Questions tagged [mathematica]
For questions concerning the popular computational software program published by Wolfram Research. (Note: you are more likely to get quicker and more accurate response if you ask the question on their user forum or on the Mathematica Stack Exchange site.)
45
questions
14
votes
9
answers
28k
views
Drawing heart in mathematica
It's not really a typical math question. Today, while studying graphs, I suddenly got inquisitive about whether there exists a function that could possibly draw a heart-shaped graph. Out of sheer ...
- 22.5k
4
votes
3
answers
31k
views
How to plot a phase portrait for this system of differential equations?
I beg your help.. I'd like the phase portrait for this system:
\begin{aligned}
\frac{dx}{dt} &= x (7-x-2y) \\
\frac{dy}{dt} &= y (5-y-x)
\end{aligned}
I don't know how to use Mathematica/...
- 101
1
vote
3
answers
227
views
Integrating $\int_0^\infty \frac{x^n}{e^x+1} \,dx$, where $n$ is an integer
If the general case is too hard for some reason, I mostly need the $n=2$ case of the following integral:
$$ \int_0^\infty \frac{x^n}{e^x+1} \,dx $$
For some reason Mathematica fails me, as it claims ...
- 61
0
votes
1
answer
346
views
Inverse Fourier transform to find out $\hat c_1$
If we have an integration which is need to solve inversely $$a_0 e^{-r^2/R^2} = \int_0^\infty \hat{c}_1(k) \frac{\sin(k r)}{r} dk,$$
If I transform the $\sin(kr)$, then we get imaginary part.
Please ...
user52950
39
votes
3
answers
1k
views
Do we really know the reliability of PrimeQ[n] (for $n>10^{16}$)?
The algorithm Mathematica uses for its PrimeQ function is described on MathWorld. That web page says PrimeQ uses, "the multiple ...
- 1,207
7
votes
4
answers
3k
views
Drawing a thickened Möbius strip in Mathematica
I would like to have Mathematica plot a "thickened Möbius strip", i.e. a torus with square cross section that is given a one-half twist. Ideally, I would like this thickened Möbius strip to be ...
- 131k
26
votes
1
answer
850
views
The positive root of the transcendental equation $\ln x-\sqrt{x-1}+1=0$
I numerically solved the transcendental equation
$$\ln x-\sqrt{x-1}+1=0$$
and obtained an approximate value of its positive real root $$x \approx 14.498719188878466465738532142574796767250306535...$$
...
- 1,928
15
votes
4
answers
59k
views
How do I convert the distance between two lat/long points into feet/meters?
I've been reading around the net and everything I find is really confusing. I just need a formula that will get me 95% there. I have a tool that outputs the distance between two lat/long points.
<...
- 251
4
votes
2
answers
917
views
Plotting graphs using numerical/mathematica method
From the author's equation 13, 14 We can write by inserting V''(A)=0,
Solving for R we get,
$$R= \frac{6^{D/4} \sqrt{D}}{\sqrt{-2^{1+\frac{D}{2}} 3^{D/2}+3 2^{1+D} A-3^{1+\frac{D}{2}} A^2}}$$
Now ...
user52950
4
votes
1
answer
326
views
Why does (Full)Simplify return terms with $0^n$ coefficients?
When I use Simplify[] or FullSimplify[], specifying domain reals, I get terms with $0^n$ as the coefficient. Isn't that always ...
- 1,059
3
votes
1
answer
738
views
Closed form with of a series Mathematica
I've these two series, and I would like a closed form:
$$ \sum_{k=-\infty}^{\infty} \frac{x+kx_0-h}{|x+kx_0|^3}$$
$$ 3\sum_{k=-\infty}^{\infty} \frac{(x+kx_0-h)(x+kx_0)^2}{|x+kx_0|^5} $$
...
- 578
1
vote
3
answers
1k
views
Plot of x^(1/3) has range of 0-inf in Mathematica and R
Just doing a quick plot of the cuberoot of x, but both Mathematica 9 and R 2.15.32 are not plotting it in the negative space. However they both plot x cubed just fine:
...
- 113
0
votes
1
answer
573
views
How to solve integral in Mathematica?
I need matrix H. G is working, but H is just derivative?? How to obtain?
...
- 225
0
votes
3
answers
1k
views
solve an implicit function
I have seen that an example of implicit function that can be solved only numerically is (solving for x knowing y):
$$
\sin(x) = y\cdot x
$$
I was wondering if the following function can also be ...
0
votes
1
answer
143
views
Is $198585576189$ a member of OEIS sequence A228059?
I currently do not have enough computing power, so please pardon me for my question, which occurred just recently to me.
So here it goes:
Is the Descartes spoof
$$\mathscr{D} = {3^2}\cdot{7^2}\...
- 8,010