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4
votes
0answers
148 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
395 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
vote
1answer
57 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
170 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
62 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
vote
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
149 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
44 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
233 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
66 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
vote
1answer
301 views

Newton backward interpolation in Mathematica

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 + ...
0
votes
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 ...
1
vote
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
vote
1answer
105 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 ...
1
vote
0answers
55 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
98 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 ...
3
votes
1answer
90 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
votes
1answer
206 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
votes
1answer
93 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 ?
1
vote
1answer
131 views

Difference between validity and satisfiability?

I am having problems understanding the difference between validity and satisfiability. Given the following: (i) For all F, F is satisfiable or ~F is satisfiable. (ii) For all F, F is valid or ~F is ...
0
votes
1answer
63 views

What is the meaning of log(0,1)[x] in Mathematica 9.0?

everyone.I want to know the meaning of "log(0,1)[2,x]" in the out[8].What's the difference between log[2,x] and log(0,1)[2,x] in Mathematica?
2
votes
2answers
175 views

Convergence of hypergeometric 2F1 with z=-1

Encountering the hypergeometric function $_2F_1(4n+3,\ m+1;\ m+3;\ -1)$ where $n\in\textbf{N}$ and $m\in\{2,4,6,\ldots,4n-2\}$ I'm a bit confused about its convergence. According to Erdélyi's ...
0
votes
1answer
69 views

Understanding the Wolfram Demonstration “Distance of a Point to a Polygon”

I've recently came across a neat Wolfram Demonstration script by Jaime Rangel-Mondragon that calculates the minimum distance from a point to an arbitrary convex or non-convex polygon: ...
1
vote
2answers
105 views

Bessel function to $\sin(kr)$

$J_{\frac{1}{2}}(kr)=\frac{\sqrt{\frac{2}{\pi }} \text{Sin}[\text{kr}]}{\sqrt{\text{kr}}})$ This can be easily obtained by Mathematica, How to do the details?
0
votes
2answers
66 views

simple question: the eigenvectors of a matrix.

\begin{align*}A=\left(\begin{array}{cccc} 1 & 2 & 3 & 4 \\ 0 & 1 & 2 & 3 \\ 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 1 \\\end{array}\right);\end{align*} The ...
2
votes
2answers
563 views

What does Mathematica do that Wolfram Alpha can't?

It isn't clear to me what Mathematica does that Wolfram Alpha can't do. (Obviously I have never used Mathematica.) Here (http://www.wolframalpha.com/faqs4.html) it says that Wolfram Alpha "has ...
0
votes
4answers
100 views

Statistics independence question

A newly-minted sixteen year old takes the written and road drivers's license test repeatedly until he passes them. It is given that the probability he passes the written test is 0.9, that he passes ...
2
votes
0answers
77 views

Solution of nonlinear waves( breathers)

The sine-Gordon equation is known as $$\frac{\partial^2 u}{\partial t^2} - \frac{\partial^2 u}{\partial x^2} + \sin u = 0,$$ Can you please derive the equation which is known as breather equation ...
6
votes
2answers
213 views

Finding the largest circle that contains a single point in a set (and no other point)

Given a bounded $A \times B$ rectangle with a set of chosen coordinates, generated for example with the command: ...
-1
votes
1answer
252 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 ...
0
votes
1answer
157 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 ...
0
votes
1answer
95 views

How to plot (y vs x) a not invertible function say F(x,y)=const?

I am trying to plot (y vs x) for a not invertible function PolyLogarithm[1.5,y/x]=const. Any Ideas how to do this, say on Mathematica?
1
vote
1answer
103 views

help to write the Mathematica or Maple code for $\log(1+x)$ as MeijerG

I am having difficulties working with some integral and I believe that if the natural logarithm in that integral is converted to its MeijerG equivalent, then it will be solved easily. can somebody ...
1
vote
1answer
85 views

Plotting large equation in mathematica

I have this rather large equation which needs to be solved with respect to I1 so that I can plot it against X: -1 - (0.742611 I1 (1/(-(-14 + 16/I2)^2 + (1 - 15/I1 + 16/I2)^2) - ( 30 (1 - 15/I1 + ...
1
vote
1answer
181 views

Master degree require Matlab? [closed]

I'm devon. I'm in second year math integrated computer concentrate in statistic. I love math and I'm very interested in finance. So I'm planning to get the master degree in Financial Mathematic. What ...
2
votes
2answers
68 views

applying plus to sublevels of sparsearray in Wolfram Mathematica converts it to a normal list. How to avoid it?

I have a sparse array of tuples of positive real numbers (in fact a probability distribution) say ...
0
votes
1answer
283 views

Fourier Transform for a Convolution

Alright, so I am using the Convolution property of Fourier Transforms to find a function $f(x)$. So the obvious equation: $h(x) = f(x) \ast g(x)$. Definitions: $$g(x)=Rect\left[\frac x w ...
3
votes
1answer
386 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
0answers
43 views

How to visualize a function to aid in optimization?

I am working on minimization of a function with more than two parameters. I want to see variations, local extremes, saddle points, etc. of this function to get some idea of how is this function in ...
0
votes
1answer
48 views

Graphing a function

A function is defined in a article equation 37, $$A(t)= 0.456+\frac{2.58}{(1+0.136 t)^{0.249}}$$ The simulation of the equation is: But I have tried like by this: ...
4
votes
2answers
290 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 ...
1
vote
2answers
486 views

What is the area of the shaded region of the square?

To find area of shaded portion in the below figure, the picture generate by following mathematica code. ...
20
votes
1answer
350 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 $$x \approx 14.498719188878466465738532142574796767250306535...$$ ...
0
votes
1answer
69 views

Postfix notation in MAPLE

I usually use MATHEMATICA as a computer algebra system and there I heavily employ the postfix notation (achieved by "//" at the end of some command), e.g. ...
0
votes
2answers
111 views

Series expansion with remaining $log n$

I'm studying the asymptotic behavior $(n \rightarrow \infty)$ of the following formula, where $k$ is a given constant. $$ \frac{1}{n^{k(k+1)/(2n)}(2kn−k(1+k) \ln n)^2}$$ I'm trying to do a series ...
0
votes
1answer
652 views

Mathematica vs Wolfram Alpha integration results

When I insert the following integration command in wolframalpha: ...
0
votes
2answers
131 views

WolframAlpha functionality: Computing nested integrals

Can wolframpalpha support the numerical calculation of the following type: $$ \int_{x=0}^\infty f(x) e^{\int_{z=0}^\infty g(x,z)dz} dx $$ Note that the inside integral is in such form where ...
1
vote
0answers
40 views

What are the available libraries or programs for finding extremes of a function with no symbolic definition?

In my current mathematical inquiry, I would like to gain insight on behaviour of a $d$-dimensional continuous function by locating its maximum over the hyperplane $\sum_{i=1}^d x_i = 1$ for $x_i$ ...
1
vote
1answer
92 views

Help calculating variance of a random variable

This is related to this question Average end point of 1-dimensional random walk? Given several discrete random variables such that $p(Z_i=1-2k)=p$, where $k$ is a small real number, and ...
0
votes
1answer
45 views

Is there a closed-form expression that allows me to triangulate a point in 2D?

Please consider the case where I have three points on a 2D plane - $(p_1, p_2, p_3)$ - and a third point, $p_0$, at some unknown position $(x_0,y_0)$. However, I know that $p_0$ is a distance $d_1$ ...