7,767 reputation
2832
bio website supermath.info
location Virgina USA
age 36
visits member for 2 years, 1 month
seen yesterday

I'm interested in mathematics which is used to frame physical theory. I guess that means I'm at least a little interested in just about anything.

Currently I'm trying to understand Cartan's Method of moving frames as it applies to various classification questions of low-dimensional geometry.

I also have interest in superanalysis and certain problems of hypercomplex analysis.

More generally, I'm just looking for interested students who want to exceed the status-quo of undergraduate mathematics. Ideally, our interests overlap.


Sep
17
comment Problem 30 of GR8767 how is improper integral defined?
Yes. That's the method intended. We can twist this problem many different directions in view of the above comment.
Sep
17
accepted Problem 30 of GR8767 how is improper integral defined?
Sep
17
comment Problem 30 of GR8767 how is improper integral defined?
I had hoped there might be some slick countermeasure to direct calculation, but, on the other hand, it's not that bad. Thanks for your assistance, my student will appreciate it.
Sep
16
comment Problem 30 of GR8767 how is improper integral defined?
ah ha. I did not notice that, this would help, although, it remains to show why it must be zero. I assume there is some easy method? Care to add that to your answer, I'd accept it then.
Sep
16
asked Problem 30 of GR8767 how is improper integral defined?
Sep
15
comment Continuity and Differentability of a Partial derivative
I think, d,e,i, j are correct. Partial derivatives can exist, but, that doesn't say much about continuity due to the examples where all linear paths agree but quadratics differ. I hope someone comes along with some specific counter examples soon, I must run.
Sep
15
comment Is a horizontal line considered periodic?
Periods are ambiguous in other cases. For example, $\sin \theta$ has periods $2\pi k$ for any $k \in \mathbb{Z}$. Of course, you could pick a minimal period in that case. But, I don't see the problem. I mean, the constant function is part of the family of periodic functions built over any period. This is a good thing.
Sep
15
comment Geometric proof for triple vector product Jacobi identity
The basic geometric idea here is also used in this math.stackexchange.com/a/400732/36530
Sep
9
revised Geometric proof for triple vector product Jacobi identity
added picture and some organization
Sep
8
answered Geometric proof for triple vector product Jacobi identity
Sep
8
comment Geometric proof for triple vector product Jacobi identity
perhaps, but it doesn't seem there is an adequate answer in the duplicate.
Sep
8
comment Quaternion integration
It seems you need to add detail to this question as to your precise definitions of differentiation etc. on the quaternions.
Sep
8
comment Does an exponential brand of calculus make sense?
I don't know, but I have accidentally built super-exponential growth into applied calculus problems before. Imagine my surprise that all possible solutions could not be continued to $t = \infty$. Gulp.
Sep
7
revised why does directional derivative move fastest along the gradient?
added 4 characters in body
Sep
7
answered why does directional derivative move fastest along the gradient?
Sep
7
comment Is this an ordinary differential equation?
Thanks! I felt guilty to post it without at least adding a link or two, so, there you go.
Sep
7
answered Is this an ordinary differential equation?
Sep
7
comment Is this an ordinary differential equation?
As far as I have ever read, ODE means just one independent variable whereas PDE means several. Although, sometimes one considers families of ODEs which perhaps blurs the line a bit. The family is indexed by some other parameter which doesn't have the same role as the independent variable in the ODE... in any event, so far as I've seen yes my initial comment is standard.
Sep
6
comment Is this an ordinary differential equation?
still a PDE. It is the presence of several independent variables that makes it a PDE. At least, this is my opinion.
Sep
3
comment Confusion with Euler-Lagrange Derivation
This is a standard notation, we write $df/du$ to denote $f'(u)$. To be explicit, we could write $(df/dx)(u)$, but $df/du$ compactly expresses the derivative evaluated at $u$. It is the same with $Y$ verses $y$.