Recent content by stanford1463

Bump...any suggestions?

Homework Statement Find all solutions of the IVP y'' + a(t)y' + b(t)y = 0, y(t0) = 0, y'(t0) = 0 where t0 is any fixed point on the t-axis and the coefficients are continuous. The Attempt at a Solution I know this has to do with the Existence and Uniqueness theorem. How would I apply...

These are what I think I'm not sure how to find graph solutions from my equation: y = 4 + Ce^(-.5t) Thanks for your help!

So...first interval - exponentially decreasing graph when y = R/k, it's a constant, straight line along R/k? and when y is big, it's increasing?

Homework Statement We have the ODE y' = -ky + R for a population y(t) where death rate exceeds birth rate, counteracted by a constant restocking rate. I'm assuming k is the decay constant and R is the restocking rate The population at time t0 = 0 is y0, and I have to find a formula for...

thanks! but is there anyway to bypass all this initial info? I just want to jump straight to learning about quandles and shadow colorings of knots :]

bump. specifically, I'm interested in the shape and origin of the Universe. how can knot theory explain the shape of the Universe? specific info would be helpful. thanks!

bump .

so what are some simple unsolved problems in astrophysics, that are interesting. could someone just list some topics out? I've been researching on the interwebz, but can't seem to find a topic that is interesting/simple. also are there any such topics related to Newtonian mechanics/electricity...

So I was looking at wikipedia. It seems that the unknot is simply a circle in R2? idk. what are some good websites/sources for learning a bit about algebraic topology? thanks!

bump pl0x ?

So I know that quandles are associated with knot theory, etc. but what are "shadow colorings" ? on a broader context, can someone please give me a simple definition of a "knot invariant" and a "quandle" ? and what does this have to do with "racks" ? sorry, all this esoteric language is...

Homework Statement Newspaper Boat- So I have been thinking about designing a newspaper boat out of pure entertainment. I want to build a boat out of shellack, tape, and newspaper, to maximize speed (to race people in swimming pools). considering i have some amount of these supplies, what...

alright thanks, any others? Bumpppppppppp

Ok I feel this is the best place to place this subject. Well, I have been interested in materials science and crystallography lately, especially the future applications of this. What are some future materials we could make from studying crystal growth? How could we go about accomplishing this...