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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5
votes
0answers
940 views

Choosing the branch of a logarithm

The problem: I am integrating complex logarithms over an angle $\phi$ over $[0,2\pi]$. It is quite complex (pun not intended) and I called Mathematica in to aid me. I am calculating an energy of a ...
4
votes
0answers
174 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 ...
3
votes
0answers
72 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 ...
3
votes
0answers
47 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 ...
3
votes
0answers
142 views

Perturbation problem

This is a mathematica exercise that I have to do, where $y(x) = x - \epsilon \sin(2y)$ and it wants me to express the solution $y$ of the equation as a power series in $ \epsilon$.
2
votes
0answers
39 views

Is this system of inequalities (and equality) tractable?

I have some real parameters here. The $\mu_i$ - for $i=1,2,3,4,5$ - are 'convex coefficents' in that $\mu_i\geq 0$ and $\sum_{i}\mu_i=1$. The $x$ and $z$ are such that $x^2+z^2\leq 1$. The ...
2
votes
0answers
24 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 ...
2
votes
0answers
88 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 ...
2
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0answers
40 views

Algorithm for FindSequenceFunction

What algorithm might Mathematica be using to compute FindSequenceFunction? Does anybody know if there is any online material on this topic?
2
votes
0answers
79 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 ...
2
votes
0answers
311 views

$\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$

I'm trying to solve the integral $\int^{\infty}_{0}x^{r +s- 1}(1 + x)^{-s}(1 + x^2)^{-\frac{rm}{2}}dx$, where $s$, $r$ and $m$>1 are positive integers. My question is whether a closed form ...
2
votes
0answers
442 views

Calculate periodicity in 1-dimensional array with noise

I have a 1-dimensional array with some integers, which are periodically increasing. Something like this (1 period here): ...
1
vote
0answers
27 views

Convergence of a hypergeometric function

The hypergeometric function, ${}_{2}F_1(a,b,c;z)$ can be written in terms of a power series in $z$ as follows, $${}_{2}F_1(a,b,c;z) = \sum_{n=0}^{\infty} \frac{(a)_n (b)_n}{(c)_n} ...
1
vote
0answers
61 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 ...
1
vote
0answers
37 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 ...
1
vote
0answers
41 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 ...
1
vote
0answers
18 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 & = ...
1
vote
0answers
20 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) ...
1
vote
0answers
29 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 ...
1
vote
0answers
26 views

Computer Code Friendly Books On Differential Equations?

When I need a differential equation for this or that application I generally search (by hand) through old paper and ink books written by mechanical or electronical (electrical) engineers. Sometimes my ...
1
vote
0answers
176 views

SAGE vs. Mathematica for Lie algebras / groups?

What math software is better for working with Lie algebras and Lie groups, SAGE or Mathematica?
1
vote
0answers
44 views

Can nodes of Gaussian quadrature shift range?

I used my Python program to generate Gaussian's nodes and their weights. My python program could generate nodes as default in rage of (-1, 1). And my friend used Mathematica to generate them also but ...
1
vote
0answers
44 views

How to evaluate Bessel functions $K_{i x+\frac{9}{4}}(2\pi)+K_{i x-\frac{9}{4}}(2\pi)$ with $x>1.5*10^8$ in Mathematica 7?

I am trying to evaluate Bessel functions $K_{i x+\frac{9}{4}}(2\pi)+K_{i x-\frac{9}{4}}(2\pi)$ with $x>1.5*10^8$ in Mathematica 7. This function is the first Polya approximation to Riemann ...
1
vote
0answers
47 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 $$ \psi={-k\over 2\pi r}\sin(\theta_0-\theta) $$ ...
1
vote
0answers
120 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 ...
1
vote
0answers
52 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 ...
1
vote
0answers
137 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
vote
0answers
56 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
vote
0answers
69 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
0answers
63 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 ...
1
vote
0answers
45 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
0answers
238 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
0answers
514 views

How to make iteration for Newmark method in Mathematica 8

How to make iteration method for solving differential equations by Newmark method? There are just three equations which describe the Newmark method. I need q for time step for example 0.01. Also, for ...
1
vote
0answers
195 views

Euler method on differential equation problem

I have this problem to solve. I want to compute the inclination of a plane $\theta(t)$ at every frame of a simulation given the following rule for its angular speed of rotation $\omega(t)$ $$ ...
1
vote
0answers
553 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
0answers
31 views

Using Mathematica to calculate expected time to absorption

I am trying to solve a standard ETA on a birth-death process with $n$ states $\in \{0,\cdots,n-1\}$ where state $n-1$ is absorbing. Also $\mu_i$ is the expected time to absorption starting at state ...
0
votes
0answers
30 views

Requesting programming implementations for $\mathbb{F}_{p^n}$ and $SL_2(\mathbb{F}_{p^n})$.

