I. Sketch the figure for the following vector functions. Propose the values for u and v and adjust the graphic to get a good
view of the functions. Include the required MatLab code for each graphic.
1) r(u, v) = u cos vi+usin vj + vk
2) r(u, v) = u cos vi + usin vj + sinu k
3) r(u, v) = sin vi + cos u sin 2v j + sin u sin 2v k
II. Sketch the vector field for the following vector functions. Consider that -3?x?3 and
-3? y ?3. Adjust the graphics to get a good view of the functions. Include the required MatLab code for each graphic.
1) F(x, y) = (cos (x + y), x)
2) F(x,y) = (y,x - y)
3) F(x,y) = (y, y + 2)
III. Given the following scalar functions, sketch their gradient vector field. Consider that -4 ? x ? 4 and -4 ? y ? 4.
Adjust the graphics to get a good view of the fields. Include the required MatLab code for each graphic.
1) f(x, y) = x(x + y)
2) f(x,y) = (x + y)²
3) f(x, y) = sin\sqrt{x^2 + y^2}