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 StackExchange site.)

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Using Orthogonal Collocation to solve Coupled Ordinary Differential Equations

I am trying to solve six first order coupled ODE's, two of these are associated with a heat balance of a catalyst pellet, and four are mass balances. I have been trying to solve these equations using ...
3
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2answers
160 views

Solving $\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$ (using wolfram/mathematica)

I would like to solve the following non-linear ordinary differential equation: $$\frac{dx}{dt} = A \frac{ (1-x)}{(t-t^2)} - \frac{(B*x -C*x^2)}{(t-t^2 )*(t-x)}$$ -I need an analytic solution. -I ...
3
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1answer
140 views

Fun/Frustration With Coding Coding Theory

it's time for practical coding theory. I am trying to write a simple program that will detected if a given binary code word is "correct" or not. If it is not correct, I want to detect/correct (since ...
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1answer
55 views

Mathematica - Searching a clever way to do a computation

I am solving this differential equation using Mathematica $$x ~y''(x)+\alpha ~ y'(x)+\frac{1-3\mu (x)}{(1-x) x}=0$$ where $\mu(x)$ is a polynomial: $$\mu (x)=a+b\left(\frac{1}{1-x}\right)+c\left(\frac{...
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1answer
124 views

Mathematical symbol for Symbolic Replacement

(Posted at mathematica.SE, as it might be better there) I'm searching for a mathematical symbol, that describes the symbolic replacement done for instance in Mathematica: ...
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1answer
184 views

How to plot a phase portrait for system of differential equations in mathematica or R?

Please, help me. I'd like the phase portrait for this system: If anyone can make this portrait and post a print screen here, I would thank you very much.
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1answer
77 views

How can i view solutions of Solve as multiples of pi in mathematica 10

i am new to Mathematica and can't find the option to show solutions of Equations like Solve[6.5 == 2 \[Pi]*r] as multiple of pi. I only get the numerical output ...
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1answer
155 views

How can I solve numerically this partial differential equation?

I am reading this paper and came across a system of differential equations with 4 ODEs and 1 PDE. The PDE is given below. My question is how to solve this numerically in MATLAB , Python or Mathematica?...
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1answer
47 views

Graphing Fourier transforms on a frequency versus intensity plot (how to deal with complex numbers)

I am trying to understand how Fourier transforms are used to make HNMR plots. HNMR basically consists of hitting some molecules with some radiation and listening to the radio signal that results. ...
2
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1answer
110 views

Is the adjacency matrix of a given graph (OR any graphs isomorphic to a given graph) a Kronecker product, and if so what are the factors?

I have a few triangular grid graphs that I am trying to express as the direct products of smaller graphs, if possible. ...
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2answers
97 views

Techniques to solve nonlinear first-order ODEs

I am trying to solve the following nonlinear ODE: $$\frac{dy}{dx} = \frac{1}{x(ayx-b)},$$ where $a, b$ are constants and $a>0$. Moreover, you may assume that $b \neq 0$ if necessary. This ...
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2answers
353 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 ...
3
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1answer
197 views

Help me understand Gröbner basis result please

I'm practicing a bit with Gröbner bases but I'm not understanding the following result I obtain from Mathematica: ...
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1answer
57 views

Summation giving incorrect value (I think) in Mathematica

I have the problem $\displaystyle\sum\limits_{x=2}^4 \dfrac{1}{x^2}$. I know the answer to this problem should be $\dfrac{61}{144}$. When I type the problem into Wolfram Mathematica, I get the answer $...
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0answers
73 views

What is $\int (1-e^{-x})^n dx$?

For my purposes, $n$ is a non-negative integer, and $x > 0$. I didn't know how to evaluate this integral, so I plugged it into Mathematica. It told me the solution is $(-1)^n B(e^x; -n, n+1)$ I ...
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0answers
45 views

Precision of starting values in FindMinimum

I am currently working on an optimization of chemical kinetic model. Starting points for FindMinimum is defined as: k10 = 2.45*10^-1 and k20 = 8.65*10^-11. The step monitor is used to show calculated ...
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2answers
68 views

Solving differential equations with Wolfram Mathematica

So I saw this differential equations in my textbook $$\frac{{{d^4}\omega }}{{d{x^4}}} + 4{\lambda ^4}\omega = 0$$ and I figured why not solve it with majestic Wolfram Mathematica. So I wrote this ...
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1answer
72 views

Dual curve of the lemniscate of Bernoulli?

