Question

http://math.stackexchange.com/questions/923137/find-a-solution-to-laplaces-equation-that-satisfies-polar-coordinates-and-show

Answer 1

@dan815

Answer 2

7b.... stuck...

Answer 3

:( ... where did everyone go?

Answer 4

@Kainui

Answer 5

he ain't here foo

Answer 6

@satellite73

Answer 7

@tkhunny

Answer 8

I'm gone sry gl

Answer 9

@kainui what do you mean you're gone? as in afk?

Answer 10

can you give me a hint on the second one.. besides plotting on the x,y plane as opposed to x y z since we're not in 3d. Like how do I plot the points? I know that the perpendicular lines intersect where as parallel lines don't.

Answer 11

so any solution of the equation ... has at least one point in common.

Answer 12

I can't read all that, I barely know how to read. Ask a more succinct question. Ain't got time for all that.

Answer 13

and on top of that we need to satisfy the bc... WHAT! hold on. click on the link to see it. XD

Answer 14

You want to know how to plot a graph z(x,y)? I can show you that.

Answer 15

I have done it in Latex on stackexchange XD. I just post the link here because it is too hard here.

Answer 16

No I looked lol. I literally am not reading. tl;dr is my soul's motto

Answer 17

it's the song of my soul, I have to be true to myself, and right now that means being a lazy turd.

Answer 18

ok how about.. we plot whatever I got from a and at least one of the equations from b. HOw's that? And it needs to satisfy the boundary conditions...which means I have to be inside the circle when r = 1 so that's pretty small.

Answer 19

\[u(x,y) = \frac{1}{2}x^2+xy-\frac{1}{2}y^2\]
from A


THIS IS B which is half of A

\[\frac{1}{4}x^2+\frac{1}{2}xy-\frac{1}{4}y^2\]

Answer 20

and here's another B which is DOUBLE THE A
\[x^2+2xy-y^2\]

Answer 21

now how to do I plot those bad boys?

Answer 22

xy-plane in a pair of perpendicular lines through (0,0), Ok so any solution must past (0,0)... alright... I see that already if I have x = 0 and y =0 but now what?

Answer 23

set x=0 and draw a curve on the yz-plane then set y=0 and draw a curve on the xz plane. You should be able to sort of figure out the rest maybe?

Answer 24

It should look like a saddle kind of mabob I guess. I don't know, is that what you're looking for?

Answer 25

what
!

Answer 26

why are we involving the z plane? We just have 2 variables x and y

Answer 27

x^2+y^2 = 1