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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 ...
5
votes
0answers
801 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
129 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
42 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
46 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
votes
0answers
22 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
362 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
10 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: g (m1 + 2 (m2 + md)) (b - h1 [Theta]10) + 4 kd (h1^2 [Theta]10 + h1 h2 ...
1
vote
0answers
14 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
15 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
20 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
23 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
33 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
39 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
82 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
30 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
72 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
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 ...
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
226 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
422 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
516 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
11 views

Mean Absolute Percentage Error with mathematica

I have problem with MAPE code in mathematica. I have a data fitted from Hidden Markov Model and I will make a code for MAPE. Can you give me a code to MAPE please?
0
votes
0answers
35 views

SAGE vs. Mathematica for Lie algebras / groups?

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

Finding circle which touches two functions

I wasn't sure whether my issue is with my Mathematica code or the actual way I am trying to figure out my problem so if it is a Mathematica issue I can ask it on that stack exchange. Firstly I have ...
0
votes
0answers
32 views

traingular matrix

I am not much in to the matrices. so I am sorry if I can not put forward the question properly. Assume $G_{n\times n}$ is a rank $n$ matrix (Indeed $G$ is the generator matrix of a lattice). I need ...
0
votes
0answers
21 views

Need Suggestion: good CAD tool to solve inequality

I want to solve the inequality: $f(x,y,z,w)-g(x,y,z,w)>0$ $s.t. $ $ x>0$, $0<y<1$, $ z>0$ , $ 0<=w<=1$, $f(x,y,z,w)>1,$ $g(x,y,z,w)>1$ where $f$ and ...
0
votes
0answers
33 views

Implementing formula correctly in matlab for neuroscience: total soma membrane potential?

Please help me to understand: am I correctly implementing a total soma membrane potential (TSMP) equation in Matlab? Due to being a new member I need to use this list link to refer to the links ...
0
votes
0answers
35 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
38 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
26 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
26 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
60 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
33 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
54 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
49 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
25 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
107 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
47 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
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
63 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 ...