Tagged Questions

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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0answers
40 views

Plotting in Mathematica

I'm new to mathematica. How would I plot the following functions in the polar complex plane? $$ \phi={-k\over 2\pi r}\cos(\theta_0-\theta) $$ and $$ \psi={-k\over 2\pi r}\sin(\theta_0-\theta) $$ ...
0
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0answers
64 views

In Maple or Mathematica, syntax : Finding the fundamental sol. of the Heat eq., with Dirac-Delta initial condition

I use this question as a case example for later solving more complex equations of this type : When trying to find the fundamental solution of the Heat equation using Maple (software) , I get the ...
1
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0answers
88 views

What is the Fourier series of $e^{\mu\cos\theta}$?

Motivation: I want to solve this convolution problem on the circle: find $f$, given $g$ and $$ g(\theta) = \int_{S^1} e^{\mu\cos(\theta-\phi)}g(\phi)\ d\phi. $$ To do this, I want to find the Fourier ...
0
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3answers
73 views

Plotting a region in $3D$ space

I would like to know if someone knows of a software where I can plot the following region $$ D = \{ (x,y,z) \in \mathbb{R}^3: 0 \leq x \leq 1 , \; x^2 \leq y \leq x, \; \; 0 \leq z \leq x \} $$ ...
1
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0answers
32 views

Roots and Weights

I use a Mathematica package to compute roots and weights (and other things) but the package gives me only the expression of the roots in $\omega$-basis (basis of fundamental weights) and in the ...
2
votes
1answer
43 views

How does the base of a group determine the “sort” of the elements in the group

I'm trying to study groups in Mathematica, and I've asked a question on Mathematica.SE that perhaps only someone from Math.SE could answer. Related: How does ...
5
votes
3answers
114 views

Find min of $\frac{\left( \sum kx_k \right) \left( \sum x^2_k \right)}{\left( \sum x_k \right)^3}$

With $n \ge 2$ and $x_1,\ x_2,\ \dots,\ x_n > 0$. Find the minimum of: $$ M = \frac{(x_1 + 2 x_2 + ...+ nx_n)( x^2_1 + x^2_2 +...+x^2_n)} {\left( x_1 + x_2 +...+ x_n \right)^3}$$ For specific ...
1
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0answers
87 views

Which symbolic programming language for manipulation of nonlinear equations?

I have a set of (multivariate, nonlinear) equations which I want wo modify according to my own rules, i.e. not in a standard ways such as matlab's simplify function. I am looking for a mathematical ...
1
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1answer
32 views

Mathematica DSolve input

I'm trying to solve this differetial eqation. dy/dx=3y^(2/3). This is my input: DSolve[{y'[x] = 3 y[x]^(2/3), y[2] = 0}, y[x], x] This is my output: DSolve::deqn: "Equation or list of equations ...
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2answers
58 views

Difficulty finding Expectation of a special function

I have a special function given as: $${\rm f}\left(r\right) ={1 \over \beta\lambda}\,2^{r/\beta} \exp\left({\left[2^{r/\beta} - 1\right]K \over \lambda}\right)$$ I should find the Expectation of ...
0
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1answer
47 views

Mathematica Homework Question

I had a mathematica assignment the other day that was fairly simple. I thought I did it correctly, but I guess not. Question: Write a single Mathematica Command which will display (plot) both $y = ...
0
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0answers
16 views

Mathematica question about value of a function

I wrote this on Mathematica. *f[x_] := Prime[x + 1] - 1 g[x_] := (6 - (f[x]*f[x]) - f[x])/(2*log[f[x]]) + 2* ExpIntegralEi[2*log[f[x]]] + LogIntegral[f[x]] - (2*x*x) - (2*x) N[g[1200]]* I pressed ...
0
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0answers
28 views

Condition number of covariance matrix

I am interested in generating a covariance matrix of dimension say 100. I managed to get a correlation matrix with finite condition number. To construct a covariance matrix I need to have standard ...
1
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1answer
107 views

Good software package to help Maths learning

I'm a mature student enrolling at a Maths degree course soon at the university. I'd like to be able to use some software package to help me visualize equations, graphs, play around with variables with ...
0
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1answer
77 views

How to Expand $f(x) = \sqrt{x^2-y^2}$ about $x=y$

How would one go about expanding $f(x) = \sqrt{x^2-y^2}$ about $x=y$? You can't do a Taylor series, because $f'(x=y)$ diverges. I tried a few other things, but to no avail. Interestingly enough, ...
2
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1answer
126 views

