17,733 reputation
43367
bio website mai.liu.se/~halun
location Linköping, Sweden
age 44
visits member for 4 years, 4 months
seen 3 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.


3h
comment Jacobi Elliptic Functions Special Case
This is not true. Even though the case $-1<k<1$ is the most important, the Jacobi elliptic functions can be defined for any complex number $k$.
3h
comment Jacobi Elliptic Functions Special Case
Well, the Jacobi sn and cn functions parametrize the unit circle for any $k$, but this doesn't imply that they can be simplified to elementary functions...
22h
answered Jacobi Elliptic Functions Special Case
1d
comment $ \int_\gamma \frac{1}{z\sin z}dz$ where $\gamma$ is the circle $|z| = 5$
The notation is inconsistent. The interval $[0,2\pi]$ on the real line is not the same as the circle of radius 5 in the complex plane.
1d
comment Initial conditions of a transformed differential equation
I'm afraid I don't understand what you mean by finding $y_0$... It's already given in (1), isn't it?
1d
revised Is {(1, 1), (2, 2)} symmetric and/or antisymmetric?
edited tags
1d
comment Initial conditions of a transformed differential equation
$y(x_0)=y_0$. (But why do you want to do this when (1) and (2) are so easy to solve as they stand?)
1d
revised What is this picture?
edited tags
Dec
16
comment What is the importance of $\sinh(x)$?
+1. This way of writing the solution (instead of the equivalent form $f(x)=c e^x + d e^{-x}$) is particularly useful if there is an initial condition at $x=0$ of a certain form: if the condition is $f(x)=0$, then only the sinh term will appear in the solution, and if the condition is $f'(x)=0$, then only the cosh term survives. (This is the same thing that happens with the solution $f(x)= a \sin x + b \cos x$ to the ODE $f''=-f$.)
Dec
12
comment On consequences of $\int_{0}^1f(x)x^ndx=0 , \forall n \in \mathbb Z^+\cup\{0\}$
See here: math.stackexchange.com/questions/16831/…
Dec
10
comment Simple system of nonlinear ordinary differential equations
For a start, $(a+b)''$ is identically zero, and $(a+b)'(0)=0$, so $a(t)+b(t)$ is constant. You can use this to reduce the problem to an ODE in just one of the variables (say $a$).
Dec
9
awarded  Caucus
Dec
8
comment Specific function
$z=1/(1+x^2 y^2)$?
Dec
8
comment Is there a term for “finite and non-zero”?
All right, I've done that.
Dec
8
answered Is there a term for “finite and non-zero”?
Dec
7
comment In what sense is $\int_{-\infty }^{\infty } \frac{x}{x^2+1} \, dx = \pi i$?
The rule $\ln(zw)=\ln z + \ln w$ isn't necessarily valid for complex numbers; you have to be very careful with branch cuts (and define what you mean by "ln" to begin with). (And also $\ln(-x-i)$ should be $\ln(-x+i)$.)
Dec
7
comment Is there a term for “finite and non-zero”?
@Sesquipedal: Goldblatt (Lectures on the Hyperreals, p. 50) calls such numbers "appreciable" (= "limited but not infinitesimal").
Dec
6
comment Retarded green function integration
No need for complex analysis; the antiderivative is $\ln(1+z)$ so the integral is divergent.
Dec
4
comment Limit of $\sqrt{x-x^2}$ as $x$ approaches $1$
It's impossible to answer this question unless you say exactly what definition of limit your book is using. With the definition of limit that we teach in the calculus courses at our department, the limit does exist (and equals zero), but other sources may have a different opinion.
Dec
4
comment Is metric always quadratic?
Try googling for "Finsler geometry", perhaps that's what you're after.