Reputation
8,978
Next privilege 10,000 Rep.
Access moderator tools
Badges
3 17 65
Newest
 Proofreader
Impact
~112k people reached

2d
revised Is there a physical interpretation of the alternating property?
added 85 characters in body
2d
answered Is there a physical interpretation of the alternating property?
Jun
28
comment Strange integral test for convergence in my Analysis Script (proof flawed ?)
This is just a tautology. The convergence criterion you mention is different.
Jun
23
comment How do you avoid getting rusty at applied math after univeristy
There is an indetermination principle at play here. You have two poles:focus on your task, the one you are paid for, and losing the opportunity to learn new and master old mathematics, and spend time on general mathematical workout, at the risk of dispersing your concentration and your time. The right way is of course to find the delicate equilibrium between the two. This is arguably the hardest part of a PhD-postdoc program, for me at least.
Jun
20
comment Frechet derivative of an operator
... In the problem at hand you have to do exactly the same computation, the only difference being that your independent variable is now called $u$ instead of $q$.
Jun
20
comment Frechet derivative of an operator
...How do you compute $dS(u)$? You take an "admissible variation" $\delta q$ and you compute $$\begin{split} \left.\frac d{d\epsilon}S(q+\epsilon \delta q)\right|_{\epsilon=0} &= \int_{t_0}^{t_1}\left.\frac\partial{\partial \epsilon}L(\dot q+\epsilon\dot{\delta q}, q+\epsilon\delta q)\right|_{\epsilon =0}\, dt \\ &=\int_{t_0}^{t_1}\frac{\partial L}{\partial \dot q}\dot{\delta q } + \frac{\partial L}{\partial q}\delta q\, dt\end{split}$$And so on. This is the way you find Euler-Lagrange's equations of motion.
Jun
20
comment Frechet derivative of an operator
Have you ever studied Lagrangian or Hamiltonian mechanics? There is a principle called "the stationary action principle", in which you have an integral (the "action") $$S(q)=\int_{a_0}^{a_1}L(\dot q(t), q(t))\, dt$$ and the principle tells you that the equation of motion is $$dS(u)=0.$$
Jun
20
comment Frechet derivative of an operator
The standard way. Take a variation $v$, form the increment $T(u+\varepsilon v)$ take the derivative $\left.\frac{d}{d\varepsilon}\right|_{\epsilon=0}T(u+\varepsilon v)$. Switch derivative and integral and so on.
Jun
19
answered How to solve a simple differential equation in the way of weak solutions?
Jun
19
comment Does $\Vert f-s_n \Vert_\infty \to 0$ still hold for $f\in C^0[a,b]$?
Yes. The point is that you lose the error estimate.
Jun
17
comment Question about the signature of a matrix
I have made a small edit, please see if it suits your thoughts.
Jun
17
revised Question about the signature of a matrix
"sufficiently small" instead of "arbitrarily small"
Jun
17
answered Question about the signature of a matrix
Jun
17
comment Definition of Bounded Variation Function with vectorial arguments
Related.
Jun
17
reviewed Approve Is it a composite number?
Jun
17
comment $\mathcal{L}_2$ continuous functions with $f(0)=\alpha$ are dense in $\mathcal{L}_2 [-1,1]$
P.S. Only now I realize that this approach is exactly the same of Callus's answer.
Jun
17
answered $\mathcal{L}_2$ continuous functions with $f(0)=\alpha$ are dense in $\mathcal{L}_2 [-1,1]$
Jun
16
comment Is $\lim_{p \searrow 1} \|u\|_{L^p(\Omega)} = \|u\|_{L^1(\Omega)}$ true?
Try looking for the keywords "log-convexity of p-norms".
Jun
16
comment differentiability of a function consisting of a bilinear form
For the second one, try gaining some intuition by solving the $n=1$ case first. The multidimensional case is conceptually similar, with messier formulas.
Jun
16
reviewed Reject What's the relation between different antiderivatives?