Can wolfram alpha compute symbolic vector derivatives

Can Wolfram alpha be used to find out say $$\nabla_x\left(\|y-Ax\|_2\right)$$ What command do I use? I tried some obvious ways, and googled a bit, but didn't find anything.
0
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1answer
29 views

fourier transforms with Woflram Alpha

I'm studying Fourier transform at the moment and I've noticed some weird irregularities between my textbook and Wolfram Alpha's answers. Say I ask Wolfram the following: fourier transform ...
3
votes
1answer
112 views

Fourier series for $e^x$

I'm trying to teach myself partial differential equations from Strauss' book. I have run into a very bizarre problem - I cannot figure out what is the Fourier series of $e^x$! And not even Google has ...
0
votes
1answer
94 views

Solving an ODE with Mathematica, using Lagrangian mechanics

Question: The velocity of light above a hot surface decreases with the height from that surface. The velocity is given by $v=v_0(\frac{1-y}{\alpha})$ where $y$ is the vertical distance above the ...
0
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1answer
76 views

Using Mathematica to know the number primes that are contained in a given interval

So I want to know basically how to determine how many prime numbers (integers that can only be divided by 1 and themselves) are contained in a given interval. Thank you.
0
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1answer
95 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, ...
20
votes
7answers
2k views

LaTeX/TeX Vs. Mathematica for Typesetting

I know Mathematica like the back of my hand, but I do not know a speck of $\LaTeX$ or $\TeX$. With regards to mathematical typesetting, is there something significant I can do in $\LaTeX$/$\TeX$ that ...
1
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3answers
2k 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
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1answer
31 views

inequality, complex number [closed]

let $b>0$, $y:[0,b]\rightarrow\mathbb{C}$ and $y(0)=0$, where $\mathbb{C}$ denotes the space of complex numbers. Is the following inequality true or not? $$|y(x)|\le \max_{\tau\in[0,b]} |y'(\tau)| ...
1
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2answers
92 views

Graphing a function f(x,y) on a restricted set of values for (x,y)

I'm having a hard time with this certain problem. Suppose that $S=\{(x,y): x^2 + y^2\leq 4\}$ and define $f:S\rightarrow\mathbb{R}$ as $f(x,y)=-x-2y-2y^2+cos(x\pi /4)$. How can we produce a (3d) ...
3
votes
1answer
68 views

Why these integrals are evaluated differently? $\cos(x)/(a-b\cos(x))$

In attempt to solve electrostatics problem I came up to this integral that I am trying to integrate: $$\int_0^{2\pi}\frac{\cos(x)}{a-b\cos(x)} \, dx$$ where $a>b$ and both are real numbers. For ...
0
votes
2answers
66 views

How plot $f(x,y) = \frac{x}{1-y}$ with $x^2+y^2<1$?

How do you plot $$f(x,y) = \frac{x}{1-y} \text{with}~ x^2+y^2<1$$ in Mathematica or Maple?
1
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1answer
87 views

Mismatching Results - Keno and Probability

In Keno, a player picks from 1 to 70 (at least in this version), 20 of these numbers are drawn, and the payouts are based on the number of matches. What I have tried to do is to check that the Swedish ...
1
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2answers
86 views

Newton's Method in Mathematica? [closed]

Which code should I use it for? FindRoot? or Plot? I am actually new to this program... and I would appreciate if you could tell how to mention the precision. Thanks! Solve the nonlinear ...
0
votes
2answers
56 views

Fraction Cross Multiply

Students first learning about fractions are often taught to "cross-multiply" when dealing with fraction with non-like denominators, however, in Mathematica, with the function ...
4
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0answers
136 views

How to integrate $\left(1+\ln(x)\right)\sqrt{1+(x\ln(x))^2}$ with Risch algorithm?

How would you integrate $\left(1 + \ln\left(x\right)\right)\, \sqrt{1 + \left(x\ln\left(x\right)\right)^{2}\,}$ using the Risch algorithm? I want to know this because Mathematica is using the Risch ...
2
votes
2answers
365 views

How to fit a sinusoidal function through 2 points with known slopes?

