Recent content by talolard

Homework Statement Solve using separation of variables utt = uxx+aux u(0,t)=u(1,t)=0 u(x,0)=f(x) ut=g(x) The Attempt at a Solution if not for the ux I'd set U=XT such that X''T=TX'' and using initial conditions get a solution. In my case I get T''X=T(aX'+X'') which is...

Do you think you could write the original equation as (A-3I)(A-8I). If you could justify writing it out like that, and you looked at the determinant of that expression, what would you find out?

Homework Statement given f \in C^2 such that f(a)=f'(a)=0 ^f''(a)\neq 0 prove that the modified Newton method x_{n+1}=x_n-2 \frac{f(x_n){f'(x_n)} coverges with order two. Homework Equations if g(x) is an iterative function such that the first m derivatives of g at a are zero and...

Homework Statement For what real values of the parameters a,b,c,d does the functiob f(x,y)=ax^3+by^3+cx^4+dy^4-(x+y)^5 have a local minimum at (0,0)Homework Equations I calculated the gradient at (0,0) and it is always zero regardless of parameters. The problem is that the Hessian matrix is...

yy''=y'^{2}-y'^{3} Solution Set z(y)=y' then \frac{\partial z}{\partial y}=\frac{\partial z}{\partial x}\cdot\frac{\partial x}{\partial y}=y''\cdot\frac{1}{y'}=y''\frac{1}{z}\rightarrow z\cdot z'=y'' Plugging this in and assuming z\neq0,1 yz\cdot...

I wish I had asked sooner. Thanks Tal

You are given that u is indendent of v1,v2,...,vk. What does this imply about the intersection of the sapces spanned by {v1,v2...,vk} and {u}?

Homework Statement yy''=y'^{2}-y'^{3} I'm quite sure I got lost somewhere. Can anyone show me where? Thanks Set z(y)=y' then \frac{\partial z}{\partial y}=y''\cdot y'=zy'' so y''=\frac{z'}{z} Plugging this in y\frac{z'}{z}=z^{2}\left(1-z\right) and so...

Great! Thanks

Homework Statement if p is a prime of the form p=4k+1 and g is a primitive root of p, show that -g is a primitive root. I'm not sure if this is a decent proof or not. My final argument looks suspicious. Any thoughts? Thanks Tal The Attempt at a Solution First, notive that...

Homework Statement How many solutions does x^{2}\equiv9 mod 7700 have? So my question is if this solution is "legitimate" Solution First notice that 7700=7\cdot11\cdot2^{2}\cdot5^{2} Thus we must solve the system \begin{cases} x^{2}\equiv2 & \left(7\right)\\ x^{2}\equiv9 & \left(11\right)\\...

Cool. You passed the point along, thanks! Tal

Thanks for the responses. Dick, I tried the approach that you proposed and I solved the problem but I think i used icystrikes argument. Could you take a look and let me know if I could have used a more number theoritic arguemnt? Thanks Tal By eulers theorem, the inverse of an element k is...

Maybe instead of a nudge i need a good shove. Here's what I've gotten So A=\underset{i=1}{\overset{p-1}{\sum}}\frac{\left(p-1\right)!}{i} which is an integer. Assume that A\equiv aMod(p) A=\underset{i=1}{\overset{p-1}{\sum}}\frac{\left(p-1\right)!}{i}=\underset{\begin{array}{c}...

Homework Statement if p is prime, prove that p divides A, where A satisfis 1+\frac{1}{2}+...+\frac{1}{p-1}=\frac{A}{\left(p-1\right)!} Homework Equations The chinese remainder theorem? Eulers theorem? The Attempt at a Solution So as the question marks imply, I'm at a loss as to...