Recent content by forget_f1

What is the derivative of U(X(t),t)? Is it Ut(Xt(t),t)?

Ok, got it. I forgot that then I need to evaluate along the boundaries of the region.

I have u(x,t)=-2xt-x^2 find maximum in region {-2 ≤ x ≤ 2 , 0 ≤ t ≤ 1} I believe to find the critical point first I have to take the partial derivative with respect to x and t and equate to zero. Thus Ux=-2t-2x = 0 Ut=-2x = 0 Thus the only critcal point I find is x=0, t=0. But the...

Taking A={0, 1/n + 1/m | n,m >=1 in N}. Thus the limit points are 1/n which are countable. Since the set is closed and bouned then it is compact. (theorem) Or It can prove by definition that A is compact, which is what I did since I forgot to use the theorem above which would have made life...

Note: A single point has no limit point, since a limit point of a set A is a point p such that for any neighborhood of p (ie Ball(p,r) , where p is the origin and r=radius can take any value >0) there exists a q≠p where q belongs in B(p,r) and q belongs to A.

for example {(0, 1/n) : n=1,2,3,...} is compact but the only limit point is 0. Still I need countable limit points.

Construct a compact set of real numbers whose limit points form a countable set.

Problem solved, thanks for taking the time to look at it

u(a,0)=φ(a) and Ub(a,0)=ψ(a) These are the initial conditions that would satisfy the explicit solution, in terms of a and b. φ and ψ ar functions. Now what functions they are, that is where I need help, if I need them at all that is.

solve Uxx-3Uxt-4Utt=0 (hyperbolic) help! solve Uxx-3Uxt-4Utt=0 with u(x,0)=x^2 and Ut(x,0)=e^x I know that this is hyperbolic since D=(-1.5)^2+4 >0 so I have to transform the variables x and t linearly to obtain the wave equation of the form (Utt-c^2Uxx=0). The above equation is equivalent...

If both u(x,0)=φ(x) and Ut(x,0)=ψ(x) are odd functions of x, then the solution to wave equation u(x,t) is odd for all t. odd means f(x)=- f(-x) the general solution is u(x,t)=(1/2)*[φ(x+ct)+φ(x-ct)]+(1/2c)*(integral ψ(s)ds, from x-ct to x+ct) can anyone help?

Hi, I have a question If X1,X2,...,Xn are independent random variables having chi-square distribution witn v=1 and Yn=X1+X2+...+Xn, then the limiting distribution of (Yn/n) - 1 Z= --------------- as n->infinity is the standard normal distribution. sqrt(2/n)...