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3
votes
1answer
67 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 ...
2
votes
1answer
41 views

Fourier series of oscillation in form $\cos(2 \pi \frac{k}{T}+\phi)$

I would like to calculate the fourier coefficients of $\cos(2 \pi \frac{k}{T}+\phi)$ where $T \in \mathbb{N}$ is the period and is arbitrary but fixed, $k \in [1, N-1]$ is the number of oscillations ...
2
votes
1answer
38 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 ...
1
vote
1answer
27 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 ...
1
vote
1answer
242 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 + ...
1
vote
1answer
82 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
84 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
votes
1answer
110 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
147 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 ...
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 ...
5
votes
0answers
793 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
117 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
41 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
137 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
17 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
74 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
342 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
17 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
20 views

Two factor ANOVA discrepancy with Mathematica

I have a set of two factor data I am doing ANOVA analysis on, both with Mathematica's package and manually (because learning!) Using one set of example data (found here 1) both my manual calculation ...
1
vote
0answers
32 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
36 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
72 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
25 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
58 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
48 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
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
0answers
51 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
39 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
302 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 ...
1
vote
0answers
225 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
409 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
182 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
508 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

Solving partial differential equation with mathematica.

I am trying to solve the heat equation in cylindrical coordinate. The object of inspection is a thick ring with height $\{z_0,z_L\}$ and radii $\{r_1,r_2\}$ within a heat generating environment. I ...
0
votes
0answers
33 views

complex ordinary differential equation of a real variable

reading a paper i have found the following differential equation: f''[z] - (q^2)*f[z] == i*DiracDelta[z] here f[z] is a complex function of the real variable z ...
0
votes
0answers
25 views

How to interpolate and obtain this graph?

I was interpolating with software mathematica v9, but how can I obtain a curve similar to this?, in a easy way
0
votes
0answers
24 views

Splitting a list into two lists, depending on a condition.

So I have this list of n real numbers called A, which is sorted least to greatest. Let B be a list of n real numbers with NormalDistribution[]. IF A+B = Sort[A+B], then we keep it, and if A+B != ...
0
votes
0answers
57 views

Mathematica Integrate gives back the integrand

i'm trying to Integrate the following function: (q (1 + q) - E^-q Sinh[q])/(-q + Cosh[q] Sinh[q]) - ( 2 q Tanh[q])/(-q + Cosh[q] Sinh[q]) I already solved ...
0
votes
0answers
32 views

list of all irreducible polynomials of degree at most n over the field Z/PZ.

I am trying to write a mathematica coding to give me the list of all irreducible polynomials of degree at most n over the field Z/PZ. I started by defining univariate polynomials of the form p = a_0 + ...
0
votes
0answers
44 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 ...
0
votes
0answers
15 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
votes
0answers
25 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 ...
0
votes
0answers
20 views

Is it possible to find an exact expression for system for recursion of non linear equations?

I have a system of N non-linear equations of N unknowns $\phi_i, i \in 1,2,... N$. By specifying the middle two unknowns as $\phi_{N/2} = 0, \phi_{N/2+1} = X$, I get that: \begin{align*} ...
0
votes
0answers
45 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 ...
0
votes
0answers
24 views

Mathematica problem: Solution in terms of predefined functions

Is there a way that I can have Mathematica give me the solution of a problem it has solved in terms of functions that I have predefined?
0
votes
0answers
106 views

Plotting graph For Z versus $\rho$ by applying numerical method and explanation of nodes

I want to draw a simulation for a graph by Mathematica but confused that where I have got struck, The equation I need to plot is, $$\frac{d^2Z}{d \rho^2}+ \frac{D-1}{\rho} \frac{dZ}{d \rho}-Z + 3S^2 ...
0
votes
0answers
46 views

Symbolic computations in field extensions with Mathematica

In Mathematica I would like to make symbolic computations in field extensions. For example, if $a$ is a root of $x^3+3x-1$, I would like to get $$ a^4 = a-3a^2 $$ if I asked the machine to compute ...
0
votes
0answers
176 views

A (contour?) integration (even if by using Mathematica!)

I need to be able to calculate integrals of this type where the sum over $R$ is the sum over representations of a Lie group $G$ on whom $dU$ is the Haar measure and $\chi _ R ()$ is the character of ...
0
votes
0answers
139 views

How can I show that a given system of differential equations is stiff?

I was writing a program to solve a system of equations with Runge-Kutta method, but it doesn't work well and I decided to check what Mathematica can say about it. It turns out that I have a stiff ...
0
votes
0answers
62 views

Using Fit on functions that use matrix calculation

I am struggling with using Fit to fit a (linear combination of a) list of functions, that are calculated using matrices. It seems Mathematica internally uses ...