Westminster College- Math 203 demos
var('x, y, z')
F⃗(x,y)=<−y,x>\vec{F}(x, y) = \left< -y, x \right>F(x,y)=⟨−y,x⟩
plot_vector_field((-y, x), (x, -2, 2), (y, -2, 2), aspect_ratio = 1)
F⃗(x,y)=<y,(cosx−2)sinx>\vec{F}(x, y) = \left< y, \left(\cos{x} - 2\right) \sin{x} \right>F(x,y)=⟨y,(cosx−2)sinx⟩
plot_vector_field(( y, (cos(x) - 2) * sin(x)), (x, -2*pi, 2*pi), (y, -2*pi, 2*pi))
h(x,y)=x2y−y3h(x,y) = x^{2}y - y^{3}h(x,y)=x2y−y3
F⃗(x,y)=∇h\vec{F}(x, y) = \nabla hF(x,y)=∇h
h = x^2 * y - y^3 plot_vector_field(h.gradient(), (x, -4, 4), (y, -4, 4), aspect_ratio = 1) + contour_plot(h, (x, -4, 4), (y, -4, 4), fill = false, aspect_ratio = 1)
F⃗(x,y,z)=<xcosz,−ycosz,sinz>\vec{F}(x, y, z) = \left< x\cos{z}, -y\cos{z}, \sin{z} \right>F(x,y,z)=⟨xcosz,−ycosz,sinz⟩
plot_vector_field3d((x*cos(z),-y*cos(z),sin(z)), (x,-5,5), (y,-5,5), (z,0,2*pi), plot_points=[10,10,10])
F⃗(x,y,z)=<x,1,1>\vec{F}(x, y, z) = \left< x, 1, 1 \right>F(x,y,z)=⟨x,1,1⟩
plot_vector_field3d((x, 1, 1), (x, -1, 1), (y, -1, 1), (z, -1, 1), plot_points=[5,5,5], apsect_ratio = 1)
f(x,y,z)=1x2+y2+z2f(x, y, z)= \frac{1}{\sqrt{x^{2} + y^{2} + z^{2}}}f(x,y,z)=x2+y2+z21
F⃗(x,y,z)=∇f\vec{F}(x, y, z) = \nabla fF(x,y,z)=∇f
f = 1/(sqrt(x^2 + y^2 + z^2)) plot_vector_field3d(f.gradient(), (x, -2, 2), (y, -2, 2), (z, -2, 2), plot_points = 10)
