x, -2, 2), (y, -2,2), (z, -2,2));
A = arrow((1,1/2,sqrt(5/12)),(1+6,1/2+2,sqrt(5/12)+12*sqrt(5/12)));
P = implicit_plot3d(6*(x-1)+2*(y-1/2)+12*sqrt(5/12)*(z-sqrt(5/12))==0,(x,-2,2),(y,-2,2),(z,-2,2),color='red',opacity=0.5);
(E+A+P).show()

3D rendering not yet implemented

kplot = plot3d(sin(x^2+y^2),(x,-pi,pi),(y,-pi,pi));
T2kplot = plot3d(x^2+y^2,(x,-pi,pi),(y,-pi,pi));
(kplot+T2kplot).show()

3D rendering not yet implemented


︠fabd2108-f668-4762-849f-f5df2257c442︠
k(x,y) = sin(x^2+y^2);
T6k(x,y) = k.taylor((x,0),(y,0),6); T6k;
kplot = plot3d(k,(x,-1.3,1.3),(y,-1.3,1.3),opacity=1);
T6kplot = plot3d(T6k,(x,-1.3,1.3),(y,-1.3,1.3),opacity=0.6,color='green');
(kplot+T6kplot).show()

(x, y) |--> -1/6*x^6 - 1/2*x^4*y^2 - 1/2*x^2*y^4 - 1/6*y^6 + x^2 + y^2

3D rendering not yet implemented

T14k(x,y) = k.taylor((x,0),(y,0),14);
kplot = plot3d(k,(x,-1.5,1.5),(y,-1.5,1.5),opacity=1);
T14kplot = plot3d(T14k,(x,-1.5,1.5),(y,-1.5,1.5),opacity=0.6,color='purple');
(kplot+T14kplot).show()

3D rendering not yet implemented

T32k(x,y) = k.taylor((x,0),(y,0),32); T32k;
b=2;
kplot = plot3d(k,(x,-b,b),(y,-b,b),opacity=1);
T32kplot = plot3d(T32k,(x,-b,b),(y,-b,b),opacity=0.6,color='purple');
(kplot+T32kplot).show()

(x, y) |--> -1/1307674368000*x^30 - 1/87178291200*x^28*y^2 - 1/12454041600*x^26*y^4 - 1/2874009600*x^24*y^6 - 1/958003200*x^22*y^8 - 1/435456000*x^20*y^10 - 1/261273600*x^18*y^12 - 1/203212800*x^16*y^14 - 1/203212800*x^14*y^16 - 1/261273600*x^12*y^18 - 1/435456000*x^10*y^20 - 1/958003200*x^8*y^22 - 1/2874009600*x^6*y^24 - 1/12454041600*x^4*y^26 - 1/87178291200*x^2*y^28 - 1/1307674368000*y^30 + 1/6227020800*x^26 + 1/479001600*x^24*y^2 + 1/79833600*x^22*y^4 + 1/21772800*x^20*y^6 + 1/8709120*x^18*y^8 + 1/4838400*x^16*y^10 + 1/3628800*x^14*y^12 + 1/3628800*x^12*y^14 + 1/4838400*x^10*y^16 + 1/8709120*x^8*y^18 + 1/21772800*x^6*y^20 + 1/79833600*x^4*y^22 + 1/479001600*x^2*y^24 + 1/6227020800*y^26 - 1/39916800*x^22 - 1/3628800*x^20*y^2 - 1/725760*x^18*y^4 - 1/241920*x^16*y^6 - 1/120960*x^14*y^8 - 1/86400*x^12*y^10 - 1/86400*x^10*y^12 - 1/120960*x^8*y^14 - 1/241920*x^6*y^16 - 1/725760*x^4*y^18 - 1/3628800*x^2*y^20 - 1/39916800*y^22 + 1/362880*x^18 + 1/40320*x^16*y^2 + 1/10080*x^14*y^4 + 1/4320*x^12*y^6 + 1/2880*x^10*y^8 + 1/2880*x^8*y^10 + 1/4320*x^6*y^12 + 1/10080*x^4*y^14 + 1/40320*x^2*y^16 + 1/362880*y^18 - 1/5040*x^14 - 1/720*x^12*y^2 - 1/240*x^10*y^4 - 1/144*x^8*y^6 - 1/144*x^6*y^8 - 1/240*x^4*y^10 - 1/720*x^2*y^12 - 1/5040*y^14 + 1/120*x^10 + 1/24*x^8*y^2 + 1/12*x^6*y^4 + 1/12*x^4*y^6 + 1/24*x^2*y^8 + 1/120*y^10 - 1/6*x^6 - 1/2*x^4*y^2 - 1/2*x^2*y^4 - 1/6*y^6 + x^2 + y^2

3D rendering not yet implemented

var('u v')

(u, v)

G(u,v) = u*exp(v)

G.taylor((u,0),(v,0),2)

(u, v) |--> u*v + u

Gplot = plot3d(G(u,v),(u,-1,1),(v,-1,1));

GT2plot=plot3d(
u*v+u,(u,-1,1),(v,-1,1),color='red',opacity=0.6);

(Gplot+GT2plot).show()

3D rendering not yet implemented