16,505 reputation
43362
bio website mai.liu.se/~halun
location Linköping, Sweden
age 44
visits member for 4 years
seen 2 hours ago

I liked this site better in the good old days when the questions were fewer and more interesting... I still drop in from time to time, though.


21h
awarded  Enlightened
21h
awarded  Nice Answer
Aug
25
comment Techniques for solving coupled differential equations
See here, for example: math.stackexchange.com/questions/857608/…
Aug
25
comment Techniques for solving coupled differential equations
(Those are couple ODEs, not PDEs.)
Aug
25
answered matrix multiplication, reverse order; should comformability criteria be changed?
Aug
24
revised Deriving the equations of motion. Finding the critical points and determining their nature.
edited tags
Aug
24
comment Linearizing systems about critical points.
What I was trying to say is the right-hand side should be the $2 \times 1$ matrix $\begin{pmatrix} 2y_1+y_2 \\ -5y_1+5 \end{pmatrix}$ (at least that's what I assume that you mean), not a $2 \times 2$ matrix.
Aug
24
comment Linearizing systems about critical points.
In the equation $A\vec{x} = b$, both sides are $2 \times 1$ matrices!
Aug
23
comment Linearizing systems about critical points.
The system doesn't even make sense as it's written, since you are equating a $2 \times 1$ matrix with a $2 \times 2$ matrix...
Aug
22
revised questions about the closed graph of topological curve?
edited tags
Aug
22
comment Different methods to compute $\sum\limits_{n=1}^\infty \frac{1}{n^2}$
@DavidSpeyer: That's also a neat observation! :-)
Aug
22
comment What is wrong with this separation of variables?
Yes. As I said, the usual recipe for separable ODEs is a mnemonic for that particular situation, and it works because it is the chain rule in disguise: math.stackexchange.com/a/27433/1242
Aug
21
awarded  Enlightened
Aug
21
awarded  Nice Answer
Aug
20
comment Evaluation of $\displaystyle \int \sec^3 (x)dx$
@Gahawar: To me, this is the standard way of integrating odd powers of sin or cos...
Aug
20
comment What is wrong with this separation of variables?
When you bring $u$ down on the left-hand side you get $\frac{1}{u} \frac{d}{dt}\left(\frac{du}{dt} \right)$, and this is definitely not equal to $ \frac{d}{dt}\left(\frac{1}{u} \frac{du}{dt} \right)$ (for the reason that I explained: $d/dt$ doesn't commute with multiplication by $1/u$). And what it would actually mean to take the inner $dt$ outside $\frac{d}{dt}$ and up on the right hand side, I can't even begin to imagine... I just doesn't make sense in any way.
Aug
19
comment What is wrong with this separation of variables?
Well, no. This is not about equality of mixed derivatives, it's about the fact that the operation "multiplication by $u(t)$" followed by the operation "differentiation with respect to $t$" is not the same thing as doing those operations in reverse order. (A very fundamental fact in quantum mechanics, if you want to talk physics.)
Aug
19
comment What is wrong with this separation of variables?
@user1247: No, that is not at all what you do in the usual case, because then there is no $d/dt$ "standing in the way". You can't bring $dt$ and $u$ past the differential operator $d/dt$ just like that. (Anyway, the usual way of doing separation of variables is just a mnemonic for the chain rule, so it should perhaps not be taken too literally, but that has already been discussed many times on this site.)
Aug
16
awarded  Yearling
Aug
12
comment Diophantine inequality that comes up after Vieta Jumping Hurwitz technique
Here's an "ö" for you to cut & paste if you like. I made it by pressing the "ö" key on my Swedish keyboard. :-)