Posts by musicmental85

musicmental85 · Help Me !

Hi, I'm just working through examples for revision and I've come across one that I've worked but not sure if its correct. If anyone could check it would be much appreciated:

Expand 1/z in power series about z=1

Ok you can write 1/z as 1/[1+(z-1)] in this case since expansion is about 1. Then: 1/[1+(z-1)= 1/(1+(z-1)/1)=1[1-(z-1)+(z-1)^2-+....]
oo
=SUM (-1)^k(z-1)^k
k=0

Now is this sufficient for the question or have I left anything vitally important out. I am not great at the subject so I need to make sure anything I'm using as study exercises is working out correctly!

musicmental85 · Help Me !

Hi, I'm having trouble with the following problem
I have lots of theory to work off but no examples so I cant figure out
what Im doing

Consider a unit-radius cylinder with centre running along the x-axis
a) write down a coordinate patch which covers this cylinder
b) compute the shape operater
c) find the principal curvatures and vectors
d) find the Gaussian and mean curvatures

I know one of the coordinate patches we have studied is the mange
patch. How do I know if that is a viable option here?
If it isn't I have a lemma that states for a coordinate patch PHI of a
function f:M->R we have PHI_u(f)=df/du and PHI_v(f)=df/du. Does this
mean I need to write a function for the cylinder and differentiate it
to get a patch?
The shape operater is S_p(v)=-Δ_v. n where n(p)=PHI_u(p) X
PHI_v(p)/||PHI_u(p) X PHI_v(p) but as I cannot work out what the PHI
is supposed to be I am completely stuck at the moment and can work no
further

Math Is Fun Forum

#1 Help Me ! » Quick complex analysis question » 2007-11-18 08:46:06

#2 Help Me ! » re: Differential Geometry Question » 2007-11-18 03:21:43

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