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 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! :) Aug 30 revised Applying a multidimensional variant of Taylor's Theorem deleted 4 characters in body Aug 30 asked Applying a multidimensional variant of Taylor's Theorem Aug 27 asked Sufficiency to prove the convergence of a sequence using even and odd terms Aug 23 revised Help solving differential equation Edited for easier readability Aug 23 suggested approved edit on Help solving differential equation