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13
votes
7answers
8k 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 ...
4
votes
4answers
9k 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. ...
0
votes
1answer
170 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 ...
2
votes
1answer
459 views

How to use Mathematica to solve equations in a polynomial ring?

I am sorry. But I wonder whether it is fine to ask this question here. I need some help to solve some equations in a polynomial ring: Give the ring $\mathbb{F}_p [x ]/(x^2+x+1)$, where $p$ is a ...
4
votes
2answers
304 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 ...
31
votes
3answers
508 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
vote
0answers
236 views

(Improved; Kindly assist )CSI Forensic Maths

In a square room with 7 m-long sides, five people have shot at random people. They all had two bullets and killed two people in the crowd. Other people in the room were not hurt. CCTV recordings show ...
1
vote
3answers
5k 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. I don't know how to use Mathematica/Matlab ... :( If anyone can make this portrait and post a print screen here, I would thank you ...
1
vote
0answers
548 views

Mathematica: How to convert scales to frequencies?

According to the transform $$w(u,s)=\frac{1}{\sqrt{s}}\int _{-\infty }^{\infty }x(t) \psi ^*\left(\frac{t-u}{s}\right)dt,$$ the frequency should be $f=\omega/(2\pi)=1/(2\pi s)$ (is it right?), where ...
0
votes
1answer
105 views

Trouble in proving that $\|x\|_p = \max|x_j|$

We define p-norm in this way: $\|x\|_p = \{\sum ^N_j_=_1|x_j|^p\}^ {1\over p}$ We know that It change to $\|x\|_p = \max|x_j| $ when $ p \to \infty $ How can I prove this ?
2
votes
1answer
348 views

Closed form with of a series Mathematica

I've these two series, and I would like a closed form: $$ \sum_{k=-\infty}^{\infty} \frac{x+kx_0-h}{|x+kx_0|^3}$$ $$ 3\sum_{k=-\infty}^{\infty} \frac{(x+kx_0-h)(x+kx_0)^2}{|x+kx_0|^5} $$ ...
0
votes
1answer
432 views

How to solve integral in Mathematica?

I need matrix H. G is working, but H is just derivative?? How to obtain? ...
76
votes
11answers
58k views

What should I learn first, Mathematica or MatLab? [closed]

I have a non-professional interest in math and I would like to be able to be curious and play around with some math that I'm learning about (both here and from calculus-and-higher level math classes). ...
22
votes
1answer
454 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 $$x \approx 14.498719188878466465738532142574796767250306535...$$ ...
10
votes
4answers
277 views

A numerical evaluation of $\sum_{n=1}^{\infty}(-1)^{\frac{n(n+1)}{2}}\frac1{n!}\int_0^1x^{(n)} dx$

I would like to obtain a numerical evaluation of the series $$S=\sum_{n=1}^{\infty}(-1)^{\frac{n(n+1)}{2}}\frac1{n!}\int_0^1x(x+1)\cdots(x+n-1)\: dx$$ to five significant digits. I've used ...
3
votes
4answers
200 views

A limit question (JEE $2014$)

The following is a JEE (A national level entrance test) question: Find the largest value of the non-negative integer ( a ) for which: $$ \displaystyle \lim_{x \to 1} \left( \dfrac{-ax + \sin(x-1) + ...
11
votes
2answers
301 views

Twilight Zelda Guardian Puzzle : Shortest Path (UPDATE: ADDED RULES)

I'm playing a video game right now and in it is a puzzle (see here). There are solutions to solving it (see here) on the Internet, but I'd like to know if this path is the shortest path (least amount ...
7
votes
4answers
2k 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 ...
3
votes
1answer
468 views

Switching from Mathematica to MATLAB: As a text editor?

I have been using Mathematica for almost a year, and the most indispensable feature in Mathematica to me has been the ability to write really nice documents and print them into PDF or TEX files. In ...
3
votes
1answer
131 views

The limit of the expectation of the top half+1 order stats of $n$ draws of $X$ as $n\to\infty$?

Can anyone help me compute the limit of the average of the top half +1 of order marginal order distribution of $n$ draws from $X$, as $i\to\infty$? Specifically, the limit as $i\to\infty$ of ...
1
vote
2answers
81 views

How to plot a phase potrait of a system of ODEs (in Mathematica)

I am asked to use mathematica to plot the fixed-points of the following system $$ \frac{dN}{dt} = -\gamma N \left( 1 - \left( \beta M + N\right) \right) $$ $$\frac{dM}{dt} = M \left( 1 - \left( ...
0
votes
1answer
127 views

Solving a nonlinear system of differential equations in MATLAB or Mathematica

Is it possible to solve the system $$\dot{W}=A\left(k-\frac{M}{W}\right)$$ $$\dot{M}=B\left(k-\frac{M}{W}\right)$$ with initial conditions $$W(0)=w_0$$ $$M(0)=m_0$$ in MATLAB or Mathematica? If so, ...
0
votes
1answer
294 views

How to make Runge-Kutta for solving nonlinear ODE system in Mathematica

How to make Runge Kutta method for system of non linear equations in this Matrix form. Matrices A3, B3 and B4 are functions of matrix X3. Initial conditions are X1=X2=X3=X4=0 and system is here $$ ...
0
votes
1answer
233 views

How to obtain big matrix in Mathematica?

Can you help me how to obtain big but simple matrix in Mathematica? ...
-1
votes
1answer
274 views

Finding out the nodes from spherical symmetric equation for mathematica and then plotting it in gnu-plot

What I want to do is to draw a curve for the spherical partial differential equation for S at rho=0: \begin{equation} \frac{\partial^2S}{\partial \rho^2}+\frac{d-1}{\rho}\,\frac{\partial S}{\partial ...