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Sep
14
asked Understanding tensor divergence notation in an integral
Sep
14
awarded  Citizen Patrol
Sep
14
comment Numerical solution of fractional integro-diffrential equ. using collocation method?
This question may be best posted on scicomp.stackexchange.com. It is more geared towards numerical methods for scientific computing.
Sep
14
comment Understanding Line integral notation
@MichaelBoratko: Yes, in fact, I'm evaluating the RHS integral in this notation. I'm parameterizing a curve around a quadrilateral, one segment at a time. Would $dS_{1}$ (in my case) be equivalent to ||C'(t)||dt?
Sep
14
comment Understanding Line integral notation
Its in Understanding and Implementing the Finite Element Method by M.S. Gockenbach.
Sep
14
asked Understanding Line integral notation
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