CoCalc Shared Filessupport / 2015-02-06-190915-3d.sagews
Authors: Harald Schilly, ℏal Snyder, William A. Stein
Description: Examples for support purposes.
 Plot vector field $\vec{F}(x,y,z)$ $\vec{i} +$ $\vec{j} +$ $\vec{k}$ Box: $\leq x \leq$ $,\quad$ $\leq y \leq$ $,\quad$ $\leq z \leq$ Plot parametric curve $C$ given by $\vec{r}(t)$ for $\leq t \leq$ $\vec{i} +$ $\vec{j} +$ $\vec{k}$ Plot parametric surface $S$ given by $\vec{r}(u, v)$ for $\leq u \leq$ $,\quad$ $\leq v \leq$ $\vec{i} +$ $\vec{j} +$ $\vec{k}$
Axes
Origin
Unit normals to $S$
Try to compute flux/circulation

## Notes

• If you have vanishing denominators and things don't work, try to change $xyz$-limits a little, e.g. $\vec{F} = (1/x, 0, 0)$ does not work for $x$ limits $[-1,1]$, but $[-1.1, 1]$ is OK.
• To work with 2D curves and fields (and to compute the flux across $C$), set $z$-components to zero.