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Oct
9
comment Principle Lines of curvature
Maybe working out a solution to the system of ODEs will work. Ill try that.
Oct
8
comment Principle Lines of curvature
Prof Shifrin, Im actually using your book to learn this and was working out problem 2.2.1 and consulted Do Carmo for help. The converse statement that $F=f=0$ implies lines of curature I have worked out ok. The forward statement that $M$ has no umbilics and $\alpha$ is a line of curvature implies $F=f=0$ is not coming so easy. Do Carmo's argument for it is above but Im wondering how the determinant seals the deal?
Oct
8
revised Principle Lines of curvature
added 1440 characters in body
Oct
8
asked Principle Lines of curvature
Oct
2
comment $X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
If $\left(U\times V\right)\cap\Delta=\phi$ can we immediately conclude that $U\cap V=\phi$?
Aug
28
comment Inverse Trigonometric functions - Boyce & Diprima 2.2.19
I will read about this again. thx David
Aug
28
accepted Inverse Trigonometric functions - Boyce & Diprima 2.2.19
Aug
28
comment Inverse Trigonometric functions - Boyce & Diprima 2.2.19
The second line is a general result for $arcsin(~)$? even and odd separation like this?
Aug
28
revised Inverse Trigonometric functions - Boyce & Diprima 2.2.19
added 130 characters in body
Aug
28
comment Inverse Trigonometric functions - Boyce & Diprima 2.2.19
this is equivalent to mine. the question is not about this though.
Aug
28
comment Inverse Trigonometric functions - Boyce & Diprima 2.2.19
I wrote down the original prob. with cos and sin switched. It is correct now. thx
Aug
28
revised Inverse Trigonometric functions - Boyce & Diprima 2.2.19
edited body
Aug
28
asked Inverse Trigonometric functions - Boyce & Diprima 2.2.19
Jul
5
comment Computation of the Frenet-Serret trihedron in $\Bbb L^3$ (Lorentz-Minkowski space)
Is the inner product of $N$ and $B$ really 1? I am currently under the impression that the $T,N,B$ system of coordinates is an orthonormal set that moves along the curve $\alpha$. If we know $T$ and we can then calculate $N$ as a derivative and then $B$ as $T\times N$?
Jul
2
awarded  Curious
Jun
24
comment If nonempty, nonsingleton $Y$ is a proper convex subset of a simply ordered set $X$, then $Y$ is ray or interval?
@BrianM.Scott example 3 on page 85 is the positive integers with order topology. Is this another example of a convex set with the property?
Jun
20
comment Real analysis with a non-standard topology
Hi Bryan, if I interpret your first paragraph correctly, analysis builds on some primitive topological set-up. My question is a little more specialized, suppose we start with a set say $\mathbb{R}$ and then construct two incomparable topologies on it. Do we have a feeling for what happens when we construct the rest of the required machinery on top of those two cases? In my example, do we get identical structures at completion with both the Sorgenfrey line and the standard topology? Will differences in the topology elicit a difference with metrics and linear structures?
Jun
20
revised Real analysis with a non-standard topology
edited tags
Jun
20
asked Real analysis with a non-standard topology
Jun
19
answered Finding Fixed Points for Coupled ODE