I can define my sinusoidal function as $y(x) = A\sin(B x+c) + D$ or as $y(x) = A \sin(B x) + C \cos(B x) + D$ Now, I have two points with known slopes that I must fit this sine wave to, thus my ...
1
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1answer
56 views

Mathematica question

let $S_p$ denote the sum of digits of $p$. A prime $p$ is said to be stubborn if none of $S_n+1$, $S_n$, $S_n-1$, $S_n-2$, or $S_n-3$ is a prime. Write a Mathematica program that finds the smallest ...
0
votes
2answers
145 views

Concerning the general solutions to linear ODEs Y'=AY when A has multiple eigenvalues

Given linear ODES Y'=AY, where Y is a column vector, A is a 6*6 square matrix. Clearly A has 6 eigenvalues, namely r1, r2, r3, r4, r5, r6. Herein we assume r5=r2, r6=r3.That is, r2 and r3 are two ...
0
votes
1answer
55 views

I need to use RSolve in mathematica to solve recurrence relations [closed]

I need to use the RSolve command in mathematica to solve recurrence relations and then find a9. I looked at documentations and try for about 2 hours no matter what my answer is not coming out right. ...
1
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0answers
49 views

Learning Resources: Mathematica Notebooks

A while ago, I stumbled upon someone's list of Mathematica notebooks for learning various topics. I've since lost the link, but I'm wondering now if I could find notebooks again. So my question is: ...
-1
votes
1answer
133 views

How do you set the range for ListPlot (mathematica)

I have a large set (about 2050 values) of data that I would like to make a graph out of. The data is in two columns in Excel. I copied the first column and made the list x={0, 3.6, 7.1, 10.7...} and ...
0
votes
1answer
43 views

Why the lower limit of this integral is 1?

I solve this differential equation using Mathematica. But I don't understand the solution. Why the lower limit of this integral is 1? I run: $$\text{DSolve}\left[y'(x)+y(x)=Q(x),y(x),x\right]$$ the ...
0
votes
2answers
202 views

Graeffe's root finding method

What are the practical applications of Graeffe's root finding method?I searched a lot but couldn't find.I found that it is used in aerodynamics and electric circuit analysis.But don't know much about ...
4
votes
1answer
65 views

Notation for derivatives at a certain point

Is the notation for values of a derivative at some point that I used in this question commonly accepted and understandable? Is there a more preferred one? For those who familiar with Mathematica ...
1
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1answer
262 views

Wolfram Mathematica - Newton Backward Interpolation?

I have the following task: Create a function (in Wolfram Mathematica), called $\mathrm{NewtonBackward}$[n_,x0_,h_,f_] which interpolates backwards the function $f(x)$ with nodes {x_i = x_0 + ...
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1answer
50 views

Problem with a loop in Mathematica

I am trying to create a loop in Mathamtica, where i get all $i$'s (with a certain bound, of course) for which the following expression holds: $7^{41\ast i}\equiv 3^{41}\, mod\, p$, where $p$ is just ...
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0answers
64 views

Functions generating prime numbers in math packages

Does anyone have an idea on how prime number generating functions such as Prime[n] in Mathematica generate the $n^{th}$ prime number?
1
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1answer
95 views

Can we effectively solve a system of polynomial equations (numerically).

It is known, and simple, that roots of a one polynomial in one variable $f(x)$ can be found numerically. If we restrict to the reals, one can readily give an explicit bound for any zero of $f$ in ...
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0answers
53 views

Vector calculus: Finding a model fit from a 2D grid

First of all, I am a biologist. My knowledge of math is very limited. Therefore, I come here for help, but please take into consideration that I may not be very good at asking the question in a good ...
0
votes
1answer
89 views

Write a Mathematica program to find the four known factorions

so i have come up with code that will find the four factorion numbers. I have a bunch of ideas of how it needs to be done theoretically but its still not quite clicking for me not too mention i am new ...
0
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0answers
51 views

Malliavin Derivative with Mathematica is it possible?

Note: This question was originally posted on mathematica.SE. Please check there before answering to ensure that it has not already been satisfactorily answered. Is it possible to define a ...
3
votes
1answer
88 views

solving the $ \varepsilon_{ijk}\varepsilon_{lmn}$(Levi Civita)

How can I solve this : $ \varepsilon_{ijk}\varepsilon_{lmn}=??$ I know that It can be solve with 2 determinants but I don't know how.and I don't what are the determinants!
0
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1answer
172 views

Solve 4 A (L^(3/4)) - wL (((24 - L) w)^(-3/4)) = -(((24 - L) w)^(1/4)) for L? Using Mathematica

I'm trying to solve $$4 A (L^{3/4}) - wL (((24 - L) w)^{-3/4}) = -(((24 - L) w)^{1/4})$$ for $L$ using Mathematica, and it spits the following out: ...
0
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1answer
91 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 ?