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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