Recent content by shaner-baner

I am working with a system governed by the dynamics x'=Ax (prime denotes differentiation w/ respect to t) where x is a vector and A is a matrix. Given the way our data is collected we can't measure x directly but rather a scalar function D(x)=(sum of the components of the vector x). My question...

You could put the system in a more standard form. i.e. replace the occurance of dx/dv in the second equation with a*X, not to mention that I think you can probably solve it out by hand because the system is "triangular"

I have read that in classical physics, symmetry under tranlsation implies conservation of linear momentum, and that symmetry under rotation implies conservation of angular momentum. Could you guys give me a brief explanation, or if the explanation is not brief Point me towards a good website...

After looking on the internet a little bit I found the so called cordic method. It's been around for 40 years or so and was used on the first hand calculators. Check out the website: www.emesystems.com/BS2mathC.htm

I know there are tons of ways to approximate a sine function, the most obvious being taylor series and numerical solutions of y''+y=0, but does anyone know how the "average" scientific calculator does it? The "best" way I think is to first map the argument onto (0,2pi) and then take advantage of...

Here is a question one of my physics teachers mentiones a long time ago. Say you have a 10 ft. car and a 10 ft. barn, so the car will just barely fit. Now say the car saw traveling at an appreciable fraction of the speed of light, and you are traveling next to the car, on the line perendicular...

the polynomial has to be non-zero, let f(x,y)=(y-2x)*(y-2x-1); the matrix question asks about the largest possible submatrix of all ones given that the rows are all orthogonal with entries plus or minus 1. specifically for every axb submatrix of 1's, prove ab<=n (nxn matrix). The thing is any 2...

sorry, forgot the picture. Sorry it's not very "pretty"

triangles It is usually done without calculus. Just because it is used to define the derivatives of certain functions. If you compare the areas in the graph you can come up with the inequalities and use the squeeze theorem. Probably works out to the same formula above, but with a little more...

Richard Feynman, the late Nobel Laureate in physics, was once asked by a Caltech faculty member to explain why spin one-half particles obey Fermi Dirac statistics. Rising to the challenge, he said, "I'll prepare a freshman lecture on it." But a few days later he told the faculty member, "You...

pi approximations :bugeye: There is a mathematician named Borwien who has come up with some neat algorithms. The best one in terms of speed of convergence vs. complexity converge quartically, i.e. the number of correct digit roughly quadruples every iteration, furthermore the algorithms only...

One notable exception to teaching is crytography, but since most cryptographers work for the government, usually the government trains them. My own situation is like Fourier jr said. I'm only an undergraduate, but I just started a job programming in Matlab for a soil physicist. I get to use...

I'm not sure, but I think that fourth order equations are solvable with some weird equation like third order. In practice, you might start with the rational zeros test. What you do is: take all possible factors of 'e' and divide by all possible factors of 'a'. Then test these to see if they are...

Here is a fun problem, it's hard to write out clearly, but I'll try to do it w/ little confusion. Is it, or is it not true that (2^2^...^2)(n times)=(2^2^...^2)(n-1 times) mod n so for example, when n=2, 2^2=2 -> 4=2 mod 2.

In general, the answer is no. For example, let N(w)=1 , let D(u)=sin(u) , and call P(w)=y ,then your problem is: y*Sin(y)=1 , in this case P(w) will just equal a constant which is about as simple as a function can get, but it can't be found in closed form, which I would call unsolvable. (p.s...