Math Forum / Mathematics / Undergraduate Math / March 2006

1) Let u(x,y)=e^x * (x cosy - y siny)
a) Show that u is harmonic
b) Find a harmonic Conjugate v(x,y)
HOW DO I DO THIS??

What is the Laplace transform of d(t-2pi)cos(t)?
I'm having trouble with this one, if anyone knows it could you post details on how to do the transform?
Thank you

There is a lottery drawn on 1 through 20 numbers and six distinct balls
are randomly picked by the lottery every day. To play you need to buy a
ticket and select six numbers of your choice. An example ticket might
be [1,20,6,19,5,12] You can buy any number of tickets. If any three ...

Prove:
Suppose x as a real number, and
lim F(x) = t                     (x->infinite large)
then

I'm not shure I know exactly how to ask the following question so I ask for a little patience.
I'm learning variations and understand a topic
to a point. I solved quite a few problems but then I did a rather simple problem:
On the wall there are five hangers. In how many

FIRST:
I thought I knew what implicit function was untill I saw this definition in my textbook:
Explicit function is y = f(x) ... ok
Implicit function is f(x, y) = 0 ... what?!!!!

FIRST:
-- How do I find range and zeros for function
f(x) = sin[2x] - cos[2x]
I'd say finding local maximum and minimum

The math newsgroups as far as I'm concerned have only two uses:
1.  As a place for me to talk out ideas as I brainstorm.
2.  As a place to get criticism that hopefully occasionally is freaking
useful, so that I can weed out the errors, or learn something about why

I study the newsgroups as well, which is where we can get into
sociology, which isn't exactly math related, but I do see enough
instances of people deciding to ignore history that it's worth
mentioning that I didn't start the arguing on these newsgroups.

Find all odd prime numbers that divide the number
1^p-1 + 2^p-1 +.....+2004^p-1

please could someone help me with this question:
 Given a graph G of order n.
 Prove that the maximum size that G can have for it to
 be bipartite is : n(squared)/4

I can't convolve for beans.
can somebody walk me through convolving h(t) = u(t) - u(t-1)
and x(t) = u(t)?

I have several things I've managed in terms of mathematical discoveries
that have never been done before, and I've mentioned that before and
seen at times this bizarre reply where some person will talk about when
they were in high school--the U.S. equivalent of secondary school for

Hey guys Im sure this is easy but I cant figure it out for the life of
me?
How many integers between 1 and 999,999 contain each of the digits 1,2,
and 3 at least once?  I dont just need an answer I need to know hot to

there is an infinite grid of congruent squares. a person stands at any
vertex (say origin O). his step is equal to the side of each square say 1
unit and
he can walk only along the sides of the squares. now, if he must walk