2126.sagews

# Exercise 1 (16.1 #28)
# ---------------------

var('x,y')
f = sin(x+y)
cplot = contour_plot(f,(x,-pi,pi),(y,-pi,pi),fill=False,cmap=['red'])
gplot = plot_vector_field(f.gradient(),(x,-pi,pi),(y,-pi,pi))
(cplot+gplot).show(aspect_ratio=1)

# Exercise 2 (16.1 #24)
# ---------------------
# You should be able to see from this graph that
# the integral of F along r is positive.

var('t,z')
r = (1-t)*vector((1,0,0))+t*vector((3,4,2))
F = (y+z,x+z,x+y)
rplot = parametric_plot3d(r,(t,0,1),color='black')
Fplot = plot_vector_field3d(F,(x,-3,3),(y,-4,4),(z,-2,2),center_arrows=True)
rplot + Fplot + point3d((1,0,0)) + point3d((3,4,2))

# Exercise 3 (16.6 #30)
# ---------------------
# I used y and theta as the two parameters.

var('theta')
parametric_plot3d(((4*y^2-y^4)*cos(theta), y, (4*y^2-y^4)*sin(theta)),\
  (y,-2,2),(theta,0,2*pi),rgbcolor=(0.5,1,0.5))