cp /math/calclab/MA1024/Coords_start.mws ~/My_Documents

You can copy the worksheet now, but you should read through the lab
before you load it into Maple. Once you have read to the exercises,
start up Maple, load
the worksheet `Coords_start.mws`, and go through it
carefully. Then you can start working on the exercises.

To change to cylindrical coordinates from rectangular coordinates use the conversion:

To change to spherical coordinates from rectangular coordinates use the conversion:

- Given the rectangular equation for a circular paraboloid:

**A)**- Graph the equation using the domain values of , and the range values .
**B)**- Write the equation in cylindrical coordinates and then graph the equation.
**C)**- Write the equation in spherical coordinates and graph it.
**D)**- Looking at the three equations, which coordinates appears to give the simplest equation?

- Given the equation of a torus (a.k.a. donut):

**A)**- Graph the equation using the domain values , and the range values .
**B)**- Write the equation in cylindrical coordinates and graph it.
**C)**- Write the equation in spherical coordinates (hint: use the
`factor`command outside the`simplify`command to simplify even more). Then graph your equation. **D)**- Looking at the three equations, which coordinates appear to give the simplest equation?

- A problem from your text describes a bumpy sphere or an exaggerated representation of waves on the surface of a very small planet that is covered by a very deep ocean. Such a bumpy or wrinkly sphere may also be used to model tumors. Use Maple to plot the spherical-coordinate surface

with values of the positive number and and the positive integers and given below. How does the surface depend on the value of each of these four parameters?**A)**- , , ,
**B)**- , , ,
**C)**- , , ,
**D)**- , , ,
**E)**- , , ,
**F)**- , , ,

2006-04-19