Does anybody happen to know the homogeneous equation $F(u,v,w) = 0$ for the algebraic curve dual to the lemniscate of Bernoullli: $$ F(x,y,x) = (x^2 + y^2)^2 - A (x^2 -y^2)z^2 = 0?$$ I looked at the ...
2
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0answers
31 views

Finding feasible solution of inequalities in math software

I have a Math problem where I have some true statements, and I want to know if there is a feasible solution to an equation. I would like to know how to do that in either Matlab or Mathematica. The ...
10
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4answers
295 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 ...
2
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1answer
138 views

Inverse gradient as line integral in Mathematica

I found a nice paper about inverse vector operators here. I have successfully defined a Mathematica function for inverse curl and inverse divergence, however I can't figure out how to do inverse ...
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1answer
140 views

How does Matlab, Maple, etc…solve algebraic and differential equations internally?

I would be very interested finding out how does Matlab, Maple, etc…solve algebraic and differential equations internally? Anyone know how they do it?
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2answers
347 views

How to actually use the Weierstrass-Enneper parameterization to draw a minimal surface?

I'm interested in drawing (with Mathematica for example) the generalized Scherk saddle tower with threefold symmetry, a shape that I find very attractive. In an article (see here) I found the ...
3
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0answers
128 views

The mathematics of anaglyph images

Note: I'm not quite sure whether this question properly belongs to the Mathematica or to the mathematics Stack Exchange. But because my question mainly concerns general mathematical principles rather ...
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1answer
61 views

Minimizing a function in Mathematica

Edit: I simplified the function using $\textbf{Simplify[...]}$ How can I minimize this function of $x$, where $l$ is a positive constant? $$\frac{1}{2} \sqrt{\frac{x}{l}+\frac{l}{x}+4 x^2-2}$$ ...
2
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1answer
94 views

I can't solve this integral in Mathematica

I want to calculate the following integral in Mathematica 10 $$f(x) = \frac2\pi\int_0^\infty\exp\left(-\kappa_2\frac{t^2}{2!}+\kappa_4\frac{t^4}{4!}-\dots\right)\cos\left(\kappa_1t-\kappa_3\frac{t^3}{...
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1answer
186 views

Torricelli's Law with a Sphere (Ignore Mathematica part, already solved)

Edit 1: According to this PDF, second page. The differential equation for a hemisphere becomes $$(r^2h-h^2) h' = -a^2\sqrt{2gh}$$ This differs from the equation I got, which looks like: $$\pi(r^2-h^...
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1answer
43 views

Scaling axis on Mathematica's plots

I'm trying to get the plot below only I want the ratio y:x to be 1:1 instead of 2:1. I want the ellipse to look tall and slim instead of short and fat. Here's the code line if you want to copy and ...
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1answer
2k views

How do I plot normal distribution

If I know the range (1-24) and know the area (X), how can I plot a normal distribution so that the curve has area X?
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1answer
61 views

Generating a data set that approximates another given random variable

One of the question my friend was asked in technical interview : The probability density function for a normal random variable with μ = 0.6 and σ = 0.7:​ Below is the code to generate the ...
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1answer
208 views

Expected number of passengers for the flight

One of the interview questions that I was asked was : The small commuter plane has 30 seats. The probability that any particular passenger will not show up for a flight is 0.1, independent of ...
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2answers
180 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( \...
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1answer
37 views

Exponential Distribution - Generate a fairly hefty data set X that is approximately exponentially distributed with μ = 0.7.

I encountered a question in one of the books, which asked to generate a fairly hefty data set X that is approximately exponentially distributed with μ = 0.7. I can do it for approximately normally ...
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0answers
49 views

ODE with Reflection

Some Background: I come from a computer science background and differential equations was not part of my course work. I'm still in contact with my professor that I ...
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1answer
2k views

how to substitute a variable by a number in wolframalpha

Peace be upon you, How can I compute \begin{align*} sin'(0) \end{align*} in Wolframalpha? like what in Maple, I try subs(diff(sin(x),x),x=0) But it doesn't work....
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0answers
22 views

Determining the sign of a function containing ratio

Problem We want to know for which values of $x,y,z,w$ the function $\sigma$ is positive or negative: \begin{equation} \sigma = \frac{A}{A^2-B^2}, \end{equation} where \begin{eqnarray} A & = &...
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1answer
28 views

Mathematica Cubic Polynomial

I am interested to find the roots of a cubic polynomial f(r)=r^2 - 2 r + Q^2 - [Alpha] r^3. \Alpha is positive real number hare, Q is real. I am interested in 2 complex roots and third root to be ...
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1answer
59 views

Analytical solution for bound state energies of infinite well

I am trying to find bound state energies assuming infinite potential. I have been told it can be done by analytically solving Right Hand Side and Left Hand Side of an equation such as: $$\sqrt{E}\tan^{...
3
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2answers
112 views

Reference for closed form integral of $\int_0^1 dz\,z^n/(z-a)$

Is there a closed form (non-recursive) expression for the definite integral $$\int_0^1 dz \frac{z^n}{z-a}, \qquad n\in\mathbb{Z}_+ \text{ and } a\notin (0,1)$$ for general $n$ and $a$ given in terms ...
3
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1answer
92 views

Integration: $\frac{2}{\pi} \int_0^\pi \frac{\sin(nx)}{10}x(\pi-x) \mathrm{d}x$ Can someone matlab/mathematica/maple it for me?

I want to compute $\frac{2}{\pi} \int_0^\pi \frac{\sin(nx)}{10}x(\pi-x) \mathrm{d}x$, where $n=1,2,3,4,\dots$ I worked this by hand and got the result: $-\frac{4\cos(nx)}{10n^3\pi}$ To check my ...
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1answer
85 views

Mathematica Question regarding NSolve

I'm trying to solve for 2-cycles for the equation $$x=xe^{r[1-x]}$$ using Mathematica. I've tried using NSolve, FindRoot, and Solve. When I use NSolve I input it as $$\textrm{NSolve}[xe^{r[1 - xe^{r[1 ...
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0answers
86 views

Plotting Dirichlet Series $L_{\tau}(s)$ related to Ramanujan tau function in Mathematica

According to wikipedia, Ramanujan tau function $\tau:\mathbb{N}\to\mathbb{Z}$ is defined by equating the coefficients of the power series on both sides of the identity: $$\sum_{n=1}^{\infty}\tau(n)q^...
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1answer
74 views

Mathematica Giving Me Trouble

I'm new to mathematica and am just learning the basics. I've run into a few things that I can't figure out. The first is this: "Number 11" $$r[t\_] := \{(1/3)*(t^3), 0.5 * t^2, t\}$$ (*Unit ...
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1answer
39 views

In Mathematica is it possible to define the plot range by an inequality?

For example, like Plot[Sin[x], {x, Sin[x]<0.5}] The above line is not working. I want to know if this idea is possible in Mathematica. Thank you!
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1answer
157 views

Best program for multiplying many multivariable polynomials

I want to make a table with two columns: The first column will consist of many(possibly hundreds) of polynomials in two variables. The second column will be a function applied to all of the ...
3
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0answers
125 views

Algorithm to find the “optimal” path in a given graph

Assume that $G=(V,E)$ is an undirected connected graph and that $H: V \to \mathbb R$ is a function that assign at each vertex $v \in V$ its height $H(v)$. Think of the pair $(G,H)$ as an energy ...
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0answers
25 views

Assigning a variable as constant and find out the minimum value

I have got a problem in assigning a variable as constant and solving a equations for minimum value. These are my equations: kd (2 h2 Cos[[Theta]2] - b2 Sin[[Theta]2]) (b1 - (b1 + b2) Cos[[Theta]...
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1answer
98 views

contour plot using Mathematica

I want do a contour plot in Mathematica as: ContourPlot[{Re[F[5/4, x + I y]] == 0, Im[F[5/4, x + I y]] == 0}, {x, -20, 20}, {y, -20, 20}, PlotPoints -> 100]; where function F[b,z] is defined as:...
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1answer
44 views

Help with Complicated Definite Integral

I am trying to find the integral of the following expression, with respect to $t$ from $0$ to infinity: $$\frac{e^{-a g t} \left(b-(g-1) \left(\text{H0} \left(e^{a t (-b+g- 1)}-1\right)+1\right)\...
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0answers
48 views

Is there any interactive spline fitting software?

I'd like to know if there's any software (freeware) for interactive data interpolation. What I want is to be able to visualize my data on an XY plot and drag the points to see how it affects the ...