I am looking at various ways to generate surfaces in a cylindrical coordinate system. When using the cylinderplot( ) command, the default color scheme is acceptable. However, when using the implicitplot3d( ) command, the surface comes out very dark. I've played with a few color/lighting options, but I'm still not able to have the implicit3d plot look anything like the cylinder plot. Can someone suggest any color/lighting/shading options that might acheive this. My initial results are attached.

In trying to obtain the closed form for the nth partial sum for some fairly basic telescoping series. It appears that SumTools[DefiniteSum][Telescoping] works well for rational summands. However, when the same is attempted on summands that are not rational, it fails. Below are a few examples.

For a function of one variable, I use the map command quite a bit to evaluate the function at several values of the independent variable. For example,

f:=x->x^2:

xlist:=[1,2,3]:

map(f,xlist)

How may I do something similar for a function of two variables? For example,

f:=(x,y)->x^2+y^2:

xylist:=[[1,1],[1,2],[2,1],[2,2]]:

Can the map command be used to evaluate f at each ordered pair? Maybe I'm not even using the correct data structure. Thanks!

Can anyone explain the inconsistency in the following?

I am trying to get Maple to solve the following rather simple non-linear system.

x=k/4, y=-k/3, z=3k/8, 2x^2+3y^2+4z^2=9

However, solve({x=k/4,y=-k/3,z=3k/8,2x^2+3y^2+4z^2=9},{x,y,z,k}) does not give the expected results. Why not?