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May
26
accepted Does any numerical diff.eq. solver give correct results given small step-size?
May
26
comment Does any numerical diff.eq. solver give correct results given small step-size?
What is definition of "convergence" here? (I'm new to this) I imagine naively running an Euler step from a starting point $x_0$ and seeing the the correct function will be reproduced on an fixed interval $[x_0, x_1]$ . Is this the same? Shouldn't any finite step solution be correct at least a few steps, given small $h$?
May
25
asked Does any numerical diff.eq. solver give correct results given small step-size?
May
13
awarded  Popular Question
Feb
27
awarded  Famous Question
Jan
27
revised Find maximum of a function of a complex argument
added 469 characters in body
Jan
27
asked Find maximum of a function of a complex argument
Jan
27
asked Expansion of function in polar coordinates
Jan
26
comment What is unique about the Möbius transform?
There are other maps which preserve angles, but are not bijective?
Jan
25
comment What is unique about the Möbius transform?
This most interesting :)
Jan
25
accepted What is unique about the Möbius transform?
Jan
25
asked What is unique about the Möbius transform?
Jan
23
comment Define cosine naturally
Indeed, I prefer axioms that are likely to match real-world cases. I think commutativity, associativity, invertibility (division) are a good fit. My thought was to continue this line and use the Frobensius theorem to circle in on complex number and their multiplication property. The main ingredient here is their cyclicality which isn't too abstract and is also likely to occur in natural processes. My exp() notation is just a sketch. I basically mean defining the multiplication of complex numbers.
Jan
22
comment Define cosine naturally
I'd like to collect some axioms which are likely to occur in the real world and which single out the a "cyclic addition algebra" like $\exp(i\theta)$. Not sure what the correct term is. Next I assume this "real-world case" also happens to have a structure like the distributive law. This way I want to introduce cosine.
Jan
22
revised Define cosine naturally
added 2 characters in body
Jan
22
asked Define cosine naturally
Dec
2
awarded  Notable Question
Nov
30
revised Distance function to define finite ratio of hypercube volume
added 263 characters in body
Nov
30
comment Distance function to define finite ratio of hypercube volume
It still should be a maximal object inscribed in a unit cube. So scaling wouldn't do here. It should be something that extends into the corners more than a sphere.
Nov
30
asked Distance function to define finite ratio of hypercube volume