I would like a programming language capable of doing computations over finite fields and matrix groups over those finites fields. I do not want to have to construct bases and what not on my own. What ...
0
votes
0answers
18 views

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 ...
0
votes
0answers
27 views

free tool for algebraic manipulations of commutator expressions

Is there an (ideally) free tool for algebraic manipulations of commutator expressions of the form: given $$c(A,B):=\tfrac{1}{2}[A,B]+\tfrac{1}{12}[A,[A,B]]+\tfrac{1}{12}[B,[B,A]]$$ simplify (express ...
0
votes
0answers
19 views

Closed form for a Bartlett's formula for AR(2)

Consider a stationary AR(2) process $$ Y_t=\phi_1Y_{t-1}+\phi_2Y_{t-2}+e_t $$ with $e_t$'s are i.i.d. with mean $0$ and variance $1$. Let $r_s$ be the $s$-th autocorrelation ...
0
votes
0answers
29 views

Sum of a Normal and a Truncated Normal distribution on Mathematica

I asked a question about the "Sum of a Normal and a Truncated Normal distribution" about 11 days ago, and someone helped me (I appreciate his\her help a lot). I tried to do same procedure as he\she ...
0
votes
0answers
30 views

Importing microsoft excel data to Mathematica

I used the import function in Mathematica to import an excel file and while Mathematica did perform that, the data in the cells in excel appear in curly brackets in Mathematica. What can I do to ...
0
votes
0answers
14 views

FindRoot[rhs==lhs, {X,x1,x2}] Vs. FindRoot[rhs==lhs, {X,x1}]

What is the difference between these two commands: FindRoot[rhs==lhs, {x,x1,x2}] and FindRoot[rhs==lhs,{x,x1}] They give me completely different solutions. Thanks
0
votes
0answers
25 views

Irregular Implicit Plot in Mathematica

While studying the implicit relation $ y=x\tan(a\sqrt{x^2+y^2}+b)+c$ I came across some spurious looking parts in the graph WolframAlpha produces. These are jagged circles with radii that appears to ...
0
votes
0answers
24 views

How do I compute uncertainties in the positions transformed using Helmert transformation?

I am familiar with Python, MATLAB and Mathematica. My data is given by Cartesian coordinates (positions in X,Y,Z (meters), standard deviations XX, YY, ZZ (meters) and a correlation matrix (XY, YZ, ...
0
votes
0answers
18 views

Solve multivariate exponential inequality via program

I am trying to solve a complicated exponential inequality with six parameters and one variable t. This can't be done with mathematica command "Solve, Reduce or FindInstance". Is there any other ...
0
votes
0answers
21 views

Getting a part of a matrix in mathematica

I was trying to get an element of a matrix, and use in further computation of my program. Problem was that its not reading the value unless and until I specify it again. My code is: ...
0
votes
0answers
28 views

Proving susceptibility in Lorentz Model satisy Kramers-Kronig relations

My instructor asked me to prove that the real and imaginary parts of the electric susceptibility derived from Lorentz Model satisfy the Kramers-Kronig relations using the residue theorem. The problem ...
0
votes
0answers
33 views

Simplifying expressions or expressing it in more known functions

In mathematica I asked FullSimplify[ DSolve[{y''[x] + 1/x y'[x] + y[x] (1 - 1/x^2) == x BesselJ[1, x]}, y[x], x]] and it gave as the answer {{y[x] -> BesselJ[1, x] C[1] + ...
0
votes
0answers
35 views

Ritz Approximation

I have the following problem: $1/r * d/dr(r*d \theta/dr) - N_1(\theta-\theta_a)^2 -N_2(\theta^4-\theta_a~^4)=0$ where $N_1, N_2,$ and $\theta_a$ are constants Subject to $r=1$ : $\theta=1$ $r=L$ ...