@BalarkaSen hi, you must be like grown up by now! I'm obviously still teaching. Trying to teach some basic numerical mathematics this semester, so I need update my Mathematica skills again. I used it like 10 years ago in uni and have forgotten everything.
I want to write a short code using the `Manipulate[]` function in Mathematica. Namely, I want to be able to vary the degree of the Taylor polynomial `n` but with (for now) fixed function and fixed expansion point. If `n` is fixed, then it is simply:
`t[x_] = Normal[Series[f[x], {x, 0, 6}]];`
Note that using `:=` (`SetDelayed`) will cause an error here. Now the issue is that if I simply replace the `6` with an `n` and use `t[x_,n_]` instead, the `n` would expect a `:=` (`SetDelayed`) instead of `=`. However, that is incompatible with the `x_`.
@TedShifrin stupid question (cause I don't do statistics) - how does one do this? look at the graph and "guess"? or is there some more mathematical way to?
I asked people from our geography faculty for help. none of them has any idea about maths or statistics or any possible mathematical model for the data :(
@TedShifrin I was thinking about extremely simplifying the process and just compute the average temperature of the 1 million data points for each time point
@TedShifrin if it is directly related to what I need, yes, otherwise, later. we have to "solve" this before Christmas because he was too shy to ask me before, when he would still have had more time to work on it...
I only remember some parts from numerical analysis because I haven't applied them since my exams in uni - but if I know what I have to look up again, I'll do it of course
@TedShifrin a student of mine wants to extrapolate climate data. he collected data from some website e.g. for August 2020 in the format "average sea temperature, latitude, longitude". there is also data for August 2019, August 2018, etc.
do you know what would be a reasonable way to interpolate and then extrapolate so many data points? I only remember basics on how to interpolate data sets of the form (x, y) with different methods.
One particularly nice class of bijections from $\Bbb R$ to $\Bbb C = \Bbb R^2$, which is in my opinion a little bit similar to the spiral around the grid, is given by the space-filling curves.
anyone know a nice geometric proof that the cardinality of C is the same as R? I know the construction with alternating digits but was hoping for something visual
I want to write a short code using the `Manipulate[]` function in Mathematica. Namely, I want to be able to vary the degree of the Taylor polynomial `n` but with (for now) fixed function and fixed expansion point. If `n` is fixed, then it is simply:
`t[x_] = Normal[Series[f[x], {x, 0, 6}]];`
Note that using `:=` (`SetDelayed`) will cause an error here. Now the issue is that if I simply replace the `6` with an `n` and use `t[x_,n_]` instead, the `n` would expect a `:=` (`SetDelayed`) instead of `=`. However, that is incompatible with the `x_`.
One particularly nice class of bijections from $\Bbb R$ to $\Bbb C = \Bbb R^2$, which is in my opinion a little bit similar to the spiral around the grid, is given by the space-filling curves.
