Anyone know where I can find a good introduction to rindler coordinates and uniformly accelerating frames of reference in minkowski space? I have searched the internet but haven't been able to find anything too helpful. I would especially like a good derivation of the rindler coordinates. Thanks!
Homework Statement
I was just wondering how I would go about proving that the euclidean metric is always smaller than or equal to the taxicab metric for a given vector x in R^n. The result seems obvious but I am not sure how I would show this.
Homework Equations
The Attempt at a Solution
okay, once I have shown -x^2<=|F(x)|< x^2 then taking the limit as x tends to zero shows that F(x) is zero. My question now is how does this give us any information on the differentiability of F(x)? Is there something that I am missing?
Thank you for your time
Homework Statement
Does the function F(x)=int(sin(1/t)dt,0,x) (integral of sin(1/t) with lower limit 0 to upper limit x) have a derivative at x=0?
Homework Equations
The Attempt at a Solution
I was thinking that F(x) shouldn't have a derivative at x=0 because the integrand isn't even...
Homework Statement
Let f be any function on the real line and suppose that: |f(x)-f(y)|<=|x-y|^2 for all x,y in R. Prove that f is a constant function. Note: "<=" reads "less than or equal to"
Homework Equations
The Attempt at a Solution
I have tried proof by contradiction, it...
2Uxxy+3Uxyy-Uxy=0 where U=U(x,y)
I made the substitution W=Uxy and then used a change of coordinates (n= 2x+3y, and r=3x-2y) which reduced the problem to solving Uxy=f(3x-2y)exp((2x+3y)/3) because W=f(r)exp(n/3). Now I have no idea where to go from there. Any help would be much appreciated...