792 reputation
424
bio website math.utep.edu/faculty/…
location El Paso, TX
age 33
visits member for 2 years, 10 months
seen Nov 21 at 5:10

Computational Science PhD student
University of Texas El Paso
Climate & Energy Science Student Organization President
National Energy Technology Laboratory Intern
NSF LSAMP Fellow


Sep
9
comment Proving the Kantorovich inequality
Could you post your answer? There may be others interested in the same question... i.e. me! :)
Sep
7
comment Accumulation points of sequences as limits of subsequences?
Ah, so it does work both ways! That's awesome! :)
Sep
7
comment Accumulation points of sequences as limits of subsequences?
As I'm working in $R^n$ space, I think that should work! :)
Sep
7
asked Accumulation points of sequences as limits of subsequences?
Sep
7
comment Evaluating $\iiint x\,dx\,dy\,dz$ limited by paraboloid of equation $x=4 y^2+4z^2$ & for plane $x=4$
Sometimes, books can be mistaken as well.
Sep
7
comment Evaluating $\iiint x\,dx\,dy\,dz$ limited by paraboloid of equation $x=4 y^2+4z^2$ & for plane $x=4$
You don't need to substitute anything for x... the change in variables result in a differential of the form: $r dxdrd\theta$.
Sep
7
answered Evaluating $\iiint x\,dx\,dy\,dz$ limited by paraboloid of equation $x=4 y^2+4z^2$ & for plane $x=4$
Aug
31
comment Verifying an error estimate on a multidimensional function using its jacobian
Thanks, copper.hat! :)
Aug
31
accepted Verifying an error estimate on a multidimensional function using its jacobian
Aug
31
comment Verifying an error estimate on a multidimensional function using its jacobian
You're answer makes a lot sense now! Just one little question: I'm not quite sure I understand how we can make the assumption that $\epsilon \le ||J(x^*)||$ "without loss of generality". Could you elaborate on that? What allows us to make such a claim?
Aug
31
comment Verifying an error estimate on a multidimensional function using its jacobian
I think I understand it now... The main purpose of the statement in the first line of the second paragraph is to ensure that $||x+t(x^*-x)-x||$ is in the ball so that continuity ensures that we can bound $||J(x+t(x^*-x)-x)-J(x)||$ by epsilon. It's a subtle detail that I just couldn't see at first.
Aug
31
comment Verifying an error estimate on a multidimensional function using its jacobian
Hi copper.hat. In the second line of the second paragraph, you wrote $||x+t(x^*-x) -x||$, but I think you meant to write $||x+t(x^*-x) -x^*||$. Otherwise, $||x+t(x^*-x) -x||=t||x^*-x||$. Do you agree?
Aug
31
revised Verifying an error estimate on a multidimensional function using its jacobian
corrected slight error in notation
Aug
31
accepted Sufficiency to prove the convergence of a sequence using even and odd terms
Aug
31
revised Verifying an error estimate on a multidimensional function using its jacobian
corrected formatting
Aug
31
asked Verifying an error estimate on a multidimensional function using its jacobian
Aug
30
comment How do I obtain an appropriate energy functional from the weak formulation of a partial differential equation?
Substituting v=u into the weak formulation accounts for most of the functional $F(u)$ except for the term $\frac{1}{2}au^2$. Where did the $\frac{1}{2}$ come from?
Aug
30
comment Applying a multidimensional variant of Taylor's Theorem
Thanks so much, shoda! :)
Aug
30
accepted Applying a multidimensional variant of Taylor's Theorem
Aug
30
comment Applying a multidimensional variant of Taylor's Theorem
@shoda: Yes, you are correct. In the process of copying and pasting, I neglected to change the limits. Thanks for the heads